Peter Balazs

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Peter Balazs

Fellow Professor of Acoustics, Analysis, and AI

PD Dr. 

Austrian Academy of Sciences (ÖAW)

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Title

Year

Injectivity of ReLU layers: Tools from frame theory

2025

Daniel Haider, Martin Ehler, Peter Balazs
Mathematical Foundations of Machine Learning 1 (1), 1-40
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Authors:	Daniel Haider, Martin Ehler, Peter Balazs
Publication date:	12/01/2025
Journal:	Mathematical Foundations of Machine Learning
Volume:	1
Issue:	1
Pages:	1-40
Publisher:	Springer International Publishing
Description:	Injectivity is the defining property of a mapping that ensures no information is lost and any input can be perfectly reconstructed from its output. By performing hard thresholding, the ReLU function naturally interferes with this property, making the injectivity analysis of ReLU layers in neural networks a challenging yet intriguing task that has not yet been fully solved. This article establishes a frame theoretic perspective to approach this problem. The main objective is to develop a comprehensive characterization of the injectivity behavior of ReLU layers in terms of all three involved ingredients:(i) the weights,(ii) the bias, and (iii) the domain where the data is drawn from. Maintaining a focus on practical applications, we limit our attention to bounded domains and present two methods for numerically approximating a maximal bias for given weights and data domains. These methods provide sufficient conditions for the …
Cited by:	2
Resources:	[HTML] from springer.com

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Wiener pairs of Banach algebras of operator-valued matrices

2025

Lukas Koehldorfer, Peter Balazs
Journal of Mathematical Analysis and Applications 549 (2), 129525
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Authors:	Lukas Koehldorfer, Peter Balazs
Publication date:	09/15/2025
Journal:	Journal of Mathematical Analysis and Applications
Volume:	549
Issue:	2
Pages:	129525
Publisher:	Academic Press
Description:	In this article we consider several new examples of Wiener pairs A⊆ B, where B= B (ℓ 2 (X; H)) is the Banach algebra of bounded operators acting on the Hilbert space-valued Bochner sequence space ℓ 2 (X; H) and A= A (X) is a Banach algebra consisting of operator-valued matrices indexed by some relatively separated set X⊂ R d. In particular, we consider B (H)-valued versions of the Jaffard algebra, of certain weighted Schur-type algebras, of Banach algebras which are defined by more general off-diagonal decay conditions than polynomial decay, of weighted versions of the Baskakov-Gohberg-Sjöstrand algebra, and of anisotropic variations of all of these matrix algebras, and show that they are inverse-closed in B (ℓ 2 (X; H)). In addition, we obtain that each of these Banach algebras is symmetric.
Cited by:	10
Resources:	[HTML] from sciencedirect.com

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Robust Deconvolution with Parseval Filterbanks

2025

Rossen Nenov, Vincent Lostanlen, Peter Balazs
IEEE International Conference on Sampling Theory and Applications (SampTA)
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Authors:	Rossen Nenov, Vincent Lostanlen, Peter Balazs
Publication date:	07/28/2025
Journal:	IEEE International Conference on Sampling Theory and Applications (SampTA)
Description:	This article introduces two contributions: Multiband Robust Deconvolution (Multi-RDCP), a regularization approach for deconvolution in the presence of noise; and Subband-Normalized Adaptive Kernel Evaluation (SNAKE), a first-order iterative algorithm designed to efficiently solve the resulting optimization problem. Multi-RDCP resembles Group LASSO in that it promotes sparsity across the subband spectrum of the solution. We prove that SNAKE enjoys fast convergence rates and numerical simulations illustrate the efficiency of SNAKE for deconvolving noisy oscillatory signals.
Cited by:	1
Resources:	[PDF] from hal.science

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Banach distribution spaces for a Hilbert space

2025

Nikolas Hauschka, Peter Balazs, Lukas Köhldorfer
2025 International Conference on Sampling Theory and Applications (SampTA), 1-5
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Authors:	Nikolas Hauschka, Peter Balazs, Lukas Köhldorfer
Publication date:	07/28/2025
Journal:	2025 International Conference on Sampling Theory and Applications (SampTA)
Pages:	1-5
Publisher:	IEEE
Description:	Associated with every separable Hilbert space and given localized frame, there exists a natural test function Banach space and a Banach distribution space so that . In this article we close some gaps in the literature and rigorously introduce the space and its weighted variants under minimal assumptions and discuss some of their properties. In particular, we compare several topologies associated with and show that is a Banach space.
Cited by:	1

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Aliasing in Convnets: A Frame-Theoretic Perspective

2025

Daniel Haider, Vincent Lostanlen, Martin Ehler, Nicki Holighaus, Peter Balazs
arXiv preprint arXiv:2507.06152
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Authors:	Daniel Haider, Vincent Lostanlen, Martin Ehler, Nicki Holighaus, Peter Balazs
Publication date:	07/08/2025
Journal:	arXiv preprint arXiv:2507.06152
Description:	Using a stride in a convolutional layer inherently introduces aliasing, which has implications for numerical stability and statistical generalization. While techniques such as the parametrizations via paraunitary systems have been used to promote orthogonal convolution and thus ensure Parseval stability, a general analysis of aliasing and its effects on the stability has not been done in this context. In this article, we adapt a frame-theoretic approach to describe aliasing in convolutional layers with 1D kernels, leading to practical estimates for stability bounds and characterizations of Parseval stability, that are tailored to take short kernel sizes into account. From this, we derive two computationally very efficient optimization objectives that promote Parseval stability via systematically suppressing aliasing. Finally, for layers with random kernels, we derive closed-form expressions for the expected value and variance of the terms that describe the aliasing effects, revealing fundamental insights into the aliasing behavior at initialization.
Resources:	[PDF] from arxiv.org

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The Lifting Property for Frame Multipliers and Toeplitz Operators

2025

Peter Balazs, Karlheinz Gröchenig
arXiv preprint arXiv:2506.18441
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Authors:	Peter Balazs, Karlheinz Gröchenig
Publication date:	06/23/2025
Journal:	arXiv preprint arXiv:2506.18441
Description:	Frame multipliers are an abstract version of Toeplitz operators in frame theory and consist of a composition of a multiplication operator with the analysis and synthesis operators. Whereas the boundedness properties of frame multipliers on Banach spaces associated to a frame, so-called coorbit spaces, are well understood, their invertibility is much more difficult. We show that frame multipliers with a positive symbol are Banach space isomorphisms between the corresponding coorbit spaces. The results resemble the lifting theorems in the theory of Besov spaces and modulation spaces. Indeed, the application of the abstract lifting theorem to Gabor frames yields a new lifting theorem between modulation spaces. A second application to Fock spaces yields isomorphisms between weighted Fock spaces. The main techniques are the theory of localized frames and existence of inverse-closed matrix algebras.
Resources:	[PDF] from arxiv.org

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Residual Hybrid Filterbanks

2025

Vincent Lostanlen, Xiran Zhang, Daniel Haider, Mathieu Lagrange, Martin Ehler, Peter Ba…
IEEE Statistical Signal Processing Workshop (SSP)
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Authors:	Vincent Lostanlen, Xiran Zhang, Daniel Haider, Mathieu Lagrange, Martin Ehler, Peter Balazs
Publication date:	06/08/2025
Journal:	IEEE Statistical Signal Processing Workshop (SSP)
Description:	A hybrid filterbanks is a convolutional neural network (convnet) whose learnable filters operate over the subbands of a non-learnable filterbank, which is designed from domain knowledge. While hybrid filterbanks have found successful applications in speech enhancement, our paper shows that they remain susceptible to large deviations of the energy response due to randomness of convnet weights at initialization. Against this issue, we propose a variant of hybrid filterbanks, by inspiration from residual neural networks (ResNets). The key idea is to introduce a shortcut connection at the output of each non-learnable filter, bypassing the convnet. We prove that the shortcut connection in a residual hybrid filterbank lowers the relative standard deviation of the energy response while the pairwise cosine distances between non-learnable filters contributes to preventing duplicate features.
Cited by:	1
Resources:	[PDF] from hal.science

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Localized frames without inequalities

2025

Peter Balazs, Lukas Köhldorfer, Michael Speckbacher
arXiv preprint arXiv:2506.02862
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Authors:	Peter Balazs, Lukas Köhldorfer, Michael Speckbacher
Publication date:	06/03/2025
Journal:	arXiv preprint arXiv:2506.02862
Description:	We consider countable families of vectors in a separable Hilbert space, which are mutually localized with respect to a fixed localized Riesz basis. We prove the equivalence of the frame property and nine conditions that do not involve any inequalities. This is done by studying the properties of their frame-related operators on the co-orbit spaces generated by the reference Riesz basis. We apply our main result to the setting of shift-invariant spaces and obtain new conditions for stable sets of sampling.
Resources:	[PDF] from arxiv.org

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Kernel theorems for operators on co-orbit spaces associated with localised frames

2025

Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs
Journal of Mathematical Analysis and Applications, 129678
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Authors:	Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs
Publication date:	05/13/2025
Journal:	Journal of Mathematical Analysis and Applications
Pages:	129678
Publisher:	Academic Press
Description:	Kernel theorems provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised integral operator, in a way reminiscent of the matrix representation of linear operators acting on finite dimensional vector spaces. We prove kernel theorems for bounded linear operators acting on co-orbit spaces associated with localised frames. Our two main results characterise the spaces of operators whose generalised integral kernels belong to the co-orbit spaces of test functions and distributions associated with the tensor product of the localised frames respectively. Moreover, using a version of Schur's test, we establish a characterisation of the bounded linear operators between some specific co-orbit spaces and kernels in mixed-norm co-orbit spaces.
Cited by:	1
Resources:	[HTML] from sciencedirect.com

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ISAC: An Invertible and Stable Auditory Filter Bank with Customizable Kernels for ML Integration

2025

Daniel Haider, Felix Perfler, Peter Balazs, Clara Hollomey, Nicki Holighaus
arXiv preprint arXiv:2505.07709
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Authors:	Daniel Haider, Felix Perfler, Peter Balazs, Clara Hollomey, Nicki Holighaus
Publication date:	05/12/2025
Journal:	arXiv preprint arXiv:2505.07709
Description:	This paper introduces ISAC, an invertible and stable, perceptually-motivated filter bank that is specifically designed to be integrated into machine learning paradigms. More precisely, the center frequencies and bandwidths of the filters are chosen to follow a non-linear, auditory frequency scale, the filter kernels have user-defined maximum temporal support and may serve as learnable convolutional kernels, and there exists a corresponding filter bank such that both form a perfect reconstruction pair. ISAC provides a powerful and user-friendly audio front-end suitable for any application, including analysis-synthesis schemes.
Cited by:	1
Resources:	[PDF] from arxiv.org

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Robust Multicomponent Tracking of Ultrasonic Vocalizations

2025

Reyhaneh Abbasi, Nicki Holighaus, Peter Balazs, Vincent Lostanlen, Dustin J Penn, Sarah…
ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processi…
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Authors:	Reyhaneh Abbasi, Nicki Holighaus, Peter Balazs, Vincent Lostanlen, Dustin J Penn, Sarah M Zala
Publication date:	04/06/2025
Journal:	ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Pages:	1-5
Publisher:	IEEE
Description:	Ultrasonic vocalizations (USV) convey information about individual identity and arousal status in mice. We propose to track USV as ridges in the time–frequency domain via a variant of time– frequency reassignment (TFR). The key idea is to perform TFR with empirical Wiener shrinkage and multitapering to improve robustness to noise. Furthermore, we perform TFR over both the short-term Fourier transform and the constant-Q transform so as to detect both the fundamental frequency and its harmonic partial (if any). Experimental results show that our approach effectively estimates multicomponent ridges with high precision and low frequency deviation.
Resources:	[PDF] from hal.science

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HybrA: Learnable, interpretable, and stable filterbanks for feature extraction

2025

Peter Balazs, Daniel Haider, Felix Perfler, Vincent Lostanlen
The Journal of the Acoustical Society of America 157 (4_Supplement), A353-A353
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Authors:	Peter Balazs, Daniel Haider, Felix Perfler, Vincent Lostanlen
Publication date:	04/01/2025
Journal:	The Journal of the Acoustical Society of America
Volume:	157
Issue:	4_Supplement
Pages:	A353-A353
Publisher:	Acoustical Society of America
Description:	When designing machine learning models, especially for acoustics applications, there is an ever-repeating question: how should feature extraction be done? The two most common approaches are to use a hand-crafted fixed filterbank or to process the audio signal directly in an end-to-end manner. Each has its own pros and cons, e.g., the first is not adaptive, and the second is poorly interpretable. We present a hybrid approach that combines the strengths of both. This approach involves convolving each filter of a fixed filterbank with a short learned kernel. In this way, we obtain a new hybrid filterbank that keeps (some) interpretability while being able to adapt to the problem at hand. To ensure that no information is lost during this initial processing stage, we additionally incorporate a regularizer that maintains stability. We present a concrete example of constructing a hybrid filterbank using an audlet transform—an …

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Localised frames for tensor product spaces

2025

Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs
arXiv preprint arXiv:2503.09764
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Authors:	Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs
Publication date:	03/12/2025
Journal:	arXiv preprint arXiv:2503.09764
Description:	In this paper, we investigate whether the tensor product of two frames, each individually localised with respect to a spectral matrix algebra, is also localised with respect to a suitably chosen tensor product algebra. We provide a partial answer by constructing an involutive Banach algebra of rank-four tensors that is built from two solid spectral matrix algebras. We show that this algebra is inverse-closed, given that the original algebras satisfy a specific property related to operator-valued versions of these algebras. This condition is satisfied by all commonly used solid spectral matrix algebras. We then prove that the tensor product of two self-localised frames remains self-localised with respect to our newly constructed tensor algebra. Additionally, we discuss generalisations to localised frames of Hilbert-Schmidt operators, which may not necessarily consist of rank-one operators.
Resources:	[PDF] from arxiv.org

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Details on the distribution co-orbit space

2025

Nikolas Hauschka, Peter Balazs, Lukas Köhldorfer
arXiv preprint arXiv:2502.07378
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Authors:	Nikolas Hauschka, Peter Balazs, Lukas Köhldorfer
Publication date:	02/11/2025
Journal:	arXiv preprint arXiv:2502.07378
Description:	Associated with every separable Hilbert space and a given localized frame, there exists a natural test function Banach space and a Banach distribution space so that . In this article we close some gaps in the literature and rigorously introduce the space and its weighted variants in a slightly more general setting and discuss some of their properties. In particular, we compare the underlying weak- with the norm topology associated with and show that is a Banach space.
Resources:	[PDF] from arxiv.org

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On the inverse-closedness of operator-valued matrices with polynomial off-diagonal decay

2025

Lukas Köhldorfer, Peter Balazs
arXiv preprint arXiv:2501.09603
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Authors:	Lukas Köhldorfer, Peter Balazs
Publication date:	01/16/2025
Journal:	arXiv preprint arXiv:2501.09603
Description:	We give a self-contained proof of a recently established -valued version of Jaffards Lemma. That is, we show that the Jaffard algebra of -valued matrices, whose operator norms of their respective entries decay polynomially off the diagonal, is a Banach algebra which is inverse-closed in the Banach algebra of all bounded linear operators on , the Bochner-space of square-summable -valued sequences.
Cited by:	2
Resources:	[PDF] from arxiv.org

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Construction of generalized samplets in Banach spaces

2024

Peter Balazs, Michael Multerer
arXiv preprint arXiv:2412.00954
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Authors:	Peter Balazs, Michael Multerer
Publication date:	12/01/2024
Journal:	arXiv preprint arXiv:2412.00954
Description:	Recently, samplets have been introduced as localized discrete signed measures which are tailored to an underlying data set. Samplets exhibit vanishing moments, i.e., their measure integrals vanish for all polynomials up to a certain degree, which allows for feature detection and data compression. In the present article, we extend the different construction steps of samplets to functionals in Banach spaces more general than point evaluations. To obtain stable representations, we assume that these functionals form frames with square-summable coefficients or even Riesz bases with square-summable coefficients. In either case, the corresponding analysis operator is injective and we obtain samplet bases with the desired properties by means of constructing an isometry of the analysis operator's image. Making the assumption that the dual of the Banach space under consideration is imbedded into the space of compactly supported distributions, the multilevel hierarchy for the generalized samplet construction is obtained by spectral clustering of a similarity graph for the functionals' supports. Based on this multilevel hierarchy, generalized samplets exhibit vanishing moments with respect to a given set of primitives within the Banach space. We derive an abstract localization result for the generalized samplet coefficients with respect to the samplets' support sizes and the approximability of the Banach space elements by the chosen primitives. Finally, we present three examples showcasing the generalized samplet framework.
Cited by:	1
Resources:	[PDF] from arxiv.org

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An unbounded operator theory approach to lower frame and Riesz-Fischer sequences

2024

Peter Balazs, Mitra Shamsabadi
Applied and Computational Harmonic Analysis 73, 101685
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Authors:	Peter Balazs, Mitra Shamsabadi
Publication date:	11/01/2024
Journal:	Applied and Computational Harmonic Analysis
Volume:	73
Pages:	101685
Publisher:	Academic Press
Description:	Frames and orthonormal bases are important concepts in functional analysis and linear algebra. They are naturally linked to bounded operators. To describe unbounded operators those sequences might not be well suited. This has already been noted by von Neumann in the 1920ies. But modern frame theory also investigates other sequences, including those that are not naturally linked to bounded operators. The focus of this manuscript will be two such kind of sequences: lower frame and Riesz-Fischer sequences. We will discuss the inter-relation of those sequences. We will fill a hole existing in the literature regarding the classification of these sequences by their synthesis operator. We will use the idea of generalized frame operator and Gram matrix and extend it. We will use that to show properties for canonical duals for lower frame sequences, such as a minimality condition regarding its coefficients. We will …
Cited by:	2
Resources:	[PDF] from arxiv.org

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Trainable signal encoders that are robust against noise

2024

Peter Balazs, Daniel Haider, Vincent Lostanlen, Felix Perfler
INTER-NOISE and NOISE-CON Congress and Conference Proceedings 270 (10), 1836-1844
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Authors:	Peter Balazs, Daniel Haider, Vincent Lostanlen, Felix Perfler
Publication date:	10/04/2024
Journal:	INTER-NOISE and NOISE-CON Congress and Conference Proceedings
Volume:	270
Issue:	10
Pages:	1836-1844
Publisher:	Institute of Noise Control Engineering
Description:	Within the deep learning paradigm, finite impulse response (FIR) filters are often used to encode audio signals, yielding flexible and adaptive feature representations. We show that a stabilization of FIR filterbanks with fixed filter lengths (convolutional layers with 1-D filters) by means of their condition number leads to encoders that are optimally robust against noise and can be inverted with perfect reconstruction by their transposes. To maintain their flexibility as regular neural network layers we implement the stabilization via a computationally efficient regularizing term in the objective function of the learning problem. In this way, the encoder keeps its expressive power and is optimally stable and noise-robust throughout the whole learning procedure. We show in a denoising task where noise is additionally present in the encoder representation of the signals, that the proposed stabilization of the trainable filterbank …
Cited by:	5
Resources:	[PDF] from hal.science

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(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Number

2024

Rossen Nenov, Daniel Haider, Peter Balazs
arXiv preprint arXiv:2410.00169
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Authors:	Rossen Nenov, Daniel Haider, Peter Balazs
Publication date:	09/30/2024
Journal:	arXiv preprint arXiv:2410.00169
Description:	Maintaining numerical stability in machine learning models is crucial for their reliability and performance. One approach to maintain stability of a network layer is to integrate the condition number of the weight matrix as a regularizing term into the optimization algorithm. However, due to its discontinuous nature and lack of differentiability the condition number is not suitable for a gradient descent approach. This paper introduces a novel regularizer that is provably differentiable almost everywhere and promotes matrices with low condition numbers. In particular, we derive a formula for the gradient of this regularizer which can be easily implemented and integrated into existing optimization algorithms. We show the advantages of this approach for noisy classification and denoising of MNIST images.
Resources:	[PDF] from arxiv.org

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Hold me tight: Stable encoder-decoder design for speech enhancement

2024

Daniel Haider, Felix Perfler, Vincent Lostanlen, Martin Ehler, Peter Balazs
arXiv preprint arXiv:2408.17358
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Authors:	Daniel Haider, Felix Perfler, Vincent Lostanlen, Martin Ehler, Peter Balazs
Publication date:	08/30/2024
Journal:	arXiv preprint arXiv:2408.17358
Description:	Convolutional layers with 1-D filters are often used as frontend to encode audio signals. Unlike fixed time-frequency representations, they can adapt to the local characteristics of input data. However, 1-D filters on raw audio are hard to train and often suffer from instabilities. In this paper, we address these problems with hybrid solutions, i.e., combining theory-driven and data-driven approaches. First, we preprocess the audio signals via a auditory filterbank, guaranteeing good frequency localization for the learned encoder. Second, we use results from frame theory to define an unsupervised learning objective that encourages energy conservation and perfect reconstruction. Third, we adapt mixed compressed spectral norms as learning objectives to the encoder coefficients. Using these solutions in a low-complexity encoder-mask-decoder model significantly improves the perceptual evaluation of speech quality (PESQ) in speech enhancement.
Cited by:	4
Resources:	[PDF] from arxiv.org

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Injectivity of ReLU-layers: Perspectives from Frame Theory

2024

Daniel Haider, Martin Ehler, Peter Balazs
arXiv e-prints, arXiv: 2406.15856
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Authors:	Daniel Haider, Martin Ehler, Peter Balazs
Publication date:	06/01/2024
Journal:	arXiv e-prints
Pages:	arXiv: 2406.15856
Description:	Injectivity is the defining property of a mapping that ensures no information is lost and any input can be perfectly reconstructed from its output. By performing hard thresholding, the ReLU function naturally interferes with this property, making the injectivity analysis of ReLU-layers in neural networks a challenging yet intriguing task that has not yet been fully solved. This article establishes a frame theoretic perspective to approach this problem. The main objective is to develop the most general characterization of the injectivity behavior of ReLU-layers in terms of all three involved ingredients:(i) the weights,(ii) the bias, and (iii) the domain where the data is drawn from. Maintaining a focus on practical applications, we limit our attention to bounded domains and present two methods for numerically approximating a maximal bias for given weights and data domains. These methods provide sufficient conditions for the …
Cited by:	1

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Instabilities in convnets for raw audio

2024

Daniel Haider, Vincent Lostanlen, Martin Ehler, Peter Balazs
IEEE Signal Processing Letters 31, 1084-1088
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Authors:	Daniel Haider, Vincent Lostanlen, Martin Ehler, Peter Balazs
Publication date:	04/08/2024
Journal:	IEEE Signal Processing Letters
Volume:	31
Pages:	1084-1088
Publisher:	IEEE
Description:	What makes waveform-based deep learning so hard? Despite numerous attempts at training convolutional neural networks (convnets) for filterbank design, they often fail to outperform hand-crafted baselines. These baselines are linear time-invariant systems: as such, they can be approximated by convnets with wide receptive fields. Yet, in practice, gradient-based optimization leads to suboptimal results. In our article, we approach this problem from the perspective of initialization. We present a theory of large deviations for the energy response of FIR filterbanks with random Gaussian weights. We find that deviations worsen for large filters and locally periodic input signals, which are both typical for audio signal processing applications. Numerical simulations align with our theory and suggest that the condition number of a convolutional layer follows a logarithmic scaling law between the number and length of the …
Cited by:	4
Resources:	[PDF] from arxiv.org

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Quantitative bounds for unconditional pairs of frames

2024

Peter Balazs, Daniel Freeman, Roxana Popescu, Michael Speckbacher
Journal of Mathematical Analysis and Applications 531 (1), 127874
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Authors:	Peter Balazs, Daniel Freeman, Roxana Popescu, Michael Speckbacher
Publication date:	03/01/2024
Journal:	Journal of Mathematical Analysis and Applications
Volume:	531
Issue:	1
Pages:	127874
Publisher:	Academic Press
Description:	We formulate a quantitative finite-dimensional conjecture about frame multipliers and prove that it is equivalent to Conjecture 1 in [22]. We then present solutions to the conjecture for certain classes of frame multipliers. In particular, we prove that for all C> 0 and N∈ N the following is true: Let (x j) j= 1 N and (f j) j= 1 N be sequences in a finite dimensional Hilbert space which satisfy‖ x j‖=‖ f j‖ for all 1≤ j≤ N and‖∑ j= 1 N ε j< x, f j> x j‖≤ C‖ x‖, for all x∈ ℓ 2 M and\| ε j\|= 1. If the frame operator for (f j) j= 1 N has eigenvalues λ 1≥...≥ λ M and β> 0 is such that λ 1≤ β M− 1∑ j= 1 M λ j then (f j) j= 1 N has Bessel bound 27 β 2 C. The same holds for (x j) j= 1 N.
Cited by:	2
Resources:	[PDF] from sciencedirect.com

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Time-frequency analysis on flat tori and Gabor frames in finite dimensions

2024

Luis Daniel Abreu, Peter Balazs, Nicki Holighaus, Franz Luef, Michael Speckbacher
Applied and Computational Harmonic Analysis 69, 101622
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Authors:	Luis Daniel Abreu, Peter Balazs, Nicki Holighaus, Franz Luef, Michael Speckbacher
Publication date:	03/01/2024
Journal:	Applied and Computational Harmonic Analysis
Volume:	69
Pages:	101622
Publisher:	Academic Press
Description:	We provide the foundations of a Hilbert space theory for the short-time Fourier transform (STFT) where the flat tori T N 2= R 2/(Z× N Z)=[0, 1]×[0, N] act as phase spaces. We work on an N-dimensional subspace S N of distributions periodic in time and frequency in the dual S 0′(R) of the Feichtinger algebra S 0 (R) and equip it with an inner product. To construct the Hilbert space S N we apply a suitable double periodization operator to S 0 (R). On S N, the STFT is applied as the usual STFT defined on S 0′(R). This STFT is a continuous extension of the finite discrete Gabor transform from the lattice onto the entire flat torus. As such, sampling theorems on flat tori lead to Gabor frames in finite dimensions. For Gaussian windows, one is lead to spaces of analytic functions and the construction allows to prove a necessary and sufficient Nyquist rate type result, which is the analogue, for Gabor frames in finite dimensions …
Cited by:	8
Resources:	[HTML] from sciencedirect.com

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A Survey of Fusion Frames in Hilbert Spaces

2024

Lukas Köhldorfer, Peter Balazs, Pete Casazza, Sigrid Heineken, Clara Hollomey, Patricia…
Sampling, Approximation, and Signal Analysis: Harmonic Analysis in the Spirit of J. Row…
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Authors:	Lukas Köhldorfer, Peter Balazs, Pete Casazza, Sigrid Heineken, Clara Hollomey, Patricia Morillas, Mitra Shamsabadi
Publication date:	01/05/2024
Journal:	Sampling, Approximation, and Signal Analysis: Harmonic Analysis in the Spirit of J. Rowland Higgins
Pages:	245-328
Publisher:	Springer International Publishing
Description:	Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing, and much more. They provide a great flexibility for designing sets of vectors for applications and are therefore prominent in all these areas, including, e.g., mitigating the effects of noise in a signal or giving robustness to erasures. In this chapter, we present the fundamentals of fusion frame theory with an emphasis on their delicate relation to frame theory. The goal here is to provide researchers and students with an easy entry into this topic. Proofs for fusion frames will be self-contained and differences between frames and fusion frames are analyzed. In particular, we focus on the subtleties of fusion frame duality. We also provide a reproducible research implementation.
Cited by:	11
Resources:	[PDF] from arxiv.org

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Representation of operators using fusion frames

2024

Peter Balazs, Mitra Shamsabadi, Ali Akbar Arefijamaal, Gilles Chardon
Applied and Computational Harmonic Analysis 68, 101596
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Authors:	Peter Balazs, Mitra Shamsabadi, Ali Akbar Arefijamaal, Gilles Chardon
Publication date:	01/01/2024
Journal:	Applied and Computational Harmonic Analysis
Volume:	68
Pages:	101596
Publisher:	Academic Press
Description:	To solve operator equations numerically, matrix representations are employing bases or more recently frames. For finding the numerical solution of operator equations a decomposition in subspaces is needed in many applications. To combine those two approaches, it is necessary to extend the known methods of matrix representation to the utilization of fusion frames. In this paper, we investigate this representation of operators on a Hilbert space H with Bessel fusion sequences, fusion frames and fusion Riesz bases. Fusion frames can be considered as a frame-like family of subspaces. Taking the particular property of the duality of fusion frames into account, this allows us to define a matrix representation in a canonical as well as an alternate way, the later being more efficient and well behaved in respect to inversion. We will give the basic definitions and show some structural results, like that the functions assigning …
Cited by:	5
Resources:	[PDF] from arxiv.org

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Comparisons between Fourier and STFT multipliers: The smoothing effect of the short-time Fourier transform

2024

Peter Balazs, Federico Bastianoni, Elena Cordero, Hans G Feichtinger, Nina Schweighofer
Journal of Mathematical Analysis and Applications 529 (1), 127579
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Authors:	Peter Balazs, Federico Bastianoni, Elena Cordero, Hans G Feichtinger, Nina Schweighofer
Publication date:	01/01/2024
Journal:	Journal of Mathematical Analysis and Applications
Volume:	529
Issue:	1
Pages:	127579
Publisher:	Academic Press
Description:	We study the connection between STFT multipliers A 1⊗ m g 1, g 2 having windows g 1, g 2, symbols a (x, ω)=(1⊗ m)(x, ω)= m (ω),(x, ω)∈ R 2 d, and the Fourier multipliers T m 2 with symbol m 2 on R d. We find sufficient and necessary conditions on symbols m, m 2 and windows g 1, g 2 for the equality T m 2= A 1⊗ m g 1, g 2. For m= m 2 the former equality holds only for particular choices of window functions in modulation spaces, whereas it never occurs in the realm of Lebesgue spaces. In general, the STFT multiplier A 1⊗ m g 1, g 2, also called localization operator, presents a smoothing effect due to the so-called two-window short-time Fourier transform which enters in the definition of A 1⊗ m g 1, g 2. As a by-product we prove necessary conditions for the continuity of anti-Wick operators A 1⊗ m g, g: L p→ L q having multiplier m in weak L r spaces. Finally, we exhibit the related results for their discrete …
Cited by:	9
Resources:	[PDF] from arxiv.org

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Accelerated Griffin-Lim algorithm: A fast and provably converging numerical method for phase retrieval

2023

Rossen Nenov, Dang-Khoa Nguyen, Peter Balazs, Radu Ioan Boţ
IEEE Transactions on Signal Processing 72, 190-202
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Authors:	Rossen Nenov, Dang-Khoa Nguyen, Peter Balazs, Radu Ioan Boţ
Publication date:	12/12/2023
Journal:	IEEE Transactions on Signal Processing
Volume:	72
Pages:	190-202
Publisher:	IEEE
Description:	The recovery of a signal from the magnitudes of its transformation, like the Fourier transform, is known as the phase retrieval problem and is of big relevance in various fields of engineering and applied physics. In this paper, we present a fast inertial/momentum based algorithm for the phase retrieval problem. Our method can be seen as an extended algorithm of the Fast Griffin-Lim Algorithm, a method originally designed for phase retrieval in acoustics. The new numerical algorithm can be applied to a more general framework than acoustics, and as a main result of this paper, we prove a convergence guarantee of the new scheme. Consequently, we also provide an affirmative answer for the convergence of its ancestor Fast Griffin-Lim Algorithm, whose convergence remained unproven in the past decade. In the final chapter, we complement our theoretical findings with numerical experiments for the Short Time …
Cited by:	11
Resources:	[PDF] from arxiv.org

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Weighted frames, weighted lower semi frames and unconditionally convergent multipliers

2023

Peter Balazs, Rosario Corso, Diana Stoeva
arXiv preprint arXiv:2310.18957
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Authors:	Peter Balazs, Rosario Corso, Diana Stoeva
Publication date:	10/29/2023
Journal:	arXiv preprint arXiv:2310.18957
Description:	In this paper we ask when it is possible to transform a given sequence into a frame or a lower semi frame by multiplying the elements by numbers. In other words, we ask when a given sequence is a weighted frame or a weighted lower semi frame and for each case we formulate a conjecture. We determine several conditions under which these conjectures are true. Finally, we prove an equivalence between two older conjectures, the first one being that any unconditionally convergent multiplier can be written as a multiplier of Bessel sequences by shifting of weights, and the second one that every unconditionally convergent multiplier which is invertible can be written as a multiplier of frames by shifting of weights. We also show that these conjectures are also related to one of the newly posed conjectures.
Resources:	[PDF] from arxiv.org

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Fitting auditory filterbanks with multiresolution neural networks

2023

Vincent Lostanlen, Daniel Haider, Han Han, Mathieu Lagrange, Peter Balazs, Martin Ehler
2023 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA)…
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Authors:	Vincent Lostanlen, Daniel Haider, Han Han, Mathieu Lagrange, Peter Balazs, Martin Ehler
Publication date:	10/22/2023
Journal:	2023 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA)
Pages:	1-5
Publisher:	IEEE
Description:	Waveform-based deep learning faces a dilemma between nonparametric and parametric approaches. On one hand, convolutional neural networks (convnets) may approximate any linear time-invariant system; yet, in practice, their frequency responses become more irregular as their receptive fields grow. On the other hand, a parametric model such as LEAF is guaranteed to yield Gabor filters, hence an optimal time-frequency localization; yet, this strong inductive bias comes at the detriment of representational capacity. In this paper, we aim to overcome this dilemma by introducing a neural audio model, named multiresolution neural network (MuReNN). The key idea behind MuReNN is to train separate convolutional operators over the octave subbands of a discrete wavelet transform (DWT). Since the scale of DWT atoms grows exponentially between octaves, the receptive fields of the subsequent learnable …
Cited by:	7
Resources:	[PDF] from arxiv.org

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Double preconditioning for Gabor frame operators: Algebraic, functional analytic and numerical aspects

2023

Hans G Feichtinger, Peter Balazs, Daniel Haider
Applied and Computational Harmonic Analysis 66, 101-137
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Authors:	Hans G Feichtinger, Peter Balazs, Daniel Haider
Publication date:	09/01/2023
Journal:	Applied and Computational Harmonic Analysis
Volume:	66
Pages:	101-137
Publisher:	Academic Press
Description:	This paper provides algebraic and analytic, as well as numerical arguments why and how double preconditioning of the Gabor frame operator yields an efficient method to compute approximate dual (respectively tight) Gabor atoms for a given time-frequency lattice. We extend the definition of the approach to the continuous setting, making use of the so-called Banach Gelfand Triple, based on the Segal algebra (S 0 (R d),‖⋅‖ S 0) and show the continuous dependency of the double preconditioning operators on their parameters. The generalization allows to investigate the influence of the order of the two main single preconditioners (diagonal and convolutional). In the applied section we demonstrate the quality of double preconditioning over all possible lattices and adapt the method to approximate the canonical tight Gabor window, which yields a significant generalization of the FAB-method used in OFDM …
Cited by:	1

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Outer kernel theorem for co-orbit spaces of localised frames

2023

Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs
2023 International Conference on Sampling Theory and Applications (SampTA), 1-5
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Authors:	Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs
Publication date:	07/10/2023
Journal:	2023 International Conference on Sampling Theory and Applications (SampTA)
Pages:	1-5
Publisher:	IEEE
Description:	We prove a so-called outer kernel theorem for bounded linear operators between co-orbit spaces generated from a localised frame Ψ. In particular, we show that there is a bijective correspondence between the bounded linear operators mapping the co-orbit space of test functions to the co-orbit space of distributions and their kernels in . The proof of the theorem relies on general properties of localised frames, tensor products and Galerkin's method for matrix represention of operators.
Cited by:	2
Resources:	[PDF] from openreview.net

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Sampling and Frame Expansions for UWB Signals

2023

Peter Balazs, Stephen D Casey
2023 International Conference on Sampling Theory and Applications (SampTA), 1-5
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Authors:	Peter Balazs, Stephen D Casey
Publication date:	07/10/2023
Journal:	2023 International Conference on Sampling Theory and Applications (SampTA)
Pages:	1-5
Publisher:	IEEE
Description:	This article outlines sampling and frame expansions designed specifically for ultra-wideband (UWB) signals. We present two different types of expansions: ON windows with modified Gegenbauers and generalized frame expansions. They represent a contrast in the computability and flexibility of frames versus the rigid structure and precision in the sampling expansion. Both approaches rely on the multiplication of some super-windowing functions and given orthonormal sequences. We generalize this approach to the redundant case, investigating windowed families of frame sequences.

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Convex geometry of ReLU-layers, injectivity on the ball and local reconstruction

2023

Daniel Haider, Martin Ehler, Peter Balazs
International Conference on Machine Learning, 12339-12350
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Authors:	Daniel Haider, Martin Ehler, Peter Balazs
Publication date:	07/03/2023
Journal:	International Conference on Machine Learning
Pages:	12339-12350
Publisher:	PMLR
Description:	The paper uses a frame-theoretic setting to study the injectivity of a ReLU-layer on the closed ball of and its non-negative part. In particular, the interplay between the radius of the ball and the bias vector is emphasized. Together with a perspective from convex geometry, this leads to a computationally feasible method of verifying the injectivity of a ReLU-layer under reasonable restrictions in terms of an upper bound of the bias vector. Explicit reconstruction formulas are provided, inspired by the duality concept from frame theory. All this gives rise to the possibility of quantifying the invertibility of a ReLU-layer and a concrete reconstruction algorithm for any input vector on the ball.
Cited by:	7
Resources:	[PDF] from mlr.press

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Faster than fast: Accelerating the Griffin-Lim algorithm

2023

Rossen Nenov, Dang-Khoa Nguyen, Peter Balazs
ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processi…
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Authors:	Rossen Nenov, Dang-Khoa Nguyen, Peter Balazs
Publication date:	06/04/2023
Journal:	ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Pages:	1-5
Publisher:	IEEE
Description:	The phase retrieval problem is found in various areas of applications of engineering and applied physics. It is also a very active field of research in mathematics, signal processing and machine learning. In this paper, we present an accelerated version of the well known Fast Griffin-Lim algorithm (FGLA) for the phase retrieval problem in a general setting. It has increased the speed of convergence, and most importantly, the limit points of the generated sequence can reach a significantly smaller error than the ones generated by FGLA. We will give a motivation of the acceleration and compare it numerically to its predecessors and other algorithms typically used to solve similar problems.
Cited by:	6
Resources:	[PDF] from arxiv.org

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On the relation of the frame-related operators of fusion frame systems

2023

Lukas Köhldorfer, Peter Balazs
Sampling Theory, Signal Processing, and Data Analysis 21 (1), 9
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Authors:	Lukas Köhldorfer, Peter Balazs
Publication date:	06/01/2023
Journal:	Sampling Theory, Signal Processing, and Data Analysis
Volume:	21
Issue:	1
Pages:	9
Publisher:	Springer International Publishing
Description:	Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed processing techniques, which naturally leads to the concept of fusion frames and fusion frame systems. The latter consists of a system of subspaces, equipped with local frames on each of them, and a global frame. In this paper, we investigate the relations of the associated frame-related operators on all those three levels. For that we provide a detailed investigation on bounded block diagonal operators between Hilbert direct sums. We give the relation of the frame-related operators of the fusion frame and the corresponding frame systems in terms of operator identities. By applying these identities we prove further properties of fusion frame systems.
Cited by:	2
Resources:	[HTML] from springer.com

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The affine ensemble: determinantal point processes associated with the 𝑎𝑥+ 𝑏 group

2023

Luis Daniel Abreu, Peter Balazs, Smiljana Jakšić
Journal of the Mathematical Society of Japan 75 (2), 469-483
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Authors:	Luis Daniel Abreu, Peter Balazs, Smiljana Jakšić
Publication date:	01/01/2023
Journal:	Journal of the Mathematical Society of Japan
Volume:	75
Issue:	2
Pages:	469-483
Publisher:	The Mathematical Society of Japan
Description:	We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C+ associated with the ax+ b (affine) group, depending on an admissible Hardy function ψ. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set Ω⊂ C+. As a special case one recovers the DPP related to the weighted Bergman kernel. When ψ is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.
Cited by:	3
Resources:	[PDF] from arxiv.org

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The affine ensemble: determinantal point processes associated with the 𝑎𝑥+ 𝑏 group

2023

Abreu Luís Daniel, Balazs Peter, Jakšić Smiljana
Journal of the Mathematical Society of Japan 75 (2), 469-483
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Authors:	Abreu Luís Daniel, Balazs Peter, Jakšić Smiljana
Publication date:	01/01/2023
Journal:	Journal of the Mathematical Society of Japan
Volume:	75
Issue:	2
Pages:	469-483
Publisher:	一般社団法人日本数学会
Description:	We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane ℂ+ associated with the 𝑎𝑥+ 𝑏 (affine) group, depending on an admissible Hardy function 𝜓. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set Ω⊂ ℂ+. As a special case one recovers the DPP related to the weighted Bergman kernel. When 𝜓 is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.

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Separating and denoising seismic signals with dual-path recurrent neural network architecture

2022

Artemii Novoselov, Peter Balazs, Götz Bokelmann
Authorea Preprints
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Authors:	Artemii Novoselov, Peter Balazs, Götz Bokelmann
Publication date:	11/30/2022
Journal:	Authorea Preprints
Publisher:	Authorea
Description:	Seismologists have to deal with overlapping and noisy signals. Techniques such as source separation can be used to solve this problem. Over the past few decades, signal processing techniques used for source separation have advanced significantly for multi-station settings. But not so many options are available when it comes to single-station data. Using Machine Learning, we demonstrate the possibility of separating sources for single-station, one-component seismic recordings. The technique that we use for seismic signal separation is based on a dual-path recurrent neural network which is applied directly to the time domain data. Such source separation may find applications in most tasks of seismology, including earthquake analysis, aftershocks, nuclear verification, seismo-acoustics, and ambient-noise tomography. We train the network on seismic data from STanford EArthquake Dataset (STEAD) and demonstrate that our approach is a) capable of denoising seismic data and b) capable of separating two earthquake signals from one another. In this work, we show that Machine Learning is useful for earthquake-induced source separation. We provide a reproducible research repository with the algorithms here: https://github.com/IMGW-univie/source-separation.
Cited by:	1
Resources:	[PDF] from essopenarchive.org

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Capturing the songs of mice with an improved detection and classification method for ultrasonic vocalizations (BootSnap)

2022

Reyhaneh Abbasi, Peter Balazs, Maria Adelaide Marconi, Doris Nicolakis, Sarah M Zala, D…
PLoS Computational Biology 18 (5), e1010049
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Authors:	Reyhaneh Abbasi, Peter Balazs, Maria Adelaide Marconi, Doris Nicolakis, Sarah M Zala, Dustin J Penn
Publication date:	05/12/2022
Journal:	PLoS Computational Biology
Volume:	18
Issue:	5
Pages:	e1010049
Publisher:	Public Library of Science
Description:	House mice communicate through ultrasonic vocalizations (USVs), which are above the range of human hearing (>20 kHz), and several automated methods have been developed for USV detection and classification. Here we evaluate their advantages and disadvantages in a full, systematic comparison, while also presenting a new approach. This study aims to 1) determine the most efficient USV detection tool among the existing methods, and 2) develop a classification model that is more generalizable than existing methods. In both cases, we aim to minimize the user intervention required for processing new data. We compared the performance of four detection methods in an out-of-the-box approach, pretrained DeepSqueak detector, MUPET, USVSEG, and the Automatic Mouse Ultrasound Detector (A-MUD). We also compared these methods to human visual or ‘manual’ classification (ground truth) after assessing its reliability. A-MUD and USVSEG outperformed the other methods in terms of true positive rates using default and adjusted settings, respectively, and A-MUD outperformed USVSEG when false detection rates were also considered. For automating the classification of USVs, we developed BootSnap for supervised classification, which combines bootstrapping on Gammatone Spectrograms and Convolutional Neural Networks algorithms with Snapshot ensemble learning. It successfully classified calls into 12 types, including a new class of false positives that is useful for detection refinement. BootSnap outperformed the pretrained and retrained state-of-the-art tool, and thus it is more generalizable. BootSnap is freely available for …
Cited by:	13
Resources:	[HTML] from plos.org

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Frame-Related Sequences in Chains and Scales of Hilbert Spaces

2022

Peter Balazs, Giorgia Bellomonte, Hessam Hosseinnezhad
Axioms 11 (4), 180
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Authors:	Peter Balazs, Giorgia Bellomonte, Hessam Hosseinnezhad
Publication date:	04/16/2022
Journal:	Axioms
Volume:	11
Issue:	4
Pages:	180
Publisher:	MDPI
Description:	Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, we study how certain frame-related properties of a certain sequence in one of the spaces, such as completeness or the property of being a (semi-) frame, propagate to the other ones in a scale of Hilbert spaces. We link that to the properties of the respective frame-related operators, such as analysis or synthesis. We start with a detailed survey of the theory of Hilbert chains. Using a canonical isomorphism, the properties of frame sequences are naturally preserved between different spaces. We also show that some results can be transferred if the original sequence is considered—in particular, that the upper semi-frame property is kept in larger spaces, while the lower one is kept in smaller ones. This leads to a negative result: a sequence can never be a frame for two Hilbert spaces of the scale if the scale is non-trivial, i.e., if the spaces are not equal.
Cited by:	2
Resources:	[HTML] from mdpi.com

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Continuous frames in tensor product Hilbert spaces, localization operators and density operators

2022

Peter Balazs, Nenad Teofanov
Journal of Physics A: Mathematical and Theoretical 55 (14), 145201
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Authors:	Peter Balazs, Nenad Teofanov
Publication date:	03/08/2022
Journal:	Journal of Physics A: Mathematical and Theoretical
Volume:	55
Issue:	14
Pages:	145201
Publisher:	IOP Publishing
Description:	Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example, the consistency property, ie preservation of the frame property under the tensor product, and the description of the canonical dual tensors by those on the Hilbert space level. We show the full characterization of all dual systems for a given continuous frame, a result interesting by itself, and apply this to dual tensor frames. Furthermore, we discuss the existence on non-simple tensor product (dual) frames. Continuous frame multipliers and their Schatten class properties are considered in the context of tensor products. In particular, we give sufficient conditions for obtaining partial trace multipliers of the same form, which is illustrated with examples related to short-time Fourier …
Cited by:	7
Resources:	[HTML] from iop.org

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SEDENOSS: SEparating and DENOising seismic signals with dual‐path recurrent neural network architecture

2022

Artemii Novoselov, Peter Balazs, Götz Bokelmann
Journal of Geophysical Research: Solid Earth 127 (3), e2021JB023183
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Authors:	Artemii Novoselov, Peter Balazs, Götz Bokelmann
Publication date:	03/01/2022
Journal:	Journal of Geophysical Research: Solid Earth
Volume:	127
Issue:	3
Pages:	e2021JB023183
Description:	Seismologists have to deal with overlapping and noisy signals. Techniques such as source separation can be used to solve this problem. Over the past few decades, signal processing techniques used for source separation have advanced significantly for multi‐station settings. But not so many options are available when it comes to single‐station data. Using Machine Learning, we demonstrate the possibility of separating signals for single‐station, one‐component seismic recordings. The technique that we use for seismic signal separation is based on a dual‐path recurrent neural network which is applied directly to the time domain data. Such source separation may find applications in most tasks of seismology, including earthquake analysis, aftershocks, nuclear verification, seismo‐acoustics, and ambient‐noise tomography. We train the network on seismic data from STanford EArthquake Dataset and demonstrate …
Cited by:	34
Resources:	[PDF] from wiley.com Full View

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Akustische Phonetik und ihre multidisziplinären Aspekte-Gesamt PDF

2022

Michael Pucher, Peter Balazs
30, 154
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Authors:	Michael Pucher, Peter Balazs
Publication date:	01/01/2022
Volume:	30
Pages:	154
Publisher:	Verlag der österreichischen Akademie der Wissenschaften
Description:	The aim of this book is to honor the multidisciplinary work of Doz. Dr. Sylvia Moosmüller† in the field of acoustic phonetics. The essays in this volume range from sociophonetics, language diagnostics, dialectology, to language technology. They thus exemplify the breadth of acoustic phonetics, which has been shaped by influences from the humanities and technical sciences since its beginnings. In the first article of the volume, Barbara Soukup gives an overview of empirical research on language attitudes in Austria. Ralf Vollmann then deals with the difference between standard language and dialect from a sociophonological perspective. Brigitte Eisenwort and her co-authors dedicate themselves to the relation between growing up multilingually and language development disorders and pay tribute to Sylvia Moosmüller's research on language variation in the context of the clinical practice of language diagnostics …
Cited by:	1

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Random Time-varying Filtering with Subsampling

2022

Georg Tauböck, Shristi Rajbamshi, Peter Balazs
# PLACEHOLDER_PARENT_METADATA_VALUE# 16, 274-279
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Authors:	Georg Tauböck, Shristi Rajbamshi, Peter Balazs
Publication date:	01/01/2022
Journal:	# PLACEHOLDER_PARENT_METADATA_VALUE#
Volume:	16
Pages:	274-279
Description:	Time-varying filtering is of crucial importance in many areas of signal processing and, in particular, in audio processing. From a mathematical point of view, time-varying filters correspond to so-called “frame multipliers”. Here, the audio signal is first transformed into another signal domain, typically by means of a time-frequency transformation; then, the resulting transformed signal coefficients are multiplied with a “symbol”; and, finally, an audio signal is re-synthesized. Depending on the choice of the symbol, a frame multiplier allows to amplify certain audio components and/or to suppress others. In this contribution, we consider frame multipliers, whose symbols are chosen at random with an additional subsampling step of the output signal. We show that the corresponding subsampled random time-varying filters satisfy remarkable mathematical properties. Moreover, we demonstrate that they are highly efficient for signal compression. Our analysis is based on the recent mathematical methodology “compressive sensing”.
Cited by:	1

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Audio Inpainting

2022

Peter Balazs, Georg Tauböck, Shristi Rajbamshi, Nicki Holighaus
# PLACEHOLDER_PARENT_METADATA_VALUE# 16, 258-261
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Authors:	Peter Balazs, Georg Tauböck, Shristi Rajbamshi, Nicki Holighaus
Publication date:	01/01/2022
Journal:	# PLACEHOLDER_PARENT_METADATA_VALUE#
Volume:	16
Pages:	258-261
Description:	The objective of audio inpainting is to conceal missing or heavily distorted segments in an audio signal. This is ideally done by reconstructing the original signal or, at least, by inferring a meaningful surrogate signal. We present here a novel approach applying sparse modeling in the time-frequency (TF) domain which was recently published. In particular, we devise a dictionary learning technique which learns the dictionary from reliable parts around the gap with the goal to obtain a signal representation with improved TF sparsity. The presented method is based on a basis optimization technique that deforms a given Gabor frame such that the sparsity of the analysis coefficients of the resulting frame is maximized (with respect to a certain sparsity measure). Furthermore, we modify the SParse Audio INpainter (SPAIN) such that it is able to exploit the improved TF sparsity and—in turn—benefits from dictionary learning. As an alternative, we combine dictionary learning with weighted ℓ1-minimization adapted for audio inpainting to compensate for the loss of energy within the gap after restoration. Our experiments demonstrate that the developed methods achieve significant gains in terms of signal-to-distortion ratio (SDR) and objective difference grade (ODG) compared with several state-of-the-art audio inpainting techniques.

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Audio Inpainting via -Minimization and Dictionary Learning

2021

Shristi Rajbamshi, Georg Tauböck, Nicki Holighaus, Peter Balazs
2021 29th European Signal Processing Conference (EUSIPCO), 2149-2153
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Authors:	Shristi Rajbamshi, Georg Tauböck, Nicki Holighaus, Peter Balazs
Publication date:	08/23/2021
Journal:	2021 29th European Signal Processing Conference (EUSIPCO)
Pages:	2149-2153
Publisher:	IEEE
Description:	Audio inpainting refers to signal processing techniques that aim at restoring missing or corrupted consecutive samples in audio signals. Prior works have shown that -minimization with appropriate weighting is capable of solving audio inpainting problems, both for the analysis and the synthesis models. These models assume that audio signals are sparse with respect to some redundant dictionary and exploit that sparsity for inpainting purposes. Remaining within the sparsity framework, we utilize dictionary learning to further increase the sparsity and combine it with weighted -minimization adapted for audio inpainting to compensate for the loss of energy within the gap after restoration. Our experiments demonstrate that our approach is superior in terms of signal-to-distortion ratio (SDR) and objective difference grade (ODG) compared with its original counterpart.
Cited by:	5
Resources:	[PDF] from arxiv.org

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Phase-based signal representations for scattering

2021

Daniel Haider, Peter Balazs, Nicki Holighaus
2021 29th European Signal Processing Conference (EUSIPCO), 6-10
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Authors:	Daniel Haider, Peter Balazs, Nicki Holighaus
Publication date:	08/23/2021
Journal:	2021 29th European Signal Processing Conference (EUSIPCO)
Pages:	6-10
Publisher:	IEEE
Description:	The scattering transform is a non-linear signal representation method based on cascaded wavelet transform magnitudes. In this paper we introduce phase scattering, a novel approach where we use phase derivatives in a scattering procedure. We first revisit phase-related concepts for representing time-frequency information of audio signals, in particular, the partial derivatives of the phase in the time-frequency domain. By putting analytical and numerical results in a new light, we set the basis to extend the phase-based representations to higher orders by means of a scattering transform, which leads to well localized signal representations of large-scale structures. All the ideas are introduced in a general way and then applied using the STFT.
Cited by:	1
Resources:	[PDF] from arxiv.org

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Fast matching pursuit with multi-Gabor dictionaries

2021

Zdeněk Průša, Nicki Holighaus, Peter Balazs
ACM Transactions on Mathematical Software (TOMS) 47 (3), 1-20
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Authors:	Zdeněk Průša, Nicki Holighaus, Peter Balazs
Publication date:	06/26/2021
Journal:	ACM Transactions on Mathematical Software (TOMS)
Volume:	47
Issue:	3
Pages:	1-20
Publisher:	ACM
Description:	Finding the best K-sparse approximation of a signal in a redundant dictionary is an NP-hard problem. Suboptimal greedy matching pursuit algorithms are generally used for this task. In this work, we present an acceleration technique and an implementation of the matching pursuit algorithm acting on a multi-Gabor dictionary, i.e., a concatenation of several Gabor-type time-frequency dictionaries, each of which consists of translations and modulations of a possibly different window and time and frequency shift parameters. The technique is based on pre-computing and thresholding inner products between atoms and on updating the residual directly in the coefficient domain, i.e., without the round-trip to the signal domain. Since the proposed acceleration technique involves an approximate update step, we provide theoretical and experimental results illustrating the convergence of the resulting algorithm. The …
Cited by:	13
Resources:	[PDF] from arxiv.org

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Time-variant signal manipulation using frame multipliers

2021

Christian Kaseß, Thomas Maly, Peter Balazs, Wolfgang Kreuzer
Proceedings, 10
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Authors:	Christian Kaseß, Thomas Maly, Peter Balazs, Wolfgang Kreuzer
Publication date:	01/01/2021
Journal:	Proceedings
Pages:	10
Description:	To better understand the relation between annoyance and acoustic properties of environmental noise, laboratory studies with defined noise samples are often performed. To reduce measurement effort, sample generation through manipulation is an important approach. In some cases, it is necessary to use time-variant filters, e.g., to extract signal components whose frequency content changes over time. The method presented here is based on frame multipliers. This allows the definition of such filters directly in the time-frequency plane. The versatility of this approach is illustrated using curve squeal of railway vehicles, which can comprise narrow-band components affected by the Doppler shift but also broadband noise which may vary in intensity and frequency range. Multipliers are used to extract the relevant signal portions and to combine defined pass-by noise samples with the extracted squeal noises to produce well defined test conditions.
Cited by:	1

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Dictionary learning for sparse audio inpainting

2020

Georg Tauböck, Shristi Rajbamshi, Peter Balazs
IEEE Journal of Selected Topics in Signal Processing 15 (1), 104-119
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Authors:	Georg Tauböck, Shristi Rajbamshi, Peter Balazs
Publication date:	12/21/2020
Journal:	IEEE Journal of Selected Topics in Signal Processing
Volume:	15
Issue:	1
Pages:	104-119
Publisher:	IEEE
Description:	The objective of audio inpainting is to fill a gap in an audio signal. This is ideally done by reconstructing the original signal or, at least, by inferring a meaningful surrogate signal. We propose a novel approach applying sparse modeling in the time-frequency (TF) domain. In particular, we devise a dictionary learning technique which learns the dictionary from reliable parts around the gap with the goal to obtain a signal representation with increased TF sparsity. This is based on a basis optimization technique to deform a given Gabor frame such that the sparsity of the analysis coefficients of the resulting frame is maximized. Furthermore, we modify the SParse Audio INpainter (SPAIN) for both the analysis and the synthesis model such that it is able to exploit the increased TF sparsity and—in turn—benefits from dictionary learning. Our experiments demonstrate that the developed methods achieve significant gains in …
Cited by:	29
Resources:	[PDF] from ieee.org

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Primed to vocalize: Wild-derived male house mice increase vocalization rate and diversity after a previous encounter with a female

2020

Sarah M Zala, Doris Nicolakis, Maria Adelaide Marconi, Anton Noll, Thomas Ruf, Peter Ba…
PloS one 15 (12), e0242959
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Authors:	Sarah M Zala, Doris Nicolakis, Maria Adelaide Marconi, Anton Noll, Thomas Ruf, Peter Balazs, Dustin J Penn
Publication date:	12/09/2020
Journal:	PloS one
Volume:	15
Issue:	12
Pages:	e0242959
Publisher:	Public Library of Science
Description:	Males in a wide variety of taxa, including insects, birds and mammals, produce vocalizations to attract females. Male house mice emit ultrasonic vocalizations (USVs), especially during courtship and mating, which are surprising complex. It is often suggested that male mice vocalize at higher rates after interacting with a female, but the evidence is mixed depending upon the strain of mice. We conducted a study with wild-derived house mice (Mus musculus musculus) to test whether male courtship vocalizations (i.e., vocalizations emitted in a sexual context) are influenced by a prior direct interaction with a female, and if so, determine how long the effect lasts. We allowed sexually naïve males to directly interact with a female for five minutes (sexual priming), and then we recorded males’vocalizations either 1, 10, 20, or 30 days later when presented with an unfamiliar female (separated by a perforated partition) and female scent. We automatically detected USVs and processed recordings using the Automatic Mouse Ultrasound Detector (A-MUD version 3.2), and we describe our improved version of this tool and tests of its performance. We measured vocalization rate and spectro-temporal features and we manually classified USVs into 15 types to investigate priming effects on vocal repertoire diversity and composition. After sexual priming, males emitted nearly three times as many USVs, they had a larger repertoire diversity, and their vocalizations had different spectro-temporal features (USV length, slope and variability in USV frequency) compared to unprimed controls. Unprimed control males had the most distinctive repertoire composition compared …
Cited by:	25
Resources:	[HTML] from plos.org

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Separation and denoising of seismically-induced ground-motion signals with dual path residual neural network architecture.

2020

Artemii Novoselov, Götz Bokelmann, Gerrit Hein, Peter Balazs
AGU Fall Meeting Abstracts 2020, S052-0007
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Authors:	Artemii Novoselov, Götz Bokelmann, Gerrit Hein, Peter Balazs
Publication date:	12/01/2020
Journal:	AGU Fall Meeting Abstracts
Volume:	2020
Pages:	S052-0007
Description:	Source separation is an important task in signal processing, with application in music, speech, but also in seismic signals. Multiple signals can be added together to obtain a mixture, but a mixture can also be separated back into individual signals. In this work, we present a technique from the Machine Learning domain, called a dual-path residual neural network that utilizes the ability of the neural network to process source mixtures End-to-End in the time domain, reconstructing original sources from mixtures. We recorded data with a Raspberry Shake and Boom seismic sensor widely used by Citizen Science Community (24 bits ADC, Sigma-Delta, 144 dB dynamic range, flat frequency response from~ 2 seconds to~ 40 Hz) at the University of Vienna, with a sampling frequency of 100 Hz. The sensor is located in direct vicinity of railway tracks (S40, U4, Spittelau station). We trained the network to produce" clean" …

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Sparse audio inpainting: A dictionary learning technique to improve its performance

2020

Georg Tauboeck, Shristi Rajbamshi, Peter Balazs
Audio Engineering Society Convention 149
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Authors:	Georg Tauboeck, Shristi Rajbamshi, Peter Balazs
Publication date:	10/22/2020
Journal:	Audio Engineering Society Convention 149
Publisher:	Audio Engineering Society
Description:	The objective of audio inpainting is to fill a gap in a signal, either to be meaningful or even to reconstruct the original signal. We propose a novel approach applying sparse modeling in the time-frequency (TF) domain. In particular, we develop a dictionary learning technique which deforms a given Gabor frame such that the sparsity of the analysis coefficients of the resulting frame is maximized. A suitable modification of the SParse Audio Inpainter (SPAIN) allows to exploit the obtained sparsity gain and, hence, to benefit from the learned dictionary. Our experiments demonstrate that our methods outperforms several state-of-the-art audio inpainting techniques in terms of signal-to-noise ratio (SNR) and objective difference grade (ODG).
Cited by:	3
Resources:	[PDF] from oeaw.ac.at

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The Invertibility of U-Fusion Cross Gram Matrices of Operators

2020

Mitra Shamsabadi, Ali Akbar Arefijamaal, Peter Balazs
Mediterranean Journal of Mathematics 17 (4), 130
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Authors:	Mitra Shamsabadi, Ali Akbar Arefijamaal, Peter Balazs
Publication date:	08/01/2020
Journal:	Mediterranean Journal of Mathematics
Volume:	17
Issue:	4
Pages:	130
Publisher:	Springer International Publishing
Description:	Finding matrix representations is an important part of operator theory. Calculating such a discretization scheme is equally important for the numerical solution of operator equations. Traditionally in both fields, this was done using bases. Recently, frames have been used here. In this paper, we apply fusion frames for this task, a generalization motivated by a block representation, respectively, a domain decomposition. We interpret the operator representation using fusion frames as a generalization of fusion Gram matrices. We present the basic definition of U-fusion cross Gram matrices of operators for a bounded operator U. We give necessary and sufficient conditions for their (pseudo-)invertibility and present explicit formulas for the (pseudo-)inverse. More precisely, our attention is on how to represent the inverse and pseudo-inverse of such matrices as U-fusion cross Gram matrices. In particular, we characterize …
Cited by:	9
Resources:	[PDF] from arxiv.org

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Acoustic scene classification by the snapshot ensemble of CNNs with XGBoost

2020

Reyhaneh Abbasi, Peter Balazs
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Authors:	Reyhaneh Abbasi, Peter Balazs
Publication date:	06/01/2020
Publisher:	Technical Report, DCASE2020 Challenge
Description:	This report is to explain our system for the DCASE challenge 2020 task 1A. The aim is to implement acoustic scene classification of audio recordings into 10 predefined classes including airport, shopping mall, metro station, street pedestrian, public square, street traffic, tram, bus, metro, and park. There are main challenges to accomplish; 1-recordings are provided by six devices with different quality and 2-some of classes are very similar in terms of acoustic information. To bias correct all devices against the reference (here the device A), we have used XGBOOST algorithm fed by standardized Mel spectrogram. Our classifier consists of a CNN with mix-up augmentation and snapshot ensemble. The proposed model (baseline model) has yielded the accuracy of 62.1%(54.1%) and cross-entropy loss of 1.06 (1.36).
Cited by:	1
Resources:	[PDF] from dcase.community

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A survey on the unconditional convergence and the invertibility of frame multipliers with implementation

2020

Diana T Stoeva, Peter Balazs
Sampling: Theory and Applications: A Centennial Celebration of Claude Shannon, 169-192
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Authors:	Diana T Stoeva, Peter Balazs
Publication date:	05/21/2020
Journal:	Sampling: Theory and Applications: A Centennial Celebration of Claude Shannon
Pages:	169-192
Publisher:	Springer International Publishing
Description:	The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the unconditional convergence of multipliers, sufficient and/or necessary conditions for the invertibility of multipliers, and representation of the inverse via Neumann-like series and via multipliers with particular parameters. Multipliers for frames with specific structure, namely Gabor multipliers, are also considered. Some of the results for the representation of the inverse multiplier are implemented in Matlab-codes and the algorithms are described.
Cited by:	12

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PanDeNoise: Measurements before and during the lockdown at Zederhaus

2020

Holger Waubke, Peter Balazs, Lukas Köhldorfer, Alexander Kranabetter
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Authors:	Holger Waubke, Peter Balazs, Lukas Köhldorfer, Alexander Kranabetter
Publication date:	02/01/2020
Description:	The year 2020 will be remembered as the year of the COVID-19-pandemic caused by SARS-CoV-2, better known as Coronavirus. In many countries over the world drastic actions, such as cancellations of commercial flights, ground traffic limitations and nationwide lockdowns, have been implemented in order to slow down the spread of the virus [7]. Accordingly, on March 16th 2020 obligatory COVID-19 lockdown measures have been established in Austria to reduce face-to-face contacts and maintain social distance. In that process, people have been confined to their homes except for meeting basic needs, addressing danger, assisting people in need, fulfilling work responsibilities and practising outdoor activities alone or with people living in the same household [3]. Correspondingly, various kinds of stores with the exception of grocery and drug stores have been closed, universities and parts of school have been …
Resources:	[PDF] from dega-akustik.de

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Accelerating matching pursuit for multiple time-frequency dictionaries

2020

Zdenek Pruša, Nicki Holighaus, Peter Balazs
Proceedings of the International Conference on Digital Audio Effects
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Authors:	Zdenek Pruša, Nicki Holighaus, Peter Balazs
Publication date:	01/01/2020
Journal:	Proceedings of the International Conference on Digital Audio Effects
Description:	Matching pursuit (MP) algorithms are widely used greedy methods to find K-sparse signal approximations in redundant dictionaries. We present an acceleration technique and an implementation of the matching pursuit algorithm acting on a multi-Gabor dictionary, ie, a concatenation of several Gabor-type time-frequency dictionaries, consisting of translations and modulations of possibly different windows, time-and frequency-shift parameters. The proposed acceleration is based on pre-computing and thresholding inner products between atoms and on updating the residual directly in the coefficient domain, ie, without the round-trip to the signal domain. Previously, coefficient-domain residual updates have been dismissed as having prohibitive memory requirements. By introducing an approximate update step, we can overcome this restriction and greatly improve the performance of matching pursuit at a modest cost in terms of approximation quality per selected atom. An implementation in C with Matlab and GNU Octave interfaces is available, outperforming the standard Matching Pursuit Toolkit (MPTK) by a factor of 3.5 to 70 in the tested conditions. Additionally, we provide experimental results illustrating the convergence of the implementation.
Cited by:	3
Resources:	[PDF] from ltfat.org

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Frames, their relatives and reproducing kernel Hilbert spaces

2019

Michael Speckbacher, Peter Balazs
Journal of Physics A: Mathematical and Theoretical 53 (1), 015204
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Authors:	Michael Speckbacher, Peter Balazs
Publication date:	12/10/2019
Journal:	Journal of Physics A: Mathematical and Theoretical
Volume:	53
Issue:	1
Pages:	015204
Publisher:	IOP Publishing
Description:	This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: first, we analyze the structure of the reproducing kernel of a RKHS using frames and reproducing pairs. Second, we present a new approach to prove the result that finite redundancy of a continuous frame implies atomic structure of the underlying measure space. Our proof uses the RKHS structure of the range of the analysis operator. This in turn implies that all the attempts to extend the notion of Riesz basis to general measure spaces are fruitless since every such family can be identified with a discrete Riesz basis. Finally, we show how the range of the analysis operators of a reproducing pair can be equipped with a RKHS structure.
Cited by:	12
Resources:	[HTML] from iop.org

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Continuous warped time-frequency representations—coorbit spaces and discretization

2019

Nicki Holighaus, Christoph Wiesmeyr, Peter Balazs
Applied and Computational Harmonic Analysis 47 (3), 975-1013
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Authors:	Nicki Holighaus, Christoph Wiesmeyr, Peter Balazs
Publication date:	11/01/2019
Journal:	Applied and Computational Harmonic Analysis
Volume:	47
Issue:	3
Pages:	975-1013
Publisher:	Academic Press
Description:	We present a novel family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales. Similar to classical time-frequency or time-scale representations, the representation coefficients are obtained as inner products with the elements of a continuously indexed family of time-frequency atoms. These atoms are obtained from a single prototype function, by means of modulation, translation and warping. By warping we refer to the process of nonlinear evaluation according to a bijective, increasing function, the warping function. Besides showing that the resulting integral transforms fulfill certain basic, but essential properties, such as continuity and invertibility, we will show that a large subclass of warping functions gives rise to families of generalized coorbit spaces, ie Banach spaces of functions whose representations possess a certain localization. Furthermore, we obtain …
Cited by:	15
Resources:	[HTML] from sciencedirect.com

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Random Gabor multipliers for compressive sensing: a simulation study

2019

Shristi Rajbamshi, Georg Tauböck, Peter Balazs, Luís Daniel Abreu
2019 27th European Signal Processing Conference (EUSIPCO), 1-5
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Authors:	Shristi Rajbamshi, Georg Tauböck, Peter Balazs, Luís Daniel Abreu
Publication date:	09/02/2019
Journal:	2019 27th European Signal Processing Conference (EUSIPCO)
Pages:	1-5
Publisher:	IEEE
Description:	In this paper, we analyze by means of simulations the applicability of random Gabor multipliers as compressive measurements. In particular, we consider signals that are sparse with respect to Fourier or Gabor dictionaries, i.e., signals that are sparse in frequency or time-frequency domains. This work is an extension of our earlier contribution, where we introduced random Gabor multipliers to compress signals that are sparse in time domain. As reconstruction technique we employ the well known -minimization procedure. Finally, we evaluate the compression performance of random Gabor multipliers by applying them to a specific audio signal with inherent time-frequency sparsity. Our results highlight the strong potential of random Gabor multipliers for present and future real-world audio applications.
Cited by:	8
Resources:	[PDF] from eurasip.org

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U-cross Gram matrices and their invertibility

2019

Peter Balazs, Mitra Shamsabadi, Ali Akbar Arefijamaal, Asghar Rahimi
Journal of Mathematical Analysis and Applications 476 (2), 367-390
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Authors:	Peter Balazs, Mitra Shamsabadi, Ali Akbar Arefijamaal, Asghar Rahimi
Publication date:	08/15/2019
Journal:	Journal of Mathematical Analysis and Applications
Volume:	476
Issue:	2
Pages:	367-390
Publisher:	Academic Press
Description:	The Gram matrix is defined for Bessel sequences by combining synthesis with subsequent analysis operators. If different sequences are used and an operator U is inserted we reach so called U-cross Gram matrices. This can be seen as reinterpretation of the matrix representation of operators using frames. In this paper we investigate some necessary or sufficient conditions for Schatten p-class properties and the invertibility of U-cross Gram matrices. In particular, we show that under mild conditions the pseudo-inverse of a U-cross Gram matrix can always be represented as a U-cross Gram matrix with dual frames of the given ones. We link some properties of U-cross Gram matrices to approximate duals. Finally, we state several stability results. More precisely, it is shown that the invertibility of U-cross Gram matrices is preserved under small perturbations.
Cited by:	12
Resources:	[HTML] from sciencedirect.com

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Banach frames and atomic decompositions in the space of bounded operators on Hilbert spaces

2019

Peter Balazs
2019 13th International conference on Sampling Theory and Applications (SampTA), 1-4
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Authors:	Peter Balazs
Publication date:	07/08/2019
Journal:	2019 13th International conference on Sampling Theory and Applications (SampTA)
Pages:	1-4
Publisher:	IEEE
Description:	The concept of frames is used extensively for the representation of signal or functions. Recently, this concept is applied more and more for the representation of operators, both in theory as well as in the application for the numerical solutions of operator equations. In this paper we first give a survey about the matrix representation of operators using frames. Then we prove that the tensor product of frames forms a Banach frame and an atomic decomposition for the space of bounded operators of Hilbert spaces.
Resources:	[HTML] from academia.edu

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Random Gabor multipliers and compressive sensing

2019

Georg Tauböck, Shristi Rajbamshi, Peter Balazs, Luís Daniel Abreu
2019 13th International conference on Sampling Theory and Applications (SampTA), 1-4
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Authors:	Georg Tauböck, Shristi Rajbamshi, Peter Balazs, Luís Daniel Abreu
Publication date:	07/08/2019
Journal:	2019 13th International conference on Sampling Theory and Applications (SampTA)
Pages:	1-4
Publisher:	IEEE
Description:	We investigate the applicability of Gabor multipliers as compressive measurements. Specifically, we show that the canonical M × N matrix representation of a Gabor multiplier from ℂN to ℂM is full spark for almost all windows and multiplier symbol vectors with respect to the Lebesgue measure, provided that the length Q of the multiplier symbol vector satisfies Q ≥ N + M − 1. Hence, if used as a measurement matrix in compressive sensing, M ≥ 2S guarantees perfect recovery of all S-sparse vectors by means of ℓ0-minimization for almost all such Gabor multipliers. Furthermore, for ℓ1-minimization, we demonstrate via simulations that Gabor multipliers with randomly chosen symbol vector have excellent capabilities in recovering sparse signals.
Cited by:	3
Resources:	[PDF] from sciencesconf.org

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An operator based approach to irregular frames of translates

2019

Peter Balazs, Sigrid Heineken
Mathematics 7 (5), 449
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Authors:	Peter Balazs, Sigrid Heineken
Publication date:	05/20/2019
Journal:	Mathematics
Volume:	7
Issue:	5
Pages:	449
Publisher:	MDPI
Description:	We consider translates of functions in L2(Rd) along an irregular set of points, that is, {ϕ(·−λk)}k∈Z—where ϕ is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform.
Cited by:	4
Resources:	[HTML] from mdpi.com

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Harmonic-aligned frame mask based on non-stationary Gabor transform with application to content-dependent speaker comparison

2019

Feng Huang, Peter Balazs
arXiv preprint arXiv:1904.10380
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Authors:	Feng Huang, Peter Balazs
Publication date:	04/23/2019
Journal:	arXiv preprint arXiv:1904.10380
Description:	We propose harmonic-aligned frame mask for speech signals using non-stationary Gabor transform (NSGT). A frame mask operates on the transfer coefficients of a signal and consequently converts the signal into a counterpart signal. It depicts the difference between the two signals. In preceding studies, frame masks based on regular Gabor transform were applied to single-note instrumental sound analysis. This study extends the frame mask approach to speech signals. For voiced speech, the fundamental frequency is usually changing consecutively over time. We employ NSGT with pitch-dependent and therefore time-varying frequency resolution to attain harmonic alignment in the transform domain and hence yield harmonic-aligned frame masks for speech signals. We propose to apply the harmonic-aligned frame mask to content-dependent speaker comparison. Frame masks, computed from voiced signals of a same vowel but from different speakers, were utilized as similarity measures to compare and distinguish the speaker identities (SID). Results obtained with deep neural networks demonstrate that the proposed frame mask is valid in representing speaker characteristics and shows a potential for SID applications in limited data scenarios.
Cited by:	2
Resources:	[PDF] from arxiv.org

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Frames for the solution of operator equations in Hilbert spaces with fixed dual pairing

2019

Peter Balazs, Helmut Harbrecht
Numerical functional analysis and optimization 40 (1), 65-84
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Authors:	Peter Balazs, Helmut Harbrecht
Publication date:	01/02/2019
Journal:	Numerical functional analysis and optimization
Volume:	40
Issue:	1
Pages:	65-84
Publisher:	Taylor & Francis
Description:	For the solution of operator equations, Stevenson introduced a definition of frames, where a Hilbert space and its dual are not identified. This means that the Riesz isomorphism is not used as an identification, which, for example, does not make sense for the Sobolev spaces and . In this article, we are going to revisit the concept of Stevenson frames and introduce it for Banach spaces. This is equivalent to -Banach frames. It is known that, if such a system exists, by defining a new inner product and using the Riesz isomorphism, the Banach space is isomorphic to a Hilbert space. In this article, we deal with the contrasting setting, where and are not identified, and equivalent norms are distinguished, and show that in this setting the investigation of -Banach frames make sense.
Cited by:	13
Resources:	[PDF] from tandfonline.com

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Kernel theorems in coorbit theory

2019

Peter Balazs, Karlheinz Gröchenig, Michael Speckbacher
Transactions of the American Mathematical Society, Series B 6 (11), 346-364
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Authors:	Peter Balazs, Karlheinz Gröchenig, Michael Speckbacher
Publication date:	01/01/2019
Journal:	Transactions of the American Mathematical Society, Series B
Volume:	6
Issue:	11
Pages:	346-364
Description:	We prove general kernel theorems for operators acting between coorbit spaces. These are Banach spaces associated to an integrable representation of a locally compact group and contain most of the usual function spaces (Besov spaces, modulation spaces, etc.). A kernel theorem describes the form of every bounded operator between a coorbit space of test functions and distributions by means of a kernel in a coorbit space associated to the tensor product representation. As special cases we recover Feichtinger’s kernel theorem for modulation spaces and the recent generalizations by Cordero and Nicola. We also obtain a kernel theorem for operators between the Besov spaces and . References
Cited by:	21
Resources:	[PDF] from arxiv.org

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Applying convolutional neural networks to the analysis of mouse ultrasonic vocalizations

2019

Reyhaneh Abbasi, Peter Balazs, Anton Noll, Doris Nicolakis, Maria Adelaide Marconi, Sar…
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Authors:	Reyhaneh Abbasi, Peter Balazs, Anton Noll, Doris Nicolakis, Maria Adelaide Marconi, Sarah M Zala, Dustin J Penn
Publication date:	01/01/2019
Publisher:	Universitätsbibliothek der RWTH Aachen
Description:	Many species in diverse taxonomic groups, including rodents, bats, and insects, communicate with complex ultrasonic vocalizations (USVs)(> 20 kHz). Two main components of processing and analyzing USV recordings include detection and classification of syllable types. Recently we developed an efficient algorithm for detecting mouse USVs (Automatic Mouse Ultrasound Detector (A-MUD)). The main challenge is detecting USVs under conditions with a low signal-to-noise ratio, while minimizing rates of false positives (FP). Mice produce many short USVs (< 10 millisecond) that inflate FPs. We aimed to improve the detection of mouse USVs with A-MUD by classifying vocalizations into three discrete syllable types (with 0, 1, or≥ 2 frequency-jumps) or FP. Supervised Convolutional Neural Networks (CNNs) were fed by 2D Gammatone Spectrograms (GSs) adapted to the frequency range of mice. Evaluation of performance shows that CNNs yielded an overall accuracy of 95±1.2% and macro-F1 score of 90±2.7%. In contrast, multilayer feed-forward neural networks fed by vectorized spectrograms provided an overall accuracy of only 85.4±1.9% and macro-F1 score of 75.4±2.9%, and therefore, the chosen CNNs outperformed this conventional classification method.
Cited by:	3
Resources:	[PDF] from rwth-aachen.de

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Adhoc method to invert the reassigned time-frequency representation

2019

Shristi Rajbamshi, Peter Balazs, Nicki Holighaus
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Authors:	Shristi Rajbamshi, Peter Balazs, Nicki Holighaus
Publication date:	01/01/2019
Publisher:	Universitätsbibliothek der RWTH Aachen
Description:	In this contribution, we present a heuristic method to invert the reassigned short time Fourier transform magnitude spectrum to allow the reconstruction of the original time domain signal. This is a simple method just involving an additional smearing step before phase retrieval. Finally, we provide some numerical evidence that our method combined with existing phase retrieval methods shows excellent performance in synthesizing pure tones and synthetic signals from the reassigned coefficients. Furthermore, we also illustrate the practical importance of our results by applying our method to a real-world audio signal.
Cited by:	1
Resources:	[PDF] from dega-akustik.de

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Extraction of rhythmical features with the Gabor scattering transform

2019

Daniel Haider, Peter Balazs
Proceedings of the 14th International Symposium on Computer Music Multidisciplinary Res…
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Authors:	Daniel Haider, Peter Balazs
Publication date:	01/01/2019
Journal:	Proceedings of the 14th International Symposium on Computer Music Multidisciplinary Research (CMMR)
Pages:	916-923
Description:	In this paper we use the scattering transform to extract widescale information of musical pieces in terms of rhythmical features. This transform computes a layered structure, similar to a convolutional neural network (CNN) but with no learning involved. Applied to audio it is able to capture temporal dependencies beyond those possible for common time-frequency representations. This is already demonstrated by experiments for modulations of single tones. Here we provide a setup to include real world music signals, which extends the temporal range to the scale where rhythm and tempo live, allowing very intuitive explanations of how these scales are reached. In this way we also get an intuition of the mechanics inside a neural network when “listening” to rhythm.
Cited by:	5
Resources:	[PDF] from hal.science

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Designing Gabor windows using convex optimization

2018

Nathanaël Perraudin, Nicki Holighaus, Peter L Søndergaard, Peter Balazs
Applied Mathematics and Computation 330, 266-287
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Authors:	Nathanaël Perraudin, Nicki Holighaus, Peter L Søndergaard, Peter Balazs
Publication date:	08/01/2018
Journal:	Applied Mathematics and Computation
Volume:	330
Pages:	266-287
Publisher:	Elsevier
Description:	Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal ℓ2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g. good time–frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler–Raz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found.
Cited by:	24
Resources:	[PDF] from researchgate.net

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A survey on the unconditional convergence and the invertibility of multipliers with implementation

2018

Diana T Stoeva, Peter Balazs
arXiv preprint arXiv:1803.00415
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Authors:	Diana T Stoeva, Peter Balazs
Publication date:	03/01/2018
Journal:	arXiv preprint arXiv:1803.00415
Description:	The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the unconditional convergence of multipliers, sufficient and/or necessary conditions for the invertibility of multipliers, and representation of the inverse via Neumann-like series and via multipliers with particular parameters. Multipliers for frames with specific structure, namely, Gabor and wavelet multipliers, are also considered. Some of the results for the representation of the inverse multiplier are implemented in Matlab codes and the algorithms are described.
Cited by:	3
Resources:	[PDF] from arxiv.org

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Inpainting of long audio segments with similarity graphs

2018

Nathanael Perraudin, Nicki Holighaus, Piotr Majdak, Peter Balazs
IEEE/ACM Transactions on Audio, Speech, and Language Processing 26 (6), 1083-1094
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Authors:	Nathanael Perraudin, Nicki Holighaus, Piotr Majdak, Peter Balazs
Publication date:	02/26/2018
Journal:	IEEE/ACM Transactions on Audio, Speech, and Language Processing
Volume:	26
Issue:	6
Pages:	1083-1094
Publisher:	IEEE
Description:	We present a novel method for the compensation of long duration data loss in audio signals, in particular music. The concealment of such signal defects is based on a graph that encodes signal structure in terms of time-persistent spectral similarity. A suitable candidate segment for the substitution of the lost content is proposed by an intuitive optimization scheme and smoothly inserted into the gap, i.e., the lost or distorted signal region. Extensive listening tests show that the proposed algorithm provides highly promising results when applied to a variety of real-world music signals.
Cited by:	58
Resources:	[PDF] from arxiv.org

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Audlet filter banks: A versatile analysis/synthesis framework using auditory frequency scales

2018

Thibaud Necciari, Nicki Holighaus, Peter Balazs, Zdeněk Průša, Piotr Majdak, Olivier De…
Applied Sciences 8 (1), 96
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Authors:	Thibaud Necciari, Nicki Holighaus, Peter Balazs, Zdeněk Průša, Piotr Majdak, Olivier Derrien
Publication date:	01/11/2018
Journal:	Applied Sciences
Volume:	8
Issue:	1
Pages:	96
Publisher:	MDPI
Description:	Featured Application The proposed framework is highly suitable for audio applications that require analysis–synthesis systems with the following properties: stability, perfect reconstruction, and a flexible choice of redundancy. Abstract Many audio applications rely on filter banks (FBs) to analyze, process, and re-synthesize sounds. For these applications, an important property of the analysis–synthesis system is the reconstruction error; it has to be minimized to avoid audible artifacts. Other advantageous properties include stability and low redundancy. To exploit some aspects of auditory perception in the signal chain, some applications rely on FBs that approximate the frequency analysis performed in the auditory periphery, the gammatone FB being a popular example. However, current gammatone FBs only allow partial reconstruction and stability at high redundancies. In this article, we construct an analysis–synthesis system for audio applications. The proposed system, referred to as Audlet, is an oversampled FB with filters distributed on auditory frequency scales. It allows perfect reconstruction for a wide range of FB settings (e.g., the shape and density of filters), efficient FB design, and adaptable redundancy. In particular, we show how to construct a gammatone FB with perfect reconstruction. Experiments demonstrate performance improvements of the proposed gammatone FB when compared to current gammatone FBs in terms of reconstruction error and stability, especially at low redundancies. An application of the framework to audio source separation illustrates its utility for audio processing.
Cited by:	37
Resources:	[HTML] from mdpi.com

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Reproducing pairs and Gabor systems at critical density

2017

Michael Speckbacher, Peter Balazs
Journal of Mathematical Analysis and Applications 455 (2), 1072-1087
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Authors:	Michael Speckbacher, Peter Balazs
Publication date:	11/15/2017
Journal:	Journal of Mathematical Analysis and Applications
Volume:	455
Issue:	2
Pages:	1072-1087
Publisher:	Academic Press
Description:	We use the concept of reproducing pairs to study Gabor systems at critical density. First, we present a generalization of the Balian–Low theorem to the reproducing pairs setting. Then, we prove our main result that there exists a reproducing partner for the Gabor system of integer time-frequency shifts of the Gaussian. In other words, the coefficients for this Gabor expansion of a square integrable function can be calculated using inner products with an unstructured family of vectors in L 2 (R). This solves one of the last few open questions for this system.
Cited by:	14
Resources:	[HTML] from sciencedirect.com

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Dictionary learning for pitch estimation in speech signals

2017

Feng Huang, Peter Balazs
2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP),…
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Authors:	Feng Huang, Peter Balazs
Publication date:	09/25/2017
Journal:	2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP)
Pages:	1-6
Publisher:	IEEE
Description:	This paper presents an automatic approach for parameter training for a sparsity-based pitch estimation method that has been previously published. For this pitch estimation method, the harmonic dictionary is a key parameter that needs to be carefully prepared beforehand. In the original method, extensive human supervision and involvement are required to construct and label the dictionary. In this study, we propose to employ dictionary learning algorithms to learn the dictionary directly from training data. We apply and compare 3 typical dictionary learning algorithms, i.e., the method of optimized directions (MOD), K-SVD and online dictionary learning (ODL), and propose a post-processing method to label and adapt a learned dictionary for pitch estimation. Results show that MOD and properly initialized ODL (pi-ODL) can lead to dictionaries that exhibit the desired harmonic structures for pitch estimation, and the …
Cited by:	2

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The -modulation transform: admissibility, coorbit theory and frames of compactly supported functions

2017

Michael Speckbacher, Dominik Bayer, Stephan Dahlke, Peter Balazs
Monatshefte für Mathematik 184 (1), 133-169
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Authors:	Michael Speckbacher, Dominik Bayer, Stephan Dahlke, Peter Balazs
Publication date:	09/01/2017
Journal:	Monatshefte für Mathematik
Volume:	184
Issue:	1
Pages:	133-169
Publisher:	Springer Vienna
Description:	The -modulation transform is a time-frequency transform generated by square-integrable representations of the affine Weyl–Heisenberg group modulo suitable subgroups. In this paper we prove new conditions that guarantee the admissibility of a given window function. We also show that the generalized coorbit theory can be applied to this setting, assuming specific regularity of the windows. This then yields canonical constructions of Banach frames and atomic decompositions in -modulation spaces. In particular, we prove the existence of compactly supported (in time domain) vectors that are admissible and satisfy all conditions within the coorbit machinery, which considerably go beyond known results.
Cited by:	17
Resources:	[PDF] from arxiv.org

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Kernel-based Reconstruction of Solutions of the Helmholtz Equation

2017

Manuel Gräf, Martin Ehler, Wolfgang Kreuzer, Markus Noisternig, Peter Balazs
13th International Conference on Theoretical and Computational Acoustics
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Authors:	Manuel Gräf, Martin Ehler, Wolfgang Kreuzer, Markus Noisternig, Peter Balazs
Publication date:	08/02/2017
Journal:	13th International Conference on Theoretical and Computational Acoustics
Description:	Kernel-based Reconstruction of Solutions of the Helmholtz Equation - Archive ouverte HAL Recherche Accéder directement au contenu Pied de page Logo Logo Documentation FR Français (FR) Anglais (EN) Se connecter HAL science ouverte Recherche Loading... Recherche avancée Information de documents Titres Titres Sous-titre Titre de l'ouvrage Titre du volume (Série) Champ de recherche par défaut (multicritères) + texte intégral des PDF Résumé Texte intégral indexé des documents PDF Mots-clés Type de document Sous-type de document Tous les identifiants du document Identifiant HAL du dépôt Langue du document (texte) Pays (Texte) Ville À paraître (true ou false) Ajouter Auteur Auteur (multicritères) Auteur (multicritères) Auteur : Nom complet Auteur : Nom de famille Auteur : Prénom Auteur : Complément de nom, deuxième prénom Auteur : Organisme payeur Auteur : IdHal (chaîne de caractères) …

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Automatic mouse ultrasound detector (A-MUD): A new tool for processing rodent vocalizations

2017

Sarah M Zala, Doris Reitschmidt, Anton Noll, Peter Balazs, Dustin J Penn
PloS one 12 (7), e0181200
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Authors:	Sarah M Zala, Doris Reitschmidt, Anton Noll, Peter Balazs, Dustin J Penn
Publication date:	07/20/2017
Journal:	PloS one
Volume:	12
Issue:	7
Pages:	e0181200
Publisher:	Public Library of Science
Description:	House mice (Mus musculus) emit complex ultrasonic vocalizations (USVs) during social and sexual interactions, which have features similar to bird song (i.e., they are composed of several different types of syllables, uttered in succession over time to form a pattern of sequences). Manually processing complex vocalization data is time-consuming and potentially subjective, and therefore, we developed an algorithm that automatically detects mouse ultrasonic vocalizations (Automatic Mouse Ultrasound Detector or A-MUD). A-MUD is a script that runs on STx acoustic software (S_TOOLS-STx version 4.2.2), which is free for scientific use. This algorithm improved the efficiency of processing USV files, as it was 4–12 times faster than manual segmentation, depending upon the size of the file. We evaluated A-MUD error rates using manually segmented sound files as a ‘gold standard’ reference, and compared them to a commercially available program. A-MUD had lower error rates than the commercial software, as it detected significantly more correct positives, and fewer false positives and false negatives. The errors generated by A-MUD were mainly false negatives, rather than false positives. This study is the first to systematically compare error rates for automatic ultrasonic vocalization detection methods, and A-MUD and subsequent versions will be made available for the scientific community.
Cited by:	43
Resources:	[HTML] from plos.org

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Commutative properties of invertible multipliers in relation to representation of their inverses

2017

Diana T Stoeva, Peter Balazs
2017 International Conference on Sampling Theory and Applications (SampTA), 288-293
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Authors:	Diana T Stoeva, Peter Balazs
Publication date:	07/03/2017
Journal:	2017 International Conference on Sampling Theory and Applications (SampTA)
Pages:	288-293
Publisher:	IEEE
Description:	Recently frame multipliers and in particular their invertibility became an important subject of research. In particular, it was shown that given an invertible frame multiplier, a particular dual frame can be determined, such that the inverse is again a multiplier, using this dual sequence. In the paper we deal with the question if these particular duals keep the specific structure of the primal frames. We investigate pseudo-coherent frames and summarize results showing that the structure is kept for frame-like operators, i.e. multipliers with constant symbols. For more general symbols we show result that under additional assumptions, in particular a commutation relation, the symbol being constant is a necessary condition. We reformulate the results for the particular case of Gabor systems.
Cited by:	6

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Frame theory for signal processing in psychoacoustics

2017

Peter Balazs, Nicki Holighaus, Thibaud Necciari, Diana Stoeva
Excursions in Harmonic Analysis, Volume 5: The February Fourier Talks at the Norbert Wi…
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Authors:	Peter Balazs, Nicki Holighaus, Thibaud Necciari, Diana Stoeva
Publication date:	06/21/2017
Journal:	Excursions in Harmonic Analysis, Volume 5: The February Fourier Talks at the Norbert Wiener Center
Pages:	225-268
Publisher:	Springer International Publishing
Description:	This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field.
Cited by:	56
Resources:	[PDF] from arxiv.org

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A guide to localized frames and applications to Galerkin-like representations of operators

2017

Peter Balazs, Karlheinz Gröchenig
Frames and Other Bases in Abstract and Function Spaces: Novel Methods in Harmonic Analy…
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Authors:	Peter Balazs, Karlheinz Gröchenig
Publication date:	06/12/2017
Journal:	Frames and Other Bases in Abstract and Function Spaces: Novel Methods in Harmonic Analysis, Volume 1
Pages:	47-79
Publisher:	Springer International Publishing
Description:	This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.
Cited by:	40
Resources:	[PDF] from arxiv.org

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A noniterative method for reconstruction of phase from STFT magnitude

2017

Zdeněk Průša, Peter Balazs, Peter Lempel Søndergaard
IEEE/ACM Transactions on Audio, Speech, and Language Processing 25 (5), 1154-1164
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Authors:	Zdeněk Průša, Peter Balazs, Peter Lempel Søndergaard
Publication date:	03/30/2017
Journal:	IEEE/ACM Transactions on Audio, Speech, and Language Processing
Volume:	25
Issue:	5
Pages:	1154-1164
Publisher:	IEEE
Description:	A noniterative method for the reconstruction of the short-time fourier transform (STFT) phase from the magnitude is presented. The method is based on the direct relationship between the partial derivatives of the phase and the logarithm of the magnitude of the un-sampled STFT with respect to the Gaussian window. Although the theory holds in the continuous setting only, the experiments show that the algorithm performs well even in the discretized setting (discrete Gabor transform) with low redundancy using the sampled Gaussian window, the truncated Gaussian window and even other compactly supported windows such as the Hann window. Due to the noniterative nature, the algorithm is very fast and it is suitable for long audio signals. Moreover, solutions of iterative phase reconstruction algorithms can be improved considerably by initializing them with the phase estimate provided by the present algorithm. We …
Cited by:	122
Resources:	[PDF] from ieee.org

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Discretization in generalized coorbit spaces: extensions, annotations and errata for” Continuous Frames, Function Spaces and the Discretization Problem” by M. Fornasier and H …

2017

Nicki Holighaus, Peter Balazs
arXiv preprint arXiv:1702.06485
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Authors:	Nicki Holighaus, Peter Balazs
Publication date:	02/21/2017
Journal:	arXiv preprint arXiv:1702.06485
Description:	During the process of writing the manuscript ["Continuous warped time-frequency representations - Coorbit spaces and discretization", N. Holighaus, C. Wiesmeyr and P. Balazs], the work ["Continuous Frames, Function Spaces and the Discretization Problem" by M. Fornasier and H. Rauhut - (1)] was one of the major foundations of our results and, naturally, we found ourselves going back to reading that contribution once and again. In particular in Section 5, which is concerned with the discretization problem, we have found some typographical errors, small inaccuracies and some parts that we just would have wished to be slightly more accessible. Finally, for our own theory, a generalization of a central definition required us to verify that all the derivations in Section 5 of (1) still hold after the necessary modifications. Considering the importance of the results in (1) for the community, this was reason enough to start this side project of re-writing that least accessible portion of Fornasier and Rauhut's manuscript, eliminating the errors we found, adding annotations where we consider them useful and modifying the results to take into account the generalization we require for our own work. What you see is the result of our endeavor, a one-to-one substitute for Section 5 in (1).
Cited by:	8
Resources:	[PDF] from arxiv.org

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Redundant representation of operators

2016

Peter Balazs, Georg Rieckh
arXiv preprint arXiv:1612.06130
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Authors:	Peter Balazs, Georg Rieckh
Publication date:	12/19/2016
Journal:	arXiv preprint arXiv:1612.06130
Description:	To be able to solve operator equations numerically a discretization of those operators is necessary. In the Galerkin approach bases are used to achieve discretized versions of operators. In a more general set-up, frames can be used to sample the involved signal spaces and therefore those operators. Here we look at the redundant representation of operators resulting from a matrix representation using frames. We focus on injectivity, surjectivity and, in particular, invertibility of the involved operators and matrices. Furthermore we show sufficient conditions that the composition of matrices correspond to the composition of operators.
Cited by:	9
Resources:	[PDF] from arxiv.org

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Auditory time-frequency masking for spectrally and temporally maximally-compact stimuli

2016

Thibaud Necciari, Bernhard Laback, Sophie Savel, Sølvi Ystad, Peter Balazs, Sabine Meun…
PloS one 11 (11), e0166937
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Authors:	Thibaud Necciari, Bernhard Laback, Sophie Savel, Sølvi Ystad, Peter Balazs, Sabine Meunier, Richard Kronland-Martinet
Publication date:	11/22/2016
Journal:	PloS one
Volume:	11
Issue:	11
Pages:	e0166937
Publisher:	Public Library of Science
Description:	Many audio applications perform perception-based time-frequency (TF) analysis by decomposing sounds into a set of functions with good TF localization (i.e. with a small essential support in the TF domain) using TF transforms and applying psychoacoustic models of auditory masking to the transform coefficients. To accurately predict masking interactions between coefficients, the TF properties of the model should match those of the transform. This involves having masking data for stimuli with good TF localization. However, little is known about TF masking for mathematically well-localized signals. Most existing masking studies used stimuli that are broad in time and/or frequency and few studies involved TF conditions. Consequently, the present study had two goals. The first was to collect TF masking data for well-localized stimuli in humans. Masker and target were 10-ms Gaussian-shaped sinusoids with a bandwidth of approximately one critical band. The overall pattern of results is qualitatively similar to existing data for long maskers. To facilitate implementation in audio processing algorithms, a dataset provides the measured TF masking function. The second goal was to assess the potential effect of auditory efferents on TF masking using a modeling approach. The temporal window model of masking was used to predict present and existing data in two configurations: (1) with standard model parameters (i.e. without efferents), (2) with cochlear gain reduction to simulate the activation of efferents. The ability of the model to predict the present data was quite good with the standard configuration but highly degraded with gain reduction. Conversely …
Cited by:	10
Resources:	[HTML] from plos.org

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The pole behavior of the phase derivative of the short-time Fourier transform

2016

Peter Balazs, Dominik Bayer, Florent Jaillet, Peter Søndergaard
Applied and Computational Harmonic Analysis 40 (3), 610-621
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Authors:	Peter Balazs, Dominik Bayer, Florent Jaillet, Peter Søndergaard
Publication date:	05/01/2016
Journal:	Applied and Computational Harmonic Analysis
Volume:	40
Issue:	3
Pages:	610-621
Publisher:	Academic Press
Description:	The short-time Fourier transform (STFT) is a time–frequency representation widely used in audio signal processing. Recently it has been shown that not only the amplitude, but also the phase of this representation can be successfully exploited for improved analysis and processing. In this paper we describe a rather peculiar pole phenomenon in the phase derivative, a recurring pattern that appears in a characteristic way in the neighborhood around any of the zeros of the STFT, a negative peak followed by a positive one. We describe this phenomenon numerically and provide a complete analytical explanation.
Cited by:	29
Resources:	[HTML] from sciencedirect.com

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A perceptually motivated filter bank with perfect reconstruction for audio signal processing

2016

Thibaud Necciari, Nicki Holighaus, Peter Balazs, Zdenek Prusa
arXiv preprint arXiv:1601.06652
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Authors:	Thibaud Necciari, Nicki Holighaus, Peter Balazs, Zdenek Prusa
Publication date:	01/25/2016
Journal:	arXiv preprint arXiv:1601.06652
Description:	Many audio applications rely on filter banks (FBs) to analyze, process, and re-synthesize sounds. To approximate the auditory frequency resolution in the signal chain, some applications rely on perceptually motivated FBs, the gammatone FB being a popular example. However, most perceptually motivated FBs only allow partial signal reconstruction at high redundancies and/or do not have good resistance to sub-channel processing. This paper introduces an oversampled perceptually motivated FB enabling perfect reconstruction, efficient FB design, and adaptable redundancy. The filters are directly constructed in the frequency domain and linearly distributed on a perceptual frequency scale (e.g. ERB, Bark, or Mel scale). The proposed design allows for various filter shapes, uniform or non-uniform FB setting, and large down-sampling factors. For redundancies 3 perfect reconstruction is achieved by computing the canonical dual FB analytically. For lower redundancies perfect reconstruction is achieved using an iterative method. Experiments show performance improvements of the proposed approach when compared to the gammatone FB in terms of reconstruction error and resistance to sub-channel processing, especially at low redundancies.
Cited by:	3
Resources:	[PDF] from arxiv.org

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Audio inpainting with similarity graphs

2016

Nathanael Perraudin, Nicki Holighaus, Piotr Majdak, Peter Balazs
CoRR
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Authors:	Nathanael Perraudin, Nicki Holighaus, Piotr Majdak, Peter Balazs
Publication date:	01/01/2016
Journal:	CoRR
Description:	In this contribution, we present a method to compensate for long duration data gaps in audio signals, in particular music. To achieve this task, a similarity graph is constructed, based on a short-time Fourier analysis of reliable signal segments, eg the uncorrupted remainder of the music piece, and the temporal regions adjacent to the unreliable section of the signal. A suitable candidate segment is then selected through an optimization scheme and smoothly inserted into the gap.
Resources:	[PDF] from epfl.ch

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On the dual frame induced by an invertible frame multiplier

2016

Diana T Stoeva, Peter Balazs
Sampling Theory in Signal and Image Processing 15 (1), 119-130
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Authors:	Diana T Stoeva, Peter Balazs
Publication date:	01/01/2016
Journal:	Sampling Theory in Signal and Image Processing
Volume:	15
Issue:	1
Pages:	119-130
Publisher:	Springer International Publishing
Description:	Recently it has been established that given an invertible frame multiplier with semi-normalized symbol, a specific dual of any of the two involved frames can be determined by the inversion process. The inverse can be represented as a multiplier with the reciprocal symbol, this particular dual of one of the given frames, and any dual of the other frame. The specific dual is the only one having this property among all Bessel sequences. In this manuscript we extend the results showing that the specific dual with the above mentioned property is unique among all possible sequences. Furthermore, the symbol is allowed to be not necessarily semi-normalized. Finally we characterize cases when the canonical dual frame and the new specific dual frame coincide.
Cited by:	19
Resources:	[PDF] from arxiv.org

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Discrete coherent states for higher Landau levels

2015

LD Abreu, P Balazs, M De Gosson, Z Mouayn
Annals of Physics 363, 337-353
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Authors:	LD Abreu, P Balazs, M De Gosson, Z Mouayn
Publication date:	12/01/2015
Journal:	Annals of Physics
Volume:	363
Pages:	337-353
Publisher:	Academic Press
Description:	We consider the quantum dynamics of a charged particle evolving under the action of a constant homogeneous magnetic field, with emphasis on the discrete subgroups of the Heisenberg group (in the Euclidean case) and of the S L (2, R) group (in the Hyperbolic case). We investigate completeness properties of discrete coherent states associated with higher order Euclidean and hyperbolic Landau levels, partially extending classic results of Perelomov and of Bargmann, Butera, Girardello and Klauder. In the Euclidean case, our results follow from identifying the completeness problem with known results from the theory of Gabor frames. The results for the hyperbolic setting follow by using a combination of methods from coherent states, time-scale analysis and the theory of Fuchsian groups and their associated automorphic forms.
Cited by:	63
Resources:	[HTML] from sciencedirect.com

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Changes in smoking-related health knowledge and smoking status of Hungarian adolescents

2015

Melinda Pénzes, Péter Balázs, Kristie L Foley
New Medicine
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Authors:	Melinda Pénzes, Péter Balázs, Kristie L Foley
Publication date:	11/23/2015
Journal:	New Medicine
Description:	Introduction. School-based anti-smoking programs often educate adolescents about the adverse health effects of smoking to enable them to make informed decisions about smoking. Aim. Our study aimed to assess changes in smoking-related health knowledge and smoking status in two cohorts of adolescents. Material and methods. A three-year prospective survey (from 2010 to 2012) with annual data collection was conducted in Hungary’s six metropolitan cities among randomly selected elementary (younger cohort) and secondary school (older cohort) students (N= 1,092; 54% females). Measures included a 14-item scale for smoking-related health knowledge and variables to assess demographics and self-reported smoking status. Results. The prevalence of past month smoking increased by 8.8% in the younger cohort (p< 0.001) and 11.0% in the older cohort (p< 0.001). Throughout the study, 69.4% of the sample remained non-smoker, 12.8% remained smoker, 13.9% initiated smoking and 3.8% quit smoking. Smoking-related health knowledge changed significantly during three years with inconsistent positive and negative changes. Overall knowledge increased at a higher rate among students in the younger cohort. Those initiating smoking showed the lowest level of knowledge at the last wave of data collection. Conclusions. To reduce smoking initiation and to promote quitting, comprehensive prevention strategies should be conducted, such as school-based programs that incorporate skill-building (not exclusively health education) and peer-focused anti-smoking programs.
Cited by:	2
Resources:	[HTML] from czytelniamedyczna.pl

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Reproducing pairs and the continuous nonstationary Gabor transform on LCA groups

2015

Michael Speckbacher, Peter Balazs
Journal of Physics A: Mathematical and Theoretical 48 (39), 395201
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Authors:	Michael Speckbacher, Peter Balazs
Publication date:	09/01/2015
Journal:	Journal of Physics A: Mathematical and Theoretical
Volume:	48
Issue:	39
Pages:	395201
Publisher:	IOP Publishing
Description:	In this paper we introduce and investigate the concept of reproducing pairs as a generalization of continuous frames. Reproducing pairs yield a bounded analysis and synthesis process while the frame condition can be omitted at both stages. Moreover, we will investigate certain continuous frames (resp. reproducing pairs) on LCA groups, which can be described as a continuous version of nonstationary Gabor systems and state sufficient conditions for these systems to form a continuous frame (resp. reproducing pair). As a byproduct we identify the structure of the frame operator (resp. resolution operator). We will apply our results to systems generated by a unitary action of a subset of the affine Weyl–Heisenberg group in
Cited by:	33
Resources:	[PDF] from iop.org

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A quasi-orthogonal, invertible, and perceptually relevant time-frequency transform for audio coding

2015

Olivier Derrien, Thibaud Necciarf, Peter Balazs
2015 23rd European Signal Processing Conference (EUSIPCO), 799-803
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Authors:	Olivier Derrien, Thibaud Necciarf, Peter Balazs
Publication date:	08/31/2015
Journal:	2015 23rd European Signal Processing Conference (EUSIPCO)
Pages:	799-803
Publisher:	IEEE
Description:	We describe ERB-MDCT, an invertible real-valued time-frequency transform based on MDCT, which is widely used in audio coding (e.g. MP3 and AAC). ERB-MDCT was designed similarly to ERBLet, a recent invertible transform with a resolution evolving across frequency to match the perceptual ERB frequency scale, while the frequency scale in most invertible transforms (e.g. MDCT) is uniform. ERB-MDCT has mostly the same frequency scale as ERBLet, but the main improvement is that atoms are quasi-orthogonal, i.e. its redundancy is close to 1. Furthermore, the energy is more sparse in the time-frequency plane. Thus, it is more suitable for audio coding than ERBLet.
Cited by:	11
Resources:	[PDF] from hal.science

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Time-frequency representations for nonlinear frequency scales—Coorbit spaces and discretization

2015

Nicki Holighaus, Peter Balazs, Christoph Wiesmeyr
2015 International Conference on Sampling Theory and Applications (SampTA), 129-133
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Authors:	Nicki Holighaus, Peter Balazs, Christoph Wiesmeyr
Publication date:	05/25/2015
Journal:	2015 International Conference on Sampling Theory and Applications (SampTA)
Pages:	129-133
Publisher:	IEEE
Description:	The fixed time-frequency resolution of the short-time Fourier transform has often been considered a major drawback. In this contribution we review recent results on a class of time-frequency transforms that adapt to a large class of frequency scales in the same sense that wavelet transforms are adapted to a logarithmic scale. In particular, we show that each transform in this class of warped time-frequency representations is a tight continuous frame satisfying orthogonality relations similar to Moyal's formula. Moreover, they satisfy the prerequisites of generalized coorbit theory, giving rise to coorbit spaces and associated discrete representations, i.e. atomic decompositions and Banach frames.
Resources:	[PDF] from archive.org

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Construction of warped time-frequency representations on nonuniform frequency scales, Part II: Integral transforms, Function spaces, Atomic decompositions and Banach frames

2015

NICKI Holighaus, CHRISTOPH Wiesmeyr, PETER Balazs
arXiv preprint arXiv:1503.05439
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Authors:	NICKI Holighaus, CHRISTOPH Wiesmeyr, PETER Balazs
Publication date:	03/01/2015
Journal:	arXiv preprint arXiv:1503.05439
Description:	We present a novel family of continuous linear time-frequency transforms adapted to a multitude of (nonlinear) frequency scales. Similar to classical time-frequency or timescale representations, the representation coefficients are obtained as inner products with the elements of a continuously indexed family of time-frequency atoms. These atoms are obtained from a single prototype function, by means of modulation, translation and warping. By warping we refer to the process of nonlinear evaluation according to a bijective, increasing function, the warping function. While particular choices of warping functions allow for recovery of classical time-frequency representations, eg F (t)= ct provides the short-time Fourier transform and F (t)= loga (t) provides wavelet transforms, the proposed method allows for far greater flexibility. This is illustrated by a number of examples provided in the manuscript. Besides showing that the resulting integral transforms fulfill certain basic, but essential properties, such as continuity and invertibility, we will show that a large subclass of warping functions gives rise to families of generalized coorbit spaces, ie Banach spaces of functions whose representations possess a certain localization. Furthermore, we obtain sufficient conditions for subsampled warped time-frequency systems to form atomic decompositions and Banach frames. To this end, we extend results previously presented by Fornasier and Rauhut [34] to a larger class of function systems via a simple, but crucial modification.
Cited by:	6
Resources:	[PDF] from researchgate.net

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Representation of the inverse of a frame multiplier

2015

Peter Balazs, Diana T Stoeva
Journal of Mathematical Analysis and Applications 422 (2), 981-994
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Authors:	Peter Balazs, Diana T Stoeva
Publication date:	02/15/2015
Journal:	Journal of Mathematical Analysis and Applications
Volume:	422
Issue:	2
Pages:	981-994
Publisher:	Academic Press
Description:	Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and, naturally, mathematics. In a general setting they can be described as frame multipliers, consisting of analysis, multiplication by a fixed sequence (called the symbol), and synthesis. In this paper we show a surprising result about the inverse of such operators, if any, as well as new results about a core concept of frame theory, dual frames. We show that for semi-normalized symbols, the inverse of any invertible frame multiplier can always be represented as a frame multiplier with the reciprocal symbol and dual frames of the given ones. Furthermore, one of those dual frames is uniquely determined and the other one can be arbitrarily chosen. We investigate sufficient conditions for the special case, when both dual frames can be chosen to be the canonical duals. In connection to the above, we show that the set of …
Cited by:	60
Resources:	[HTML] from sciencedirect.com

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Admissibility for -Modulation Spaces

2014

Peter Balazs, Dominik Bayer, Michael Speckbacher
arXiv preprint arXiv:1408.4971
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Authors:	Peter Balazs, Dominik Bayer, Michael Speckbacher
Publication date:	08/21/2014
Journal:	arXiv preprint arXiv:1408.4971
Description:	This paper is concerned with frame decompositions of -modulation spaces. These spaces can be obtained as coorbit spaces for square-integrable representations of the affine Weyl-Heisenberg group modulo suitable subgroups. The theory yields canonical constructions for Banach frames or atomic decompositions in -modulation spaces. A necessary ingredient in this abstract machinery is the existence of generating functions that are admissible for the representation. For numerical purposes, admissible atoms with compact support are necessary. We show new admissibility conditions that considerably improve upon known results. In particular, we prove the existence of admissible vectors that have compact support in time domain.
Resources:	[PDF] from arxiv.org

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The continuous nonstationary Gabor transform on LCA groups with applications to representations of the affine Weyl-Heisenberg group

2014

Michael Speckbacher, Peter Balazs
arXiv preprint arXiv:1407.6830
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Authors:	Michael Speckbacher, Peter Balazs
Publication date:	07/25/2014
Journal:	arXiv preprint arXiv:1407.6830
Description:	In this paper we introduce and investigate the concept of reproducing pairs which generalizes continuous frames. We will introduce a concept that represents a unifying way to look at certain continuous frames (resp. reproducing pairs) on LCA groups, which can be described as continuous nonstationary Gabor systems and investigate conditions for these systems to form a continuous frame (resp. reproducing pair). As a byproduct we identify the structure of the frame operator (resp. resolution operator). Moreover, we ask the question, whether there always exist mutually dual systems with the same structure such that the resolution operator is given by the identity, i.e. given , if there exist , s.t. begin{equation} f=int_X langle f,A(x)psirangle A(x)varphi dmu(x), forall fin mathcal{H} end{equation} and show that the answer is not affirmative. As a counterexample we use a system generated by a unitary action of a subset of the affine Weyl-Heisenberg group in .
Cited by:	3
Resources:	[PDF] from arxiv.org

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Perceptual matching pursuit with Gabor dictionaries and time-frequency masking

2014

Gilles Chardon, Thibaud Necciari, Peter Balazs
2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),…
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Authors:	Gilles Chardon, Thibaud Necciari, Peter Balazs
Publication date:	05/04/2014
Journal:	2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Pages:	3102-3106
Publisher:	IEEE
Description:	This paper describes a method to obtain a perceptually relevant sparse representation of a sound signal. Based on matching pursuit (MP) and recent psychoacoustic data on time-frequency masking measured with Gabor atoms, a perceptual matching pursuit (PMP) algorithm is proposed. To obtain a good match between the masking model and the signal representation, a dictionary of Gabor atoms with variable sizes is chosen for MP. In the proposed method, the signal is first decomposed using MP and the masking model is applied on the resulting set of atoms. This allows for isolating the masked components from the residual. Experimental results show that exploiting time-frequency masking allows to remove more atoms than using only spectral masking. Additionally, accounting for masking effects between atoms of different sizes and at different times allows for sparser representations. The objective evaluation …
Cited by:	27
Resources:	[PDF] from academia.edu

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Designing gabor windows using convex optimization

2014

Nathanaël Perraudin, Nicki Holighaus, Peter L Søndergaard, Peter Balazs
arXiv preprint arXiv:1401.6033
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Authors:	Nathanaël Perraudin, Nicki Holighaus, Peter L Søndergaard, Peter Balazs
Publication date:	01/23/2014
Journal:	arXiv preprint arXiv:1401.6033
Description:	Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g. good time-frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler-Raz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found.
Cited by:	12
Resources:	[PDF] from arxiv.org

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A fast Griffin-Lim algorithm

2013

Nathanaël Perraudin, Peter Balazs, Peter L Søndergaard
2013 IEEE workshop on applications of signal processing to audio and acoustics, 1-4
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Authors:	Nathanaël Perraudin, Peter Balazs, Peter L Søndergaard
Publication date:	10/20/2013
Journal:	2013 IEEE workshop on applications of signal processing to audio and acoustics
Pages:	1-4
Publisher:	IEEE
Description:	In this paper, we present a new algorithm to estimate a signal from its short-time Fourier transform modulus (STFTM). This algorithm is computationally simple and is obtained by an acceleration of the well-known Griffin-Lim algorithm (GLA). Before deriving the algorithm, we will give a new interpretation of the GLA and formulate the phase recovery problem in an optimization form. We then present some experimental results where the new algorithm is tested on various signals. It shows not only significant improvement in speed of convergence but it does as well recover the signals with a smaller error than the traditional GLA.
Cited by:	251
Resources:	[PDF] from github.io

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Adapted and adaptive linear time-frequency representations: a synthesis point of view

2013

Peter Balazs, Monika Dörfler, Matthieu Kowalski, Bruno Torrésani
IEEE Signal Processing Magazine 30 (6), 20-31
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Authors:	Peter Balazs, Monika Dörfler, Matthieu Kowalski, Bruno Torrésani
Publication date:	10/16/2013
Journal:	IEEE Signal Processing Magazine
Volume:	30
Issue:	6
Pages:	20-31
Publisher:	IEEE
Description:	A large variety of techniques exist to display the time and frequency content of a given signal. In this article, we give an overview of linear time-frequency representations, focusing mainly on two fundamental aspects. The first is the introduction of flexibility, more precisely, the construction of time-frequency waveform systems that can be adapted to specific signals or specific signal processing problems. To do this, we base the constructions on frame theory, which allows many options while still ensuring perfect reconstruction. The second aspect is the choice of the synthesis framework rather than the usual analysis framework. Instead of considering the correlation, i.e. the inner product, of the signal with the chosen waveforms, we find appropriate coefficients in a linear combination of those waveforms to synthesize the given signal. We show how this point of view allows the easy introduction of prior information into the …
Cited by:	58
Resources:	[PDF] from hal.science

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The large time-frequency analysis toolbox 2.0

2013

Zdeněk Průša, Peter L Søndergaard, Nicki Holighaus, Christoph Wiesmeyr, Peter Balazs
International Symposium on Computer Music Multidisciplinary Research, 419-442
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Authors:	Zdeněk Průša, Peter L Søndergaard, Nicki Holighaus, Christoph Wiesmeyr, Peter Balazs
Publication date:	10/15/2013
Journal:	International Symposium on Computer Music Multidisciplinary Research
Pages:	419-442
Publisher:	Springer International Publishing
Description:	The Large Time Frequency Analysis Toolbox (LTFAT) is a modern Octave/Matlab toolbox for time-frequency analysis, synthesis, coefficient manipulation and visualization. It’s purpose is to serve as a tool for achieving new scientific developments as well as an educational tool. The present paper introduces main features of the second major release of the toolbox which includes: generalizations of the Gabor transform, the wavelets module, the frames framework and the real-time block processing framework.
Cited by:	159
Resources:	[PDF] from ltfat.org

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Riesz bases multipliers

2013

Diana T Stoeva, Peter Balazs
Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation: …
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Authors:	Diana T Stoeva, Peter Balazs
Publication date:	10/11/2013
Journal:	Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011
Pages:	475-482
Publisher:	Springer Basel
Description:	The paper concerns frame multipliers when one of the involved sequences is a Riesz basis. We determine the cases when the multiplier is well defined and invertible, well defined and not invertible, respectively not well defined.
Cited by:	20

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LTFAT: A Matlab/Octave toolbox for sound processing

2013

Zdenek Pruša, P Søndergaard, Peter Balazs, Nicki Holighaus
Proc. 10th International Symposium on Computer Music Multidisciplinary Research (CMMR),…
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Authors:	Zdenek Pruša, P Søndergaard, Peter Balazs, Nicki Holighaus
Publication date:	10/01/2013
Journal:	Proc. 10th International Symposium on Computer Music Multidisciplinary Research (CMMR)
Pages:	299-314
Description:	To visualize and manipulate musical signals time-frequency transforms have been used extensively. The Large Time Frequency Analysis Toolbox is an Octave/Matlab toolbox for modern signal analysis and synthesis. The toolbox provides a large variety of linear and invertible time-frequency transforms like Gabor, MDCT, constant-Q, filterbanks and wavelets transforms, and routines for modifying musical signal by manipulating coefficients by linear and non-linear methods. Combined with this the toolbox also supplies a framework for real-time processing of sound signals. It also provides demo scripts devoted either to demonstrating the main functions of the toolbox, or to exemplify their use in specific signal processing applications.
Cited by:	13
Resources:	[PDF] from ltfat.org

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Simultaneous masking additivity for short Gaussian-shaped tones: Spectral effects

2013

Bernhard Laback, Thibaud Necciari, Peter Balazs, Sophie Savel, Sølvi Ystad
The Journal of the Acoustical Society of America 134 (2), 1160-1171
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Authors:	Bernhard Laback, Thibaud Necciari, Peter Balazs, Sophie Savel, Sølvi Ystad
Publication date:	08/01/2013
Journal:	The Journal of the Acoustical Society of America
Volume:	134
Issue:	2
Pages:	1160-1171
Publisher:	AIP Publishing
Description:	Laback et al.[(2011). J. Acoust. Soc. Am. 129, 888− 897] investigated the additivity of nonsimultaneous masking using short Gaussian-shaped tones as maskers and target. The present study involved Gaussian stimuli to measure the additivity of simultaneous masking for combinations of up to four spectrally separated maskers. According to most basilar membrane measurements, the maskers should be processed linearly at the characteristic frequency (CF) of the target. Assuming also compression of the target, all masker combinations should produce excess masking (exceeding linear additivity). The results for a pair of maskers flanking the target indeed showed excess masking. The amount of excess masking could be predicted by a model assuming summation of masker-evoked excitations in intensity units at the target CF and compression of the target, using compressive input/output functions derived from the …
Cited by:	6
Resources:	[HTML] from aip.org

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The ERBlet transform: An auditory-based time-frequency representation with perfect reconstruction

2013

Thibaud Necciari, Peter Balazs, Nicki Holighaus, Peter L Søndergaard
2013 IEEE International Conference on Acoustics, Speech and Signal Processing, 498-502
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Authors:	Thibaud Necciari, Peter Balazs, Nicki Holighaus, Peter L Søndergaard
Publication date:	05/26/2013
Journal:	2013 IEEE International Conference on Acoustics, Speech and Signal Processing
Pages:	498-502
Publisher:	IEEE
Description:	This paper describes a method for obtaining a perceptually motivated and perfectly invertible time-frequency representation of a sound signal. Based on frame theory and the recent non-stationary Gabor transform, a linear representation with resolution evolving across frequency is formulated and implemented as a non-uniform filterbank. To match the human auditory time-frequency resolution, the transform uses Gaussian windows equidistantly spaced on the psychoacoustic “ERB” frequency scale. Additionally, the transform features adaptable resolution and redundancy. Simulations showed that perfect reconstruction can be achieved using fast iterative methods and preconditioning even using one filter per ERB and a very low redundancy (1.08). Comparison with a linear gammatone filterbank showed that the ERBlet approximates well the auditory time-frequency resolution.
Cited by:	75
Resources:	[PDF] from google.com

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Detailed characterization of conditions for the unconditional convergence and invertibility of multipliers

2013

Diana T Stoeva, Peter Balazs
Sampling Theory in Signal and Image Processing 12 (2), 87-125
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Authors:	Diana T Stoeva, Peter Balazs
Publication date:	05/01/2013
Journal:	Sampling Theory in Signal and Image Processing
Volume:	12
Issue:	2
Pages:	87-125
Publisher:	Springer International Publishing
Description:	In this paper we investigate the unconditional convergence and invertibility of multipliers Mm,Φ,Ψ depending on the properties of the sequences Ψ, Φ and m. We determine if unconditional convergence and invertibility is always, sometimes or never possible for the complete set of possibilities for the sequences Φ and Ψ: non-Bessel sequences, Bessel non-frames, frames non-Riesz bases, Riesz bases, combined with all the possibilities for norm-boundedness; and varying the weighting sequence m to be semi-normalized, bounded or non-bounded. The results are collected in tables as a convenient reference.
Cited by:	32
Resources:	[PDF] from arxiv.org

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Canonical forms of unconditionally convergent multipliers

2013

Diana T Stoeva, Peter Balazs
Journal of Mathematical Analysis and Applications 399 (1), 252-259
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Authors:	Diana T Stoeva, Peter Balazs
Publication date:	03/01/2013
Journal:	Journal of Mathematical Analysis and Applications
Volume:	399
Issue:	1
Pages:	252-259
Publisher:	Academic Press
Description:	Multipliers are operators that combine (frame-like) analysis, a multiplication with a fixed sequence, called the symbol, and synthesis. They are very interesting mathematical objects that also have a lot of applications for example in acoustical signal processing. It is known that bounded symbols and Bessel sequences guarantee unconditional convergence. In this paper we investigate necessary and equivalent conditions for the unconditional convergence of multipliers. In particular, we show that, under mild conditions, unconditionally convergent multipliers can be transformed by shifting weights between symbol and sequence, into multipliers with symbol (1) and Bessel sequences (called multipliers in canonical form).
Cited by:	52
Resources:	[HTML] from sciencedirect.com

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Gabor dual windows using convex optimization

2013

Nathanaël Perraudin, Nicki Holighaus, P Soendergaard, Peter Balazs
Proceeedings of the 10th International Conference on Sampling theory and Applications (…
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Authors:	Nathanaël Perraudin, Nicki Holighaus, P Soendergaard, Peter Balazs
Publication date:	01/01/2013
Journal:	Proceeedings of the 10th International Conference on Sampling theory and Applications (SAMPTA 2013)
Description:	Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, such as good time-frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler-Raz equations and optimizing various constraints. Numerical experiments show that alternate dual windows with considerably improved features can be found.
Cited by:	11
Resources:	[PDF] from eurasip.org

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The ERBlet transform, time-frequency masking and perceptual sparsity

2012

Thibaud Necciari, Peter Balazs, Bernhard Laback, Peter L Soendergaard, Richard Kronland…
2nd Workshop of the Signal Processing Lab of Brno University of Technology
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Authors:	Thibaud Necciari, Peter Balazs, Bernhard Laback, Peter L Soendergaard, Richard Kronland-Martinet, Sabine Meunier, Sophie Savel, Sølvi Ystad
Publication date:	10/24/2012
Journal:	2nd Workshop of the Signal Processing Lab of Brno University of Technology
Description:	The ERBlet transform, time-frequency masking and perceptual sparsity - Archive ouverte HAL Recherche Accéder directement au contenu Pied de page Logo Logo Documentation FR Français (FR) Anglais (EN) Se connecter HAL science ouverte Recherche Loading... Recherche avancée Information de documents Titres Titres Sous-titre Titre de l'ouvrage Titre du volume (Série) Champ de recherche par défaut (multicritères) + texte intégral des PDF Résumé Texte intégral indexé des documents PDF Mots-clés Type de document Sous-type de document Tous les identifiants du document Identifiant HAL du dépôt Langue du document (texte) Pays (Texte) Ville À paraître (true ou false) Ajouter Auteur Auteur (multicritères) Auteur (multicritères) Auteur : Nom complet Auteur : Nom de famille Auteur : Prénom Auteur : Complément de nom, deuxième prénom Auteur : Organisme payeur Auteur : IdHal (chaîne de caractères) …

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Frames, semi-frames, and Hilbert scales

2012

J-P Antoine, Peter Balazs
Numerical functional analysis and optimization 33 (7-9), 736-769
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Authors:	J-P Antoine, Peter Balazs
Publication date:	07/01/2012
Journal:	Numerical functional analysis and optimization
Volume:	33
Issue:	7-9
Pages:	736-769
Publisher:	Taylor & Francis Group
Description:	Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded but has an unbounded inverse, whereas a lower semi-frame has an unbounded frame operator with bounded inverse. For upper semi-frames, in the discrete and the continuous case, we build two natural Hilbert scales which may yield a novel characterization of certain function spaces of interest in signal processing. We present some examples and, in addition, some results concerning the duality between lower and upper semi-frames, as well as some generalizations, including fusion semi-frames and Banach semi-frames.
Cited by:	39
Resources:	[PDF] from arxiv.org

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A 2.5 D-Fourier-BEM model for vibrations in a tunnel running through layered anisotropic soil

2012

Georg Rieckh, Wolfgang Kreuzer, Holger Waubke, Peter Balazs
Engineering Analysis with Boundary Elements 36 (6), 960-967
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Authors:	Georg Rieckh, Wolfgang Kreuzer, Holger Waubke, Peter Balazs
Publication date:	06/01/2012
Journal:	Engineering Analysis with Boundary Elements
Volume:	36
Issue:	6
Pages:	960-967
Publisher:	Elsevier
Description:	A boundary element model of a tunnel running through horizontally layered soil with anisotropic material properties is presented. Since there is no analytical fundamental solution for wave propagation inside a layered orthotropic medium in 3D, the fundamental displacements and stresses have to be calculated numerically. In our model this is done in the Fourier domain with respect to space and time. The assumption of a straight tunnel with infinite extension in the x direction makes it possible to decouple the system for every wave number kx, leading to a 2.5D-problem, which is suited for parallel computation. The special form of the fundamental solution, resulting from our Fourier ansatz, and the fact, that the calculation of the boundary integral equation is performed in the Fourier domain, enhances the stability and efficiency of the numerical calculations.
Cited by:	44
Resources:	[PDF] from academia.edu

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Multipliers for continuous frames in Hilbert spaces

2012

Peter Balazs, Dominik Bayer, Asghar Rahimi
Journal of Physics A: Mathematical and Theoretical 45 (24), 244023
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Authors:	Peter Balazs, Dominik Bayer, Asghar Rahimi
Publication date:	05/30/2012
Journal:	Journal of Physics A: Mathematical and Theoretical
Volume:	45
Issue:	24
Pages:	244023
Publisher:	IOP Publishing
Description:	In this paper, we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include anti-Wick operators, STFT multipliers or Calderón–Toeplitz operators. Due to the possible peculiarities of the underlying measure spaces, continuous frames do not behave quite as their discrete counterparts. Nonetheless, many results similar to the discrete case are proven for continuous frame multipliers as well, for instance compactness and Schatten-class properties. Furthermore, the concepts of controlled and weighted frames are transferred to the continuous setting.
Cited by:	115
Resources:	[PDF] from arxiv.org

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Perceptual optimization of audio representations based on time-frequency masking data for maximally-compact stimuli

2012

Thibaud Necciari, Peter Balazs, Richard Kronland-Martinet, Sølvi Ystad, Bernhard Laback…
Proceedings of the 45th AES conference on Applications of Time-Frequency Processing in …
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Authors:	Thibaud Necciari, Peter Balazs, Richard Kronland-Martinet, Sølvi Ystad, Bernhard Laback, Sophie Savel, Sabine Meunier
Publication date:	03/01/2012
Journal:	Proceedings of the 45th AES conference on Applications of Time-Frequency Processing in Audio. Helsinki, Finland
Pages:	103-112
Description:	Many audio applications use time-frequency representations such as the Gabor and wavelet transforms. For such applications, it is often required that the signal representation matches human auditory perception and allows reconstruction. On that purpose, this paper presents the results of psychoacoustical experiment on auditory time-frequency masking using stimuli with maximal concentration in the time-frequency plane. These new data constitute a crucial basis for the prediction of auditory masking in the time-frequency representations of sound signals. An algorithm that removes the inaudible components in the wavelet transform of a sound while causing no audible difference to the original sound after re-synthesis is proposed. Preliminary results are promising, although further development is required.
Cited by:	4
Resources:	[PDF] from researchgate.net

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www. elsevier. com/locate/acha

2012

Akram Aldroubi, Amir Averbuch, Waheed U Bajwa, P Balazs, Doru C Balcan, Richard G Baran…
Appl. Comput. Harmon. Anal 33, 473
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Authors:	Akram Aldroubi, Amir Averbuch, Waheed U Bajwa, P Balazs, Doru C Balcan, Richard G Baraniuk, Gregory Beylkin, Robert Calderbank, Marie-Line Chabanol, Xuemei Chen, Ole Christensen, Charles K Chui, Ronald R Coifman, Mark A Davenport, Gil David, Maarten V de Hoop, Charles Dossal, YC Eldar, Jalal Fadili, George Fann, Matthew Fickus, Matan Gavish, Say Song Goh, Maxim J Goldberg, P Grohs, Bin Han, Robert J Harrison, Sean F Holman, Seonja Kim, Wai Yip Kong, Jelena Kovacevic, Christopher Kurcz, Triet Le, Kangwei Li, Arian Maleki, Facundo Mémoli, Dustin G Mixon, Lucas Monzón, Manjari Narayan, D Needell, Gabriel Peyré, Y Plan, Alexander M Powell, DW Pravica, N Randriampiry, Vladimir Rokhlin, Aviv Rotbart, Moshe Salhov, Hart F Smith, MJ Spurr, Gowri Srinivasa, DT Stoeva, Wenchang Sun, Gunther Uhlmann, Michael B Wakin, Guy Wolf, Haizhao Yang, Lexing Ying, Xiaosheng Zhuang
Publication date:	01/01/2012
Journal:	Appl. Comput. Harmon. Anal
Volume:	33
Pages:	473

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Invertibility of multipliers

2011

DT Stoeva, P Balazs
Applied and Computational Harmonic Analysis
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Authors:	DT Stoeva, P Balazs
Publication date:	11/06/2011
Journal:	Applied and Computational Harmonic Analysis
Publisher:	Academic Press
Description:	In the present paper the invertibility of multipliers is investigated in detail. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or necessary conditions for invertibility are determined depending on the properties of the analysis and synthesis sequences, as well as the symbol. Examples are given, showing that the established bounds are sharp. If a multiplier is invertible, a formula for the inverse operator is determined and n-term error bounds are given. The case when one of the sequences is a Riesz basis is completely characterized.
Cited by:	99
Resources:	[HTML] from sciencedirect.com

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Theory, implementation and applications of nonstationary Gabor frames

2011

Peter Balazs, Monika Dörfler, Florent Jaillet, Nicki Holighaus, Gino Velasco
Journal of computational and applied mathematics 236 (6), 1481-1496
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Authors:	Peter Balazs, Monika Dörfler, Florent Jaillet, Nicki Holighaus, Gino Velasco
Publication date:	10/15/2011
Journal:	Journal of computational and applied mathematics
Volume:	236
Issue:	6
Pages:	1481-1496
Publisher:	North-Holland
Description:	Signal analysis with classical Gabor frames leads to a fixed time–frequency resolution over the whole time–frequency plane. To overcome the limitations imposed by this rigidity, we propose an extension of Gabor theory that leads to the construction of frames with time–frequency resolution changing over time or frequency. We describe the construction of the resulting nonstationary Gabor frames and give the explicit formula for the canonical dual frame for a particular case, the painless case. We show that wavelet transforms, constant-Q transforms and more general filter banks may be modeled in the framework of nonstationary Gabor frames. Further, we present the results in the finite-dimensional case, which provides a method for implementing the above-mentioned transforms with perfect reconstruction. Finally, we elaborate on two applications of nonstationary Gabor frames in audio signal processing, namely a …
Cited by:	199
Resources:	[HTML] from sciencedirect.com

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Sound analysis and synthesis adaptive in time and two frequency bands

2011

Marco Liuni, Peter Balazs, Axel Röbel
arXiv preprint arXiv:1109.6651
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Authors:	Marco Liuni, Peter Balazs, Axel Röbel
Publication date:	09/29/2011
Journal:	arXiv preprint arXiv:1109.6651
Description:	We present an algorithm for sound analysis and resynthesis with local automatic adaptation of time-frequency resolution. There exists several algorithms allowing to adapt the analysis window depending on its time or frequency location; in what follows we propose a method which select the optimal resolution depending on both time and frequency. We consider an approach that we denote as analysis-weighting, from the point of view of Gabor frame theory. We analyze in particular the case of different adaptive time-varying resolutions within two complementary frequency bands; this is a typical case where perfect signal reconstruction cannot in general be achieved with fast algorithms, causing a certain error to be minimized. We provide examples of adaptive analyses of a music sound, and outline several possibilities that this work opens.
Cited by:	7
Resources:	[PDF] from arxiv.org

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Representation of the inverse of a multiplier as a multiplier

2011

Peter Balazs, Diana T Stoeva
arXiv preprint arXiv:1108.6286
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Authors:	Peter Balazs, Diana T Stoeva
Publication date:	08/01/2011
Journal:	arXiv preprint arXiv:1108.6286
Description:	Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and certainly mathematics. In a general setting they can be described as frame multipliers, consisting of analysis, multiplication by a fixed sequence (called the symbol), and synthesis. They are not only interesting mathematical objects, but also important for applications, for example for the realization of time-varying filters. In this paper we show a surprising result about the inverse of such operators, if existing, as well as new results about a core concept of frame theory, dual frames. We show that for semi-normalized symbols, the inverse of any invertible frame multiplier can be represented as a frame multiplier with dual frames and reciprocal symbol. Furthermore, one of those dual frames is uniquely defined and the other one is an arbitrary dual frame. We investigate sufficient conditions for the special case, when those dual frames can be chosen to be the canonical duals. In connection to the above, we show that the set of dual frames determines a frame uniquely. Finally, we investigate invertible Gabor multipliers; we show that the inverse of every invertible lattice-invariant operator (in particular, every invertible Gabor frame multiplier with a constant symbol (1)) can be represented as a Gabor frame multiplier with a constant symbol (1).

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A 3D model to simulate vibrations in a layered medium with stochastic material parameters

2011

W Kreuzer, H Waubke, G Rieckh, P Balazs
Journal of Computational Acoustics 19 (02), 139-154
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Authors:	W Kreuzer, H Waubke, G Rieckh, P Balazs
Publication date:	06/01/2011
Journal:	Journal of Computational Acoustics
Volume:	19
Issue:	02
Pages:	139-154
Publisher:	IMACS
Description:	A major problem for the simulation of the propagation of vibrations in ground layers is the fact that it is almost impossible to determine the material parameters needed for a numerical model exactly. In this work, we present a 3D model for layered soil, where in each layer the shear modulus is modeled as a stochastic process. Using the Karhunen Loeve expansion, the polynomial chaos expansion, and the Fourier transform, the stochastic system can be transformed into a linear system of equations in the wavenumber frequency domain. Unfortunately, the size of this system becomes very large and — contrary to a deterministic system — the stochastic system can no longer be decoupled for every wavenumber in the spatial Fourier domain. To solve this system efficiently, we propose an iteration procedure where the system is split into a deterministic and a stochastic part. As an external load on top of the ground, we …
Cited by:	4
Resources:	[PDF] from researchgate.net

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A logarithmic based pole-zero vocal tract model estimation for speaker verification

2011

Ewald Enzinger, Peter Balazs, Damián Marelli, Timo Becker
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),…
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Authors:	Ewald Enzinger, Peter Balazs, Damián Marelli, Timo Becker
Publication date:	05/22/2011
Journal:	2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Pages:	4820-4823
Publisher:	IEEE
Description:	In this paper we investigate the use of formant and anti formant measurements of nasal consonants for speaker verification. The features are obtained using a pole-zero vocal tract model estimate optimized by minimizing a logarithmic criterion which is motivated by the perception of amplitude by the human auditory system. A GMM-UBM approach is used for performing speaker comparisons within the likelihood-ratio framework. Results are compared with systems based on Mel Frequency Cepstral Coefficients (MFCCs) as well as formant center frequencies and bandwidths obtained using the Snack Toolkit. The formant and anti-formant based system attains comparable results to the MFCC system and outperforms the formant-based approach while offering a more straight for ward interpretation in terms of a physical speech production model.
Cited by:	9
Resources:	[PDF] from entn.at

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A time-frequency method for increasing the signal-to-noise ratio in system identification with exponential sweeps

2011

Piotr Majdak, Peter Balazs, Wolfgang Kreuzer, Monika Dörfler
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),…
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Authors:	Piotr Majdak, Peter Balazs, Wolfgang Kreuzer, Monika Dörfler
Publication date:	05/22/2011
Journal:	2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Pages:	3812-3815
Publisher:	IEEE
Description:	Exponential sweeps are widely used to measure impulse responses of electro-acoustic systems. Measurements are often contaminated by environmental noise and nonlinear distortions. We propose a method to increase the signal-to-noise ratio (SNR) by denoising the recorded signal in the time-frequency plane. In contrast to state-of-the art denoising methods, no assumption about the spectral characteristics of the noise is required. Numerical simulations demonstrate improvements in the SNR under low-SNR conditions even for measurements contaminated by colored noise.
Cited by:	62
Resources:	[PDF] from researchgate.net

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Frames and semi-frames

2011

Jean-Pierre Antoine, Peter Balazs
Journal of Physics A: Mathematical and Theoretical 44, 205201
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Authors:	Jean-Pierre Antoine, Peter Balazs
Publication date:	05/20/2011
Journal:	Journal of Physics A: Mathematical and Theoretical
Volume:	44
Pages:	205201
Publisher:	IOP Publishing
Description:	Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded inverse, whereas a lower semi-frame has an unbounded frame operator, with a bounded inverse. We study mostly upper semi-frames, both in the continuous and discrete case, and give some remarks for the dual situation. In particular, we show that reconstruction is still possible in certain cases.
Cited by:	62
Resources:	[PDF] from arxiv.org

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Auditory time-frequency masking: psychoacoustical data and application to audio representations

2011

Thibaud Necciari, Peter Balazs, Richard Kronland-Martinet, Sølvi Ystad, Bernhard Laback…
International Symposium on Computer Music Modeling and Retrieval, 146-171
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Authors:	Thibaud Necciari, Peter Balazs, Richard Kronland-Martinet, Sølvi Ystad, Bernhard Laback, Sophie Savel, Sabine Meunier
Publication date:	03/09/2011
Journal:	International Symposium on Computer Music Modeling and Retrieval
Pages:	146-171
Publisher:	Springer Berlin Heidelberg
Description:	In this paper, the results of psychoacoustical experiments on auditory time-frequency (TF) masking using stimuli (masker and target) with maximal concentration in the TF plane are presented. The target was shifted either along the time axis, the frequency axis, or both relative to the masker. The results show that a simple superposition of spectral and temporal masking functions does not provide an accurate representation of the measured TF masking function. This confirms the inaccuracy of simple models of TF masking currently implemented in some perceptual audio codecs. In the context of audio signal processing, the present results constitute a crucial basis for the prediction of auditory masking in the TF representations of sounds. An algorithm that removes the inaudible components in the wavelet transform of a sound while causing no audible difference to the original sound after re-synthesis is proposed …
Cited by:	8
Resources:	[PDF] from hal.science

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The phase derivative around zeros of the short-time Fourier transform

2011

P Balazs, D Bayer, F Jaillet, P Sondergaard
arXiv preprint arXiv:1103.0409
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Authors:	P Balazs, D Bayer, F Jaillet, P Sondergaard
Publication date:	03/01/2011
Journal:	arXiv preprint arXiv:1103.0409
Publisher:	eprint
Description:	The phase of the short-time Fourier transform (STFT) is sometimes considered difficult to interpret. However, the phase information is important for improved analysis and processing. The phase derivative, in particular, is essential for the reassignment method or the phase vocoder algorithm. In order to understand the phase derivative of the STFT more thoroughly, we describe an interesting phenomenon, a recurring pattern in the neighborhood of zeros. Contrary to the possible expectation of an arbitrary behavior, the phase derivative always shows a singularity with the same characteristic shape with a negative and a positive peak of infinite height at these points. We show this behavior in a numerical investigation, present a simple explicit analytic example and then do a complete analytical treatment. For this we present several intermediate results about the regularity of the STFT for Schwartz windows, which are of independent interest.
Cited by:	9
Resources:	[PDF] from academia.edu

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Additivity of nonsimultaneous masking for short Gaussian-shaped sinusoids

2011

Bernhard Laback, Peter Balazs, Thibaud Necciari, Sophie Savel, Solvi Ystad, Sabine Meun…
The Journal of the Acoustical Society of America 129 (2), 888-897
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Authors:	Bernhard Laback, Peter Balazs, Thibaud Necciari, Sophie Savel, Solvi Ystad, Sabine Meunier, Richard Kronland-Martinet
Publication date:	02/01/2011
Journal:	The Journal of the Acoustical Society of America
Volume:	129
Issue:	2
Pages:	888-897
Publisher:	AIP Publishing
Description:	The additivity of nonsimultaneous masking was studied using Gaussian-shaped tone pulses (referred to as Gaussians) as masker and target stimuli. Combinations of up to four temporally separated Gaussian maskers with an equivalent rectangular bandwidth of 600 Hz and an equivalent rectangular duration of 1.7 ms were tested. Each masker was level-adjusted to produce approximately 8 dB of masking. Excess masking (exceeding linear additivity) was generally stronger than reported in the literature for longer maskers and comparable target levels. A model incorporating a compressive input/output function, followed by a linear summation stage, underestimated excess masking when using an input/output function derived from literature data for longer maskers and comparable target levels. The data could be predicted with a more compressive input/output function. Stronger compression may be explained by …
Cited by:	18
Resources:	[HTML] from aip.org

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Oversampling operators: Frame representation of operators

2011

Peter Balazs, Georg Rieckh
Analele Universitatii “Eftimie Murgu 2, 107-114
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Authors:	Peter Balazs, Georg Rieckh
Publication date:	01/01/2011
Journal:	Analele Universitatii “Eftimie Murgu
Volume:	2
Pages:	107-114
Cited by:	9

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Speaker verification using pole/zero estimates of nasals

2011

E Enzinger, P Balazs
Analele Universitatii “Eftimie Murgu 18, 33-44
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Authors:	E Enzinger, P Balazs
Publication date:	01/01/2011
Journal:	Analele Universitatii “Eftimie Murgu
Volume:	18
Pages:	33-44
Cited by:	9

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www. elsevier. com/locate/acha

2011

Akram Aldroubi, Jeffrey D Blanchard, Bernhard G Bodmann, HQ Bui, Ying Cao, Coralia Cart…
Appl. Comput. Harmon. Anal 30, 428
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Authors:	Akram Aldroubi, Jeffrey D Blanchard, Bernhard G Bodmann, HQ Bui, Ying Cao, Coralia Cartis, Peter G Casazza, Di-Rong Chen, Tuan-Yow Chien, Ingrid Daubechies, M Elad, YC Eldar, Hans G Feichtinger, Matthew Fickus, R Giryes, Maxim J Goldberg, F Gómez-Cubillo, L Greengard, Rémi Gribonval, Kanghui Guo, David K Hammond, Deguang Han, Chunyan Huang, Seonja Kim, Gitta Kutyniok, Demetrio Labate, Ming-Jun Lai, RS Laugesen, EA Lebedeva, Yang Liu, Jianfeng Lu, Per-Gunnar Martinsson, Facundo Mémoli, Dustin G Mixon, Vladimir Rokhlin, Daniela Rosca, A Singer, Rob Stevenson, C Stucchio, Z Suchanecki, Hongwei Sun, Qiyu Sun, Wai-Shing Tang, Jared Tanner, Nicolae Tarfulea, Andrew Thompson, Mark Tygert, Pierre Vandergheynst
Publication date:	01/01/2011
Journal:	Appl. Comput. Harmon. Anal
Volume:	30
Pages:	428

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Classification of general sequences by frame-related operators

2011

Peter Balazs, Diana T Stoeva, Jean-Pierre Antoine
Sampling Theory in Signal and Image Processing 10 (1), 151-170
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Authors:	Peter Balazs, Diana T Stoeva, Jean-Pierre Antoine
Publication date:	01/01/2011
Journal:	Sampling Theory in Signal and Image Processing
Volume:	10
Issue:	1
Pages:	151-170
Publisher:	Springer International Publishing
Description:	This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We investigate these operators for arbitrary sequences, which in general lead to possibly unbounded operators. We characterize various classes of sequences in terms of these operators and vice-versa. Finally, we classify these sequences by operators applied on orthonormal bases.
Cited by:	43
Resources:	[PDF] from springer.com

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Multipliers for p-Bessel Sequences in Banach Spaces

2010

Asghar Rahimi, Peter Balazs
Integral Equations and Operator Theory 68 (2), 193-205
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Authors:	Asghar Rahimi, Peter Balazs
Publication date:	10/01/2010
Journal:	Integral Equations and Operator Theory
Volume:	68
Issue:	2
Pages:	193-205
Publisher:	SP Birkhäuser Verlag Basel
Description:	Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.
Cited by:	64
Resources:	[PDF] from arxiv.org

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Frames for acoustic bem

2010

Georg Rieckh, Peter Balazs, Wolfgang Kreuzer, Holger Waubke
INTER-NOISE and NOISE-CON Congress and Conference Proceedings 2010 (7), 3758-3762
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Authors:	Georg Rieckh, Peter Balazs, Wolfgang Kreuzer, Holger Waubke
Publication date:	06/13/2010
Journal:	INTER-NOISE and NOISE-CON Congress and Conference Proceedings
Volume:	2010
Issue:	7
Pages:	3758-3762
Publisher:	Institute of Noise Control Engineering
Description:	We present ideas for a boundary element method that, unlike classic formulations, does not use a basis for the solution space. Instead we use the more general concept of frames which is well established in signal processing. There are results that indicate that frames (especially wavelet frames) can be used to formulate an algorithm to solve elliptic partial differential equations with optimal computational complexity. Similar concepts have already been successfully applied in the context of finite elements.
Cited by:	1

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Frames by multiplication

2010

Peter Balazs, Carlos Cabrelli, Sigrid Heineken, Ursula Molter
arXiv preprint arXiv:1004.1429
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Authors:	Peter Balazs, Carlos Cabrelli, Sigrid Heineken, Ursula Molter
Publication date:	04/08/2010
Journal:	arXiv preprint arXiv:1004.1429
Description:	In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited function in $L^2(R^d)$. This is achieved by looking at a set of exponentials restricted to a set $E subset R^d$ with frequencies in a countable set and multiplying it by the Fourier transform of a fixed function . Using density results due to Beurling, we prove the existence and give ways to construct frames by irregular translates.
Cited by:	11
Resources:	[PDF] from arxiv.org

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Frames of Irregular Translates

2010

P Balazs, C Cabrelli, S Heineken, U Molter
arXiv preprint arXiv:1004.1429
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Authors:	P Balazs, C Cabrelli, S Heineken, U Molter
Publication date:	04/01/2010
Journal:	arXiv preprint arXiv:1004.1429
Description:	In this note we study properties of a set of irregular translates of a function in L2 (Rd). This is achieved by looking at a set of exponentials restricted to a set E⊂ Rd with frequencies in a countable set Λ. The results are obtained by analyzing which properties of this set of exponentials are preserved when multiplied by the Fourier transform of a function h∈ L2 (E). This in turn gives information on the set of Λ-translates of h. In particular we study frame and Riesz basis properties. Using density results due to Beurling, we prove the existence and give ways to construct frames by irregular translates.
Resources:	[PDF] from researchgate.net

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On pole-zero model estimation methods minimizing a logarithmic criterion for speech analysis

2010

Damián Marelli, Peter Balazs
Audio, Speech, and Language Processing, IEEE Transactions on 18 (2), 237-248
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Authors:	Damián Marelli, Peter Balazs
Publication date:	02/01/2010
Journal:	Audio, Speech, and Language Processing, IEEE Transactions on
Volume:	18
Issue:	2
Pages:	237-248
Publisher:	IEEE
Description:	A speech production model consists of a linear, slowly time-varying filter. Pole-zero models are required for a good representation of certain types of speech sounds, like nasals and laterals. From a perceptual point of view, designing them by minimizing a logarithmic criterion appears as a very suitable approach. The most accurate available results are obtained by using Newton-like search algorithms to optimize pole and zero positions, or the coefficients of a decomposition into quadratic factors. In this paper, we propose to optimize the numerator and denominator coefficients instead. Experimental results show that this is the computationally most efficient approach, especially when the optimization criterion considers a psychoacoustical frequency scale. To illustrate its applicability in speech processing, we used the proposed method for formant and anti-formant tracking as well as speech resynthesis.
Cited by:	35
Resources:	[PDF] from newcastle.edu.au

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Introducing time-frequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking

2010

Peter Balazs, Bernhard Laback, Gerhard Eckel, Werner A Deutsch
ACM Trans Audio, Speech, Language Process 18 (1), 34-49
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Authors:	Peter Balazs, Bernhard Laback, Gerhard Eckel, Werner A Deutsch
Publication date:	01/01/2010
Journal:	ACM Trans Audio, Speech, Language Process
Volume:	18
Issue:	1
Pages:	34-49
Description:	We present an algorithm for removing time-frequency components, found by a standard Gabor transform, of a “real-world” sound while causing no audible difference to the original sound after resynthesis. Thus this representation is made sparser. The selection of removable components is based on a simple model of simultaneous masking in the auditory system. Important goals were the applicability to any realworld music and speech sound, integrating mutual masking effects between time-frequency components, coping with the time-frequency spread of such an operation, and computational efficiency. The proposed algorithm first determines an estimation of the masked threshold within an analysis window. The masked threshold function is then shifted in level by an amount determined experimentally, and all components falling below this function (the irrelevance threshold) are removed. This shift gives a conservative way to deal with uncertainty effects resulting from removing time-frequency components and with inaccuracies in the masking model. The removal of components is described as an adaptive Gabor multiplier. Thirty-six normal hearing subjects participated in an experiment to determine the maximum shift value for which they could not discriminate the irrelevance filtered signal from the original signal. On average across the test stimuli, 36 percent of the time-frequency components fell below the irrelevance threshold.
Cited by:	9
Resources:	[PDF] from oeaw.ac.at

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Time–Frequency Sparsity by Removing Perceptually Irrelevant Components Using a Simple Model of Simultaneous Masking

2010

Peter Balazs, Bernhard Laback, Gerhard Eckel, Werner A Deutsch
Audio, Speech, and Language Processing, IEEE Transactions on 18 (1), 34-49
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Authors:	Peter Balazs, Bernhard Laback, Gerhard Eckel, Werner A Deutsch
Publication date:	01/01/2010
Journal:	Audio, Speech, and Language Processing, IEEE Transactions on
Volume:	18
Issue:	1
Pages:	34-49
Publisher:	IEEE
Description:	We present an algorithm for removing time-frequency components, found by a standard Gabor transform, of a ldquoreal-worldrdquo sound while causing no audible difference to the original sound after resynthesis. Thus, this representation is made sparser. The selection of removable components is based on a simple model of simultaneous masking in the auditory system. Important goals were the applicability to any real-world music and speech sound, integrating mutual masking effects between time-frequency components, coping with the time-frequency spread of such an operation, and computational efficiency. The proposed algorithm first determines an estimation of the masked threshold within an analysis window. The masked threshold function is then shifted in level by an amount determined experimentally, and all components falling below this function (the irrelevance threshold) are removed. This shift …
Cited by:	105

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Weighted and controlled frames: Mutual relationship and first numerical properties

2010

PETER Balazs, JEAN-PIERRE Antoine, A Grybos
International Journal of Wavelets, Multiresolution and Information Processing, to appear
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Authors:	PETER Balazs, JEAN-PIERRE Antoine, A Grybos
Publication date:	01/01/2010
Journal:	International Journal of Wavelets, Multiresolution and Information Processing, to appear
Description:	Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while offering a numerical advantage in the sense of preconditioning. Next, we investigate weighted frames, in particular their relation to controlled frames. We consider the special case of semi-normalized weights, where the concepts of weighted frames and standard frames are interchangeable. We also make the connection with frame multipliers. Finally, we analyze weighted frames numerically. First, we investigate three possibilities for finding weights in order to tighten a given frame, i.e. decrease the frame bound ratio. Then, we …
Cited by:	198
Resources:	[PDF] from arxiv.org

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Matrix representation of bounded linear operators by Bessel sequences, frames and Riesz sequence

2009

Peter Balazs
SAMPTA'09, General session
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Authors:	Peter Balazs
Publication date:	05/18/2009
Journal:	SAMPTA'09
Pages:	General session
Description:	In this work we will investigate how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases as an extension of the known method of matrix representation by ONBs. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on l2 and operators on H. We will show some structural results and give some examples. Furthermore in the case of Riesz bases we prove that those functions are isomorphisms. We are going to apply this idea to the connection of Hilbert-Schmidt operators and Frobenius matrices. Finally we will use this concept to show that every bounded operator is a generalized frame multiplier.
Cited by:	4
Resources:	[PDF] from hal.science

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Nonstationary Gabor Frames

2009

Florent Jaillet, Peter Balazs, Monika Dörfler
SAMPTA'09, Marseille
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Authors:	Florent Jaillet, Peter Balazs, Monika Dörfler
Publication date:	05/01/2009
Journal:	SAMPTA'09, Marseille
Description:	To overcome the limitation induced by the fixed time-frequency resolution over the whole time-frequency plane of Gabor frames, we propose a simple extension of the Gabor theory leading to the construction of frames with time-frequency resolution evolving over time or frequency. We describe the construction of such frames and give the explicit formulation of the canonical dual frame for some conditions. We illustrate the interest of the method on a simple example.
Cited by:	34
Resources:	[PDF] from hal.science

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Removing Components from a Time-Frequency Representation

2009

Monika Dörfler, Peter Balazs, Florent Jaillet
International Conference on Acoustics NAG/DAGA 2009, 1596-1599
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Authors:	Monika Dörfler, Peter Balazs, Florent Jaillet
Publication date:	03/23/2009
Journal:	International Conference on Acoustics NAG/DAGA 2009
Pages:	1596-1599
Description:	Time-frequency representations such as the spectrogram or short-time Fourier transform seem to be well suited to the task of removing certain components with approximately disjoint support in the time-frequency domain. For example, one might be interested in suppressing a certain instrument’s contribution from a music signal. Such approaches are used in Computational Auditory Scene Analysis by the name of Time-Frequency masks. However, the trivial approach of just deleting the corresponding component in the time-frequency representation leads to artefacts such as “ghost-tones”, i.e. a modified version of the deleted component is still audible, or to the perception of unnatural sound coloration comparable to a "phasing effect". We compare different approaches to tackle this problem: a soft-thresholding procedure is applied and compared to a method using statistical models. On the other hand, we draw conclusions from considering the optimal separating mask for known signal components. In this situation, a model promoting sparsity in the representation can lead to favourable results by yielding a feasible approximation of the optimal mask. We perform informal listening experiments to evaluate the resulting removal of certain components in a complex audio-signal.
Resources:	[PDF] from hal.science

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On the structure of the phase around the zeros of the short-time Fourier transform

2009

Florent Jaillet, Peter Balazs, Monika Dörfler, Nina Engelputzeder
International Conference on Acoustics NAG/DAGA 2009, 1584-1587
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Authors:	Florent Jaillet, Peter Balazs, Monika Dörfler, Nina Engelputzeder
Publication date:	03/23/2009
Journal:	International Conference on Acoustics NAG/DAGA 2009
Pages:	1584-1587
Description:	The short-time Fourier transform is a time-frequency representation widely used in audio signal processing. At first sight, the phase of the transform may appear to be difficult to interpret, a fact that led to the development of many processing schemes in audio processing relying on the modulus of the transform only. However, it has been shown, that the phase information can be successfully exploited for improved analysis and processing. This is illustrated for example by the reassignment method or the phase vocoder algorithm. In order to better exploit the phase information in audio processing, a better understanding of its structure is desirable. This study describes a particular behavior of the phase which can be observed when looking at the phase derivative over time or frequency around the points where the transform equals zero. This recurrent behavior is illustrated using numerical simulations on synthesized and real audio signals. The performed simulations show the influence of the parameters of the transform on the observed structures. Some consequences of this phase structure for audio processing are also presented.
Cited by:	13
Resources:	[PDF] from hal.science

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Auditory masking using Gaussian‐windowed stimuli

2008

Thibaud Necciari, Sophie Savel, Sabine Meunier, Solvi Ystad, Richard Kronland‐Martinet,…
The Journal of the Acoustical Society of America 123 (5_Supplement), 3563-3563
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Authors:	Thibaud Necciari, Sophie Savel, Sabine Meunier, Solvi Ystad, Richard Kronland‐Martinet, Bernhard Laback, Peter Balazs
Publication date:	05/01/2008
Journal:	The Journal of the Acoustical Society of America
Volume:	123
Issue:	5_Supplement
Pages:	3563-3563
Publisher:	Acoustical Society of America
Description:	This study investigates auditory masking with Gaussian‐windowed tones as target and masker stimuli. On the purpose of developing a time‐frequency masking model, such stimuli minimize the time‐frequency uncertainty. Also, as proposed by van Schijndel et al. (1999), they activate a single spectro‐temporal observation window of the auditory system. The study presented here measured auditory masking with Gaussian‐windowed stimuli with an ERB of 600 Hz and an effective duration of 9.6 ms. The masker was centered at 4 kHz. Its level was 60 dB SL. Four experiments were conducted. (1) Absolute thresholds for Gaussian‐windowed and 300‐ms‐sinusoidal targets were measured and compared for 11 frequencies. (2) Masking patterns were obtained with targets of various frequency separations from the masker. (3) Forward masking functions with 4‐kHz targets were measured at 5 temporal separations. (4 …
Cited by:	2

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An iterative method for approximating LTI systems using subbands

2008

Damián Marelli, Minyue Fu, Peter Balazs, Piotr Majdak
2008 IEEE International Conference on Acoustics, Speech and Signal Processing, 3533-3536
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Authors:	Damián Marelli, Minyue Fu, Peter Balazs, Piotr Majdak
Publication date:	03/31/2008
Journal:	2008 IEEE International Conference on Acoustics, Speech and Signal Processing
Pages:	3533-3536
Publisher:	IEEE
Description:	A linear system can be approximated in the time-frequency domain by the composition of an analysis filterbank, a transfer matrix (subband model) and a synthesis filterbank, a method known as subband technique. In this paper we propose an iterative method to jointly optimize the subband model, analysis and synthesis filterbank. To this end we propose a minimization criterion which we solve using the so-called alternating least-squares method. As a possible application we consider the implementation of the so-called head related transfer functions which are used in virtual acoustics. Simulation results suggest that the subband technique, optimized using the proposed method proposed method, is a promising approach.
Cited by:	4
Resources:	[PDF] from majdak.com

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Hilbert-Schmidt Operators and Frames-Classification, Approximation by Multipliers and Algorithms

2008

Peter Balazs
International Journal of Wavelets, Multiresolution and Information Processing 6 (2), 31…
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Authors:	Peter Balazs
Publication date:	03/01/2008
Journal:	International Journal of Wavelets, Multiresolution and Information Processing
Volume:	6
Issue:	2
Pages:	315-330
Description:	In this paper we deal with the theory of Hilbert–Schmidt operators, when the usual choice of orthonormal basis, on the associated Hilbert spaces, is replaced by frames. We More precisely, we provide a necessary and sufficient condition for an operator to be Hilbert–Schmidt, based on its action on the elements of a frame (i.e. an operator T is if and only if the sum of the squared norms of T applied on the elements of the frame is finite). Also, we construct Bessel sequences, frames and Riesz bases of operators using tensor products of the same sequences in the associated Hilbert spaces. We state how the inner product of an arbitrary operator and a rank one operator can be calculated in an efficient way; and we use this result to provide a numerically efficient algorithm to find the best approximation, in the Hilbert–Schmidt sense, of an arbitrary matrix, by a so-called frame multiplier (i.e. an operator which …
Cited by:	110
Resources:	[PDF] from arxiv.org

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A systematic study of frame sequence operators and their pseudoinverses

2008

P Balazs, MA El-Gebeily
arXiv preprint arXiv:0802.3589
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Authors:	P Balazs, MA El-Gebeily
Publication date:	02/25/2008
Journal:	arXiv preprint arXiv:0802.3589
Description:	In this note we investigate the operators associated with frame sequences in a Hilbert space , i.e., the synthesis operator , the analysis operator $% ell ^{2}(mathbb{N}) $ and the associated frame operator as operators defined on (or to) the whole space rather than on subspaces. Furthermore, the projection onto the range of , the projection onto the range of and the Gram matrix are investigated. For all these operators, we investigate their pseudoinverses, how they interact with each other, as well as possible classification of frame sequences with them. For a tight frame sequence, we show that some of these operators are connected in a simple way.
Cited by:	3
Resources:	[PDF] from arxiv.org

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Additivity of auditory masking using gaussian-shaped tones

2008

Bernhard Laback, Peter Balazs, Gwenael Toupin, Thibaud Necciari, Sophie Savel, Sabine M…
The Journal of the Acoustical Society of America 123 (5_Supplement), 3563-3563
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Authors:	Bernhard Laback, Peter Balazs, Gwenael Toupin, Thibaud Necciari, Sophie Savel, Sabine Meunier, Solvi Ystad, Richard Kronland-Martinet
Publication date:	01/01/2008
Journal:	The Journal of the Acoustical Society of America
Volume:	123
Issue:	5_Supplement
Pages:	3563-3563
Description:	Both temporal and spectral masking have been studied extensively in the literature. Mostly, they have been regarded as separate phenomena. Very little is known about the interaction between these two effects, ie masking in the time-frequency domain. Data on the time-frequency spread of masking evoked by a single Gaussian-shaped tone pulse are presented in an accompanying study at the same conference (Necciari et al.). The current study gathers data on the additivity of masking by up to four, approximately equally effective Gaussian maskers (ERB= 600 Hz, ERD= 1.7 ms), separated either along the time or the frequency axis. For temporal shift, the amount of masking increases with the number of maskers, with excess masking (exceeding linear additivity) of up to 25 dB. For frequency separation excess masking amounts up to 15 dB, and the higher-frequency masker (relative to the target) contributes more to the additivity than the lower-frequency maskers. The data suggest strong basilar membrane compressivity even for such short stimuli. Combined with the single masker timefrequency spread data, these data may serve as a basis for modeling time-frequency masking effects in complex signals.
Cited by:	4
Resources:	[HTML] from academia.edu

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Frames and finite dimensionality: Frame transformation, classification and algorithms

2008

Peter Balazs
Applied Mathematical Sciences 2 (43), 2131 - 2144
:read more

Authors:	Peter Balazs
Publication date:	01/01/2008
Journal:	Applied Mathematical Sciences
Volume:	2
Issue:	43
Pages:	2131 - 2144
Description:	In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an algorithm to calculate the coefficients of one frame given the analysis of another frame using their cross-Gram matrix. This is a canonical extension of the basic transformation matrix used for orthonormal bases (ONB) and is therefore called frame transformation. Furthermore we will summarize basic properties of frames in finite dimensional spaces. We will give basic algorithms to use with frames in finite dimensional spaces, useful for basic numerical experiments. Finally we will give a criteria for finite dimensional spaces using frames. Keywords: frames, discrete expansion, matrices, frame transformation, finite dimension, algorithm; MSC: 41A58, 65F30; 15A03
Cited by:	35
Resources:	[PDF] from arxiv.org

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Matrix representation of operators using frames

2008

Peter Balazs
Sampling Theory in Signal and Image Processing (STSIP) 7 (1), 39-54
:read more

Authors:	Peter Balazs
Publication date:	01/01/2008
Journal:	Sampling Theory in Signal and Image Processing (STSIP)
Volume:	7
Issue:	1
Pages:	39-54
Description:	This paper addresses how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames, and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore, it is useful to extend the known method of matrix representation by using these sequences instead of ONBs for these application areas. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on l2 and operators on H. We will show some structural results and give some examples. Furthermore, in the case of Riesz bases we prove that those functions are isomorphisms. Finally we apply this idea to the connection of Hilbert-Schmidt operators and Frobenius matrices.
Cited by:	62
Resources:	[PDF] from arxiv.org

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A stochastic 2D-model for calculating vibrations in random layers

2007

Peter Balazs, Wolfgang Kreuzer, Holger Waubke
Journal of Computational Acoustics 15 (03), 271-283
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Authors:	Peter Balazs, Wolfgang Kreuzer, Holger Waubke
Publication date:	09/01/2007
Journal:	Journal of Computational Acoustics
Volume:	15
Issue:	03
Pages:	271-283
Publisher:	IMACS
Description:	Vibrations induced by machinery and traffic have become of increasing concern in the last years, for example, when constructing buildings near railway lines. In this paper we will present a model designed to predict the vibration level in the ground. Since in practice it is nearly impossible to determine exact material parameters for soil layers, we use a model with a stochastic shear modulus G. Under moderate assumptions G can be split with the Karhunen–Loeve expansion into a mean value G0 and a stochastic part Gstoch. Using a combination method of finite elements, Fourier transformation and Polynomial Chaos, it is possible to transform the partial differential equation describing the system into a matrix-vector formulation Kx = b which can be split into a deterministic and a stochastic part (K0 + Ks) x = b analog to the shear modulus. To keep the dimensions of the matrices involved with this system small, we use …
Cited by:	16

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Multiple exponential sweep method for fast measurement of head-related transfer functions

2007

Piotr Majdak, Peter Balazs, Bernhard Laback
JOURNAL-AUDIO ENGINEERING SOCIETY 55 (7/8), 623
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Authors:	Piotr Majdak, Peter Balazs, Bernhard Laback
Publication date:	07/01/2007
Journal:	JOURNAL-AUDIO ENGINEERING SOCIETY
Volume:	55
Issue:	7/8
Pages:	623
Publisher:	AUDIO ENGINEERING SOCIETY INC

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The Linear Time/Frequency Analysis Toolbox

2007

Peter L Søndergaard, Bruno Torrésani, Peter Balazs
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Authors:	Peter L Søndergaard, Bruno Torrésani, Peter Balazs
Publication date:	06/13/2007
Cited by:	175

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A Zero-Pole Vocal Tract Model Estimation Method Accurately Reproducing Spectral Zeros

2007

Peter Balazs, Damián Marelli
Audio Engineering Society Convention 122
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Authors:	Peter Balazs, Damián Marelli
Publication date:	05/01/2007
Journal:	Audio Engineering Society Convention 122
Publisher:	Audio Engineering Society
Description:	Model based speech coding consists in modeling the vocal tract as a linear time-variant system. The all-pole model produced by the computationally efficiency Linear Predictive Coding method provides a good representation for the majority of speech sounds. However, nasal and fricative sounds, as well as stop consonants, contain spectral zeros which requires the use of a zero-pole model. Roughly speaking, a zero-pole model estimation method typically does a non-parametric estimation of the vocal tract impulse response, and tunes the zero-pole model to fit this estimation in a square sense. In this paper we propose an alternative strategy. We tune the zero-pole model to directly fit the power spectrum of the speech signal in a logarithmic scale, to be consistent with the way the human ear perceives sounds. In this way, we avoid the error introduced by the vocal tract impulse response estimation and obtain a …

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STX-Intelligent Sound Processing, Programmer’s Reference

2007

Anton Noll, Jonathan White, Peter Balazs, WA Deutsch
Acoustics Research Institute, Austrian Academy of Science
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Authors:	Anton Noll, Jonathan White, Peter Balazs, WA Deutsch
Publication date:	01/01/2007
Journal:	Acoustics Research Institute, Austrian Academy of Science
Cited by:	9

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Multiple exponential sweep method for fast measurement of head related transfer functions

2007

Peter Balazs, Bernhard Laback, Piotr Majdak
Audio Engineering Society Convention 122 (5)
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Authors:	Peter Balazs, Bernhard Laback, Piotr Majdak
Publication date:	01/01/2007
Journal:	Audio Engineering Society Convention
Volume:	122
Issue:	5
Description:	Presenting sounds in virtual environments requires filtering of free field signals with head related transfer functions (HRTF). HRTFs describe the filtering effects of pinna, head, and torso measured in the ear canal of a subject. The measurement of HRTFs for many positions in space is a time-consuming procedure. To speed up the HRTF measurement the multiple exponential sweep method (MESM) was developed. MESM speeds up the measurement by interleaving and overlapping sweeps in an optimized way and retrieves the impulse responses of the measured systems. In this paper the MESM and its parameter optimization is described. As an example of an application of MESM, the measurement duration of a HRTF set with 1550 positions is compared to the unoptimized method. Using MESM, the measurement duration could be reduced by a factor of four without a reduction of the signal-to-noise ratio.
Cited by:	311
Resources:	[PDF] from academia.edu

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Basic definition and properties of Bessel multipliers

2007

Peter Balazs
Journal of Mathematical Analysis and Applications 325 (1), 571-585
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Authors:	Peter Balazs
Publication date:	01/01/2007
Journal:	Journal of Mathematical Analysis and Applications
Volume:	325
Issue:	1
Pages:	571-585
Publisher:	Academic Press
Description:	This paper introduces the concept of Bessel multipliers. These operators are defined by a fixed multiplication pattern, which is inserted between the analysis and synthesis operators. The proposed concept unifies the approach used for Gabor multipliers for arbitrary analysis/synthesis systems, which form Bessel sequences, like wavelet or irregular Gabor frames. The basic properties of this class of operators are investigated. In particular the implications of summability properties of the symbol for the membership of the corresponding operators in certain operator classes are specified. As a special case the multipliers for Riesz bases are examined and it is shown that multipliers in this case can be easily composed and inverted. Finally the continuous dependence of a Bessel multiplier on the parameters (i.e., the involved sequences and the symbol in use) is verified, using a special measure of similarity of sequences.
Cited by:	195
Resources:	[PDF] from sciencedirect.com

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Double preconditioning for Gabor frames

2006

Peter Balazs, Hans G Feichtinger, Mario Hampejs, Gnther Kracher
IEEE Transactions on Signal Processing 54 (12), 4597-4610
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Authors:	Peter Balazs, Hans G Feichtinger, Mario Hampejs, Gnther Kracher
Publication date:	11/20/2006
Journal:	IEEE Transactions on Signal Processing
Volume:	54
Issue:	12
Pages:	4597-4610
Publisher:	IEEE
Description:	The authors present an application of the general idea of preconditioning in the context of Gabor frames. While most (iterative) algorithms aim at a more or less costly exact numerical calculation of the inverse Gabor frame matrix, we propose here the use of "cheap methods" to find an approximation for it, based on (double) preconditioning. We thereby obtain good approximations of the true dual Gabor atom at low computational costs. Since the Gabor frame matrix commutes with certain time-frequency shifts, it is natural to make use of diagonal and circulant preconditioners sharing this property. Part of the efficiency of the proposed scheme results from the fact that all the matrices involved share a well-known block matrix structure. At least, for the smooth Gabor atoms typically used, the combination of these two preconditioners leads consistently to good results. These claims are supported by numerical experiments …
Cited by:	72
Resources:	[PDF] from academia.edu

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Concept of a Time Frequency Masking Model based on Gabor filters and 2D convolution

2006

Peter Balazs
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Authors:	Peter Balazs
Publication date:	10/05/2006

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Double preconditioning for the Gabor frame operator

2006

Peter Balazs, Hans G Feichtinger, Mario Hampejs, Günther Kracher
2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceeding…
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Authors:	Peter Balazs, Hans G Feichtinger, Mario Hampejs, Günther Kracher
Publication date:	05/14/2006
Journal:	2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings
Volume:	3
Pages:	III-III
Publisher:	IEEE
Description:	We present an application of the idea of preconditioning in the context of Gabor frames. We propose a method to find an approximation for the inversion of the Gabor frame operator, based on (double) preconditioning. We thereby obtain very good approximations of the true dual Gabor atom at very low computational costs. Part of the efficiency of the proposed scheme results from the fact that all the matrices involved share a well-known block matrix structure. For Gabor atoms typically used in applications, the combination of these two preconditioners leads to very good results
Cited by:	2
Resources:	[PDF] from researchgate.net

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Ein 3D-Modell zu Berechnung der Ausbreitung von Erschutterungen in Bodenschichten

2006

H Waubke, W Kreuzer, P Balazs
FORTSCHRITTE DER AKUSTIK 32 (2), 623
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Authors:	H Waubke, W Kreuzer, P Balazs
Publication date:	01/01/2006
Journal:	FORTSCHRITTE DER AKUSTIK
Volume:	32
Issue:	2
Pages:	623
Description:	Modelle, mit deren Hilfe die Ausbreitung von Erschütterungen in Böden untersucht werden können, werden zB durch den vermehrten Aus-und Neubau von (Hochleistungs-) Bahnstrecken in der unmittelbaren Nähe von Wohngebieten immer wichtiger. Da aber Materialparameter für Bodenschichten schwer bestimmt werden können oder Messungen mit großen Unsicherheiten behaftet sind, wurde ein Modell entwickelt, mit dem es möglich ist, stochastische Materialparameter zu verwenden, und mit dem die Ausbreitung von Erschütterungen in Böden, die durch bewegte Lasten ausgelöst werden, simuliert werden können.
Cited by:	1
Resources:	[PDF] from dega-akustik.de

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Effiziente Implementierung eines stochastischen Modells zur Berechnung von Erschutterungen in Boden und Fluiden

2006

W Kreuzer, H Waubke, P Balazs
FORTSCHRITTE DER AKUSTIK 32 (2), 625
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Authors:	W Kreuzer, H Waubke, P Balazs
Publication date:	01/01/2006
Journal:	FORTSCHRITTE DER AKUSTIK
Volume:	32
Issue:	2
Pages:	625
Description:	Um die Ausbreitung von Erschütterungen in Böden zu simulieren, erscheint es sinnvoll, stochastische Modelle zu verwenden, da die Bestimmung von Materialparametern meist nur mit sehr großen Unsicherheiten möglich ist. Solche stochastischen Ansätze haben aber den großen Nachteil, dass sie sehr rechenintensiv sind. Um dennoch solche Systeme in annehmbarer Zeit numerisch lösen zu können, wird eine Iterationsmethode verwendet, mit der der Rechenaufwand erheblich reduziert werden kann.
Resources:	[PDF] from dega-akustik.de

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Waves in random layers with arbitrary covariance functions

2005

Holger Waubke, Peter Balazs, Bernhard Jilge, Wolfgang Kreuzer
12th International Congress on Sound and Vibration
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Authors:	Holger Waubke, Peter Balazs, Bernhard Jilge, Wolfgang Kreuzer
Publication date:	07/01/2005
Journal:	12th International Congress on Sound and Vibration
Description:	A new approach that allows arbitrary covariance functions for a discrete version of the Karhunen Loeve expansion (KLE) is introduced. Parseval’s theorem, together with a convolution and finite element formulation, provides the possibility of transforming a partial differential equation with non constant parameters into a linear system of equations. Assuming a constant mean value of the shear modulus, a Neumann like iteration decouples the equations for different wave numbers and reduces the matrix size to the deterministic size. A new example with an arbitrary sequence of random and deterministic layers is presented.
Cited by:	4

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Regular and irregular Gabor multipliers with application to psychoacoustic masking

2005

Peter Balazs
:read more

Authors:	Peter Balazs
Publication date:	06/01/2005
Publisher:	na
Description:	Definition 1.1. 1 The sequence G=(gk\| k∈ K) is called a frame for the (separable) Hilbert space H, if constants A, B> 0 exist, such that
Cited by:	47
Resources:	[PDF] from oeaw.ac.at

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Weighted frames and frame multipliers

2004

Diana T Stoeva, Peter Balazs
Proceedings of the International Conference UACEG2009: Science
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Authors:	Diana T Stoeva, Peter Balazs
Publication date:	01/01/2004
Journal:	Proceedings of the International Conference UACEG2009: Science
Cited by:	12

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Phasenanalyse mit akustischen Anwendungsbeispielen

2003

Peter Balazs, Holger Waubke, W Deutsch
FORTSCHRITTE DER AKUSTIK 29, 582-583
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Authors:	Peter Balazs, Holger Waubke, W Deutsch
Publication date:	01/01/2003
Journal:	FORTSCHRITTE DER AKUSTIK
Volume:	29
Pages:	582-583
Cited by:	3

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Verwendung der zeitlichen Rucktransformation zur Berucksichtigung der Kausalitat in Spektren mehrdimensionaler Fourier Transformationen

2003

H Waubke, P Balazs
FORTSCHRITTE DER AKUSTIK 29, 572-573
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Authors:	H Waubke, P Balazs
Publication date:	01/01/2003
Journal:	FORTSCHRITTE DER AKUSTIK
Volume:	29
Pages:	572-573
Cited by:	3

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Polynome über Gruppen

2001

Peter Balazs
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Authors:	Peter Balazs
Publication date:	01/01/2001
Publisher:	na
Description:	Polynome haben wir in der Schule gemacht, und von Gruppen habe ich schon gehört! Aber was sind'Polynome über Gruppen'?
Cited by:	2
Resources:	[PDF] from inode.at

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Invertibility of ReLU-Layers: A Practical Approach

Hannah Eckert, Daniel Haider, Martin Ehler, Peter Balazs
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Authors:	Hannah Eckert, Daniel Haider, Martin Ehler, Peter Balazs
Description:	Invertibility in machine learning models is a pivotal feature that bridges the gap between model complexity and interpretability. For ReLU-layers, the practical verification of invertibility has been shown to be a difficult task that still remains unsolved. Recently, a frame theoretic condition has been proposed to verify invertibility on an open or convex set, however, the computations for this condition are computationally infeasible in high dimensions. As an alternative, we propose an algorithm that stochastically samples the dataset to approximately verify the above condition for invertibility and can be efficiently implemented even in high dimensions. We use the algorithm to monitor invertibility and to enforce it during training in standard classification tasks.
Resources:	[PDF] from scitepress.org

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Frames and Acoustic BEM Georg Rieckh1, Peter Balazs1, Wolfgang Kreuzer1

Georg Rieckh, Peter Balazs, Wolfgang Kreuzer
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Authors:	Georg Rieckh, Peter Balazs, Wolfgang Kreuzer
Description:	The problem of sound propagation in a homogeneous, isotropic, friction-free medium is governed by the Helmholtz equation −(∆+ κ2) u (x)= Lu (x)= f (x) with x∈ Ω,(1) where κ∈ C, Im (κ)≥ 0 is the complex wave number, u: R3→ C is the acoustic pressure field, f: R3→ C is the excitation force which has compact support and Ω is a bounded, multiply or simply connected domain with a Lipschitz boundary Γ.
Resources:	[PDF] from dega-akustik.de

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Frames and semi-frames

Michael Speckbacher, Peter Balazs, Jean-Pierre Antoine
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Authors:	Michael Speckbacher, Peter Balazs, Jean-Pierre Antoine
Description:	The paper [1] contains a few minor errors, which could be confusing for the reader. Hence this corrigendum, which concerns three different sections.
Resources:	[PDF] from academia.edu

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Applications of Localized Frames to Galerkin-like Representations of Operators

Peter Balazs, Karlheinz Gröchenig
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Authors:	Peter Balazs, Karlheinz Gröchenig
Description:	The mathematical concept of frames [4, 3] is an active field of mathematical research and has found many applications eg in signal processing, quantum mechanics and acoustics. A sequence (ψk) k∈ K in the Hilbert space H is a frame for H, for the discrete index set K, if there exist positive constants A and B (called lower and upper frame bound, respectively) that satisfy
Resources:	[PDF] from univie.ac.at

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Classification of Lower Frame and Riesz-Fischer Sequences by Unbounded Operators

Peter Balazs, Mitra Shamsabadi
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Authors:	Peter Balazs, Mitra Shamsabadi
Description:	In this paper, we and investigate the properties of (possibly unbounded) frame-related operators of an arbitrary sequence. In particular we characterize all Riesz-Fischer sequences and lower frame sequences by (a particular version of) the synthesis operators.
Resources:	[PDF] from univie.ac.at

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Sampling and Frame Expansions for UWB Signals

Stephen D Casey, Peter Balazs
Fourteenth International Conference on Sampling Theory and Applications
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Authors:	Stephen D Casey, Peter Balazs
Journal:	Fourteenth International Conference on Sampling Theory and Applications
Description:	This article outlines sampling and frame expansions designed specifically for ultra-wideband (UWB) signals. We present two different types of expansions: ON windows with modified Gegenbauers and generalized frame expansions. They represent a contrast in computability and flexibility of frames versus the rigid structure and precision in the sampling expansion. Both approaches rely on the multiplication of some super-windowing functions and given orthonormal sequences. We generalize this approach to the redundant case, investigating windowed families of frame sequences.
Resources:	[PDF] from openreview.net

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The continuous nonstationary Gabor transform on LCA groups with applications to representations of the affine Weyl-Heisenberg group

Peter Balazs
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Authors:	Peter Balazs
Description:	In this paper we introduce and investigate the concept of reproducing pairs which generalizes continuous frames. We will introduce a concept that represents a unifying way to look at certain continuous frames (resp. reproducing pairs) on LCA groups, which can be described as continuous nonstationary Gabor systems and investigate conditions for these systems to form a continuous frame (resp. reproducing pair). As a byproduct we identify the structure of the frame operator (resp. resolution operator). Moreover, we ask the question, whether there always exist mutually dual systems with the same structure such that the resolution operator is given by the identity, ie given A: X→ B (H), if there exist ψ, ϕ∈ H, st f= X f, A (x) ψ A (x) ϕdµ (x),∀ f∈ H and show that the answer is not affirmative. As a counterexample we use a system generated by a unitary action of a subset of the affine Weyl-Heisenberg group in L 2 (R).
Cited by:	1
Resources:	[HTML] from academia.edu

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LTFAT-Die Zeit-Frequenz Toolbox

Peter Balazs, Nicki Holighaus, Frequenz Transformationen
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Authors:	Peter Balazs, Nicki Holighaus, Frequenz Transformationen
Description:	Wir geben hier einen Überblick über die Hauptfunktionen von LTFAT, darunter Kurzzeit-Fourier-und Gabor-Transformationen. Wir erwähnen die zugrundeliegende Theorie der Frames. Von diesen Konzepten sowie Filterbänken und zeitinvarianten Filtern berichten wir, wie sie in LTFAT implementiert sind. Wir schließen mit einem geschichtlichen Rückblick und einer Danksagung.
Resources:	[PDF] from dega-akustik.de

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On the Structure of the Phase around the Zeros of the Short-Time Fourier Transform

Peter Balazs, Dominik Bayer, Florent Jaillet
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Authors:	Peter Balazs, Dominik Bayer, Florent Jaillet
Description:	The short-time Fourier transform (STFT) is a timefrequency representation widely used in audio signal processing. Two conventions are commonly used for the definition of the short-time Fourier transform:
Resources:	[PDF] from dega-akustik.de

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Domain Decomposition with Fusion Frames

Mitra Shamsabadi, Peter Balazs
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Authors:	Mitra Shamsabadi, Peter Balazs
Description:	In computational acoustics the goal is to find a numerical solution of physical equations, like the Helmholtz equation. Traditionally, this is done by the boundary element or finite element method. To reduce the computational load the operator equation is split. The domain decomposition methods solves a boundary value problem by splitting it into smaller boundary problems on subdomains. It is vital to find the most applicable and tractable overlapping or non-overlapping domain decomposition for dividing a large problem to smaller one. One of the most important problems in this method is the splitting the given space and finding the global solution from the local ones, in particular in the overlapping domain case. In this paper, we approach this problem by using fusion frames, therefore allowing overlapping. At least in a mathematical setting fusion frames allows to find more numerically tractable approach on …
Resources:	[PDF] from dega-akustik.de

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Implementation of inversion of frame multipliers

Diana T Stoeva, Peter Balazs
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Authors:

Diana T Stoeva, Peter Balazs

Description:

The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the unconditional convergence of multipliers, sufficient and/or necessary conditions for the invertibility of multipliers, and representation of the inverse via Newmann-like series and via multipliers with particular parameters. Multipliers for frames with specific structure, namely, Gabor and wavelet multipliers, are also considered. Some of the results for the representation of the inverse multiplier are implemented in Matlab codes and the implementations are described.

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On the Dual Frame Induced by an Invertible Frame Multiplier

Peter Balazs
:read more

Authors:

Peter Balazs

Description:

Recently it has been established that given an invertible frame multiplier with semi-normalized symbol, a specific dual of any of the two involved frames can be determined by the inversion process. The inverse can be represented as a multiplier with the reciprocal symbol, this particular dual of one of the given frames, and any dual of the other frame. The specific dual is the only one having this property among all Bessel sequences. In this manuscript we extend the results showing that the specific dual with the above mentioned property is unique among all possible sequences. Furthermore, the symbol is allowed to be not necessarily semi-normalized. Finally we characterize cases when the canonical dual frame and the new specific dual frame coincide.

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LTFAT Reference manual

Peter L Søndergaard, Peter Balazs, Monika Dörfler, Nicki Holighaus, Florent Jaillet, Na…
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Authors:	Peter L Søndergaard, Peter Balazs, Monika Dörfler, Nicki Holighaus, Florent Jaillet, Nathanael Perraudin, Zdenek Pruša, Kai Siedenburg, Bruno Torrésani, Christoph Wiesmeyr, Jordy van Velthoven
Description:	The first line defines a key/value pair with the key’L’having an initial value of [](the empty matrix). The second line defines a group of flags by the name of phase. The group phase contains the flags’ freqinv’and’timeinv’, which can both be specified on the command line by the user. The groupname phase is just for internal use, and does not appear to the user. The flag mentioned first in the list will be selected by default, and only one flag in a group can be selected at any time. A group can contain as many flags as desired.
Resources:	[PDF] from researchgate.net

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Frames and semi-frames—Erratum

Jean-Pierre Antoine, Peter Balazs
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Authors:	Jean-Pierre Antoine, Peter Balazs
Description:	The article [2] contains a few minor errors, which could be confusing for the reader. Hence this erratum, that concerns 3 different sections.

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LTFAT: The Large Time-Frequency Analysis Toolbox v. 1.4

Peter L Søndergaard, Zdenek Pruˇsa, Nicki Holighaus, Peter Balazs
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Authors:	Peter L Søndergaard, Zdenek Pruˇsa, Nicki Holighaus, Peter Balazs
Description:	The Linear Time Frequency Analysis Toolbox (LTFAT) is a Matlab/Octave toolbox for doing time-frequency analysis. It is intended both as an educational and a computational tool.
Resources:	[PDF] from ltfat.org

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Chun, Il Yong, 460 Cohl, Howard, 246 Cuadros, Angela, 548 Dörfler, Monika, 152

Stefano De Marchi, Akram Aldroubi, Arash Amini, Joakim Andén, Stephan Antholzer, Gonzal…
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Authors:

Stefano De Marchi, Akram Aldroubi, Arash Amini, Joakim Andén, Stephan Antholzer, Gonzalo Arce, Richard Archibald, Enrico Au-Yeung, Amir Averbuch, Benjamın Béjar, Peter Balazs, Laura Balzano, Roswitha Bammer, Afonso Bandeira, Francesca Bartolucci, Saeed Basirian, Matthias Beckmann, Mouhacine Benosman, Ronny Bergmann, Brett Bernstein, Ayush Bhandari, Holger Boche, Mahdi Boloursaz Mashhadi, Anna Breger, Yoram Bresler, Alex Bronstein, Simone Brugiapaglia, Carlos Cabrelli, Valerio Cambareri, Timothy Carson, Peter Casazza, Stephen D Casey, Gilles Chardon, Zhihua Che, Yuejie Chi, Ole Christensen, Filippo De Mari, Ernesto De Vito, Benedikt Diederichs, Markus Dielacher, Sjoerd Dirksen, S Djordjevic, Monika Doerfler, Pier Luigi Dragotti, Miguel Alejandro Duval Poo, Martin Ehler, Usama Elahi, Yonina C Eldar, Wolfgang Erb, Ashkan Esmaeili, Hartmut Fuhr, Maryam Fallah, Yuri Farkov, Markus Faulhuber, Joe-Mei Feng, Carmen Fernández, Aingeru Fernandez-Bertolin, Carlos Fernandez-Granda, Jeff Fessler, Simon Foucart, Akshay Gadde, Lu Gan, Saakshi Garg, Martin Genzel, Jakob Geppert, Davis Gilton, Raja Giryes, Michel Goemans, Boris Golubov, Thomas Grill

Description:

2017 International Conference on Sampling Theory and Applications (SampTA) Page 1 Authors Abbasi, Ehsan, 101 Abreu, Luıs Daniel, 188, 199, 283 Aceska, Roza, 41 Adcock, Ben, 533 Aizenbud, Yariv, 635 Aldroubi, Akram, 46, 409 Amini, Arash, 499 Andén, Joakim, 169 Antholzer, Stephan, 556 Arce, Gonzalo, 548 Archibald, Richard, 533 Au-Yeung, Enrico, 570 Averbuch, Amir, 635 Béjar, Benjamın, 364 Balazs, Peter, 288 Balzano, Laura, 456 Bammer, Roswitha, 152, 299 Bandeira, Afonso, 124 Bartolucci, Francesca, 625 Basirian, Saeed, 427 Beckmann, Matthias, 251 Benosman, Mouhacine, 451 Bergmann, Ronny, 396 Bernstein, Brett, 60 Bhandari, Ayush, 31, 475, 649 Boche, Holger, 26, 336, 484, 494 Boloursaz Mashhadi, Mahdi, 266 Breger, Anna, 617 Bresler, Yoram, 119 Bronstein, Alex, 138 Brugiapaglia, Simone, 533 Cabrelli, Carlos, 50, 391 Cambareri, Valerio, 241 Carson, Timothy, 73 Casazza, Peter, 377 …

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WEIGHTED AND CONTROLLED FRAMES: MUTUAL RELATIONSHIP ANS SOME NUMERICAL PROPERTIES

Peter Balazs, Jean-Pierre Antoine, Anna Grybos
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Authors:	Peter Balazs, Jean-Pierre Antoine, Anna Grybos
Description:	Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while offering a numerical advantage in the sense of preconditioning. Next, we investigate weighted frames, in particular their relation to controlled frames. We consider the special case of semi-normalized weights, where the concepts of weighted frames and standard frames are interchangeable. We also make the connection with frame multipliers. Finally we analyze weighted frames numerically. First we investigate three possibilities for finding weights in order to tighten a given frame, ie, decrease the frame bound ratio. Then we examine Gabor frames and how well the canonical dual of a weighted frame is approximated by the inversely weighted dual frame.
Resources:	[PDF] from researchgate.net

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Frames for signals and linear operators: workhorse for acoustical modelling and estimation (-FLAME-)(60 ze

Peter Balazs
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Authors:

Peter Balazs

Description:

We are extending methods first presented in [A. Olivero and Torrsani, 2009, Olivero et al., pear] and apply it to speech signals. The method estimates the multiplier between two signals with regularization terms. The similarity between the two signals is then judged by a norm on the symbol. For two speech signals the frame multiplier will be estimated (using the algorithm presented in [Olivero et al., pear] which maps one signal into each other). We are going to use timefrequency shift as in MaskingPursuit [Depalle et al., 2007] and Section??. In a first step we are following the standard approach in [Olivero et al., pear]. At ARI a lot of speech signals with meta-data exist. For first numerical test we are going to use signals with approximately the same duration and fundamental frequency.

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LTFAT: The Linear Time-Frequency Analysis Toolbox v. 1.0

Peter Søndergaard, Bruno Torresani, Peter Balazs
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Authors:

Peter Søndergaard, Bruno Torresani, Peter Balazs

Description:

The Linear Time Frequency Analysis Toolbox (LTFAT) is a Matlab/Octave toolbox for doing time-frequency analysis. It is intended both as an educational and a computational tool. The toolbox contains tools for Fourier analysis, Gabor analysis, time-frequency bases, filterbanks, non-stationary Gabor systems, sparse regression, reassignment and instantaneous frequency estimation, non-linear reconstruction from magnitude of coefficients and basic auditory scales and filters. To facilitate in learning the toolbox, a number of demos are provided with the toolbox.

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Thoughts on the canonical dual of an over-complete wavelet frame in Cl

Peter Balazs
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Authors:

Peter Balazs

Description:

Let F (L) be the finite-dimensional Fourier transform F (L): CL→ CL, this is implemented using the FFT. We denote the continuous version by F: L2→ L2. We denote the discrete version by F (d): l2→ L2. In all cases we shorten notation by using f↦→ ˆf, hoping to still avoid confusion. Let us use a notation for the sampling operator, for f∈ L2 (R) let [f] T∈ l2, where [f] T (k)= f (kT). In this case we have F (L)[f] T (k)= P p

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A Review of the Invertibility of Frame Multipliers

Peter Balazs, Diana T Stoeva
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Authors:	Peter Balazs, Diana T Stoeva
Description:	In this paper we give a review of recent results on the invertibility of frame multipliers Mm, Φ, Ψ. In particular, we give sufficient, necessary or equivalent conditions for the invertibility of such operators, depending on the properties of the sequences Ψ, Φ and m. We consider Bessel sequences, frames, and Riesz bases.
Resources:	[PDF] from eurasip.org

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A STOCHASTIC 3D-MODEL FOR SIMULATING VIBRATIONS IN SOIL LAYERS

W Kreuzer, H Waubke, P Balazs
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Authors:

W Kreuzer, H Waubke, P Balazs

Description:

A major problem for the simulation of vibrations in soil is that material parameters cannot be measured exactly. To avoid this problem stochastic models can be used, but these have the general drawback that the linear system of equations which has to be solved is very large and thus a lot of computer and memory resources are needed. We present ideas for a model that allows the use of stochastic parameters, but also reduces the high costs of solving the system of equations with a special iteration scheme.

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Frame Multiplier and Irregular Gabor Filters with Application in Time Frequency Masking

Peter Balazs
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Authors:

Peter Balazs

Description:

This paper presents an overview and a summary on the mathematical background for time-frequency masking filters based on the concept of’frame multipliers’. Gabor multipliers are a current topic of research, known in signal processing as Gabor filters. Frame multipliers are a generalization of this type of time variant filters to frames without further structure. After analysis, before synthesis the coefficients are multiplied by a fixed pattern, the so called symbol. The dependency of the operator on the symbol and frames is presented here. The paper also investigates irregular Gabor frames. In particular the results on irregular Gabor filters are given such as the continuous dependency of Gabor filters on the symbol, the lattice and the windows. An approximation of arbitrary matrices by irregular Gabor multipliers is presented. Focusing on applications the finite-dimensional discrete case becomes important. An algorithm is …

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Design of Gabor dual windows using convex optimization

Nathanaël Perraudin, Nicki Holighaus, Peter L Søndergaard, Peter Balazs
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Authors:	Nathanaël Perraudin, Nicki Holighaus, Peter L Søndergaard, Peter Balazs
Description:	Design of Gabor dual windows using convex optimization Page 1 Design of Gabor dual windows using convex optimization Nathanaël Perraudin, Nicki Holighaus, Peter L. Søndergaard and Peter Balazs Acoustic Research Institute 13 march 2013, Wien Nathanaël Perraudin (ARI) Gabor windows using convex optimization 13.03.2013 1 / 35 Page 2 Overview 1 Introduction 2 Notation / Gabor theory 3 Proximal splitting methods 4 Methods 5 Numericals experiments Effect of different optimization function Compactly supported windows Tight windows 6 Conclusion Nathanaël Perraudin (ARI) Gabor windows using convex optimization 13.03.2013 2 / 35 Page 3 Why alternate Gabor dual windows? The canonical dual might not be nice. Alternate dual windows... can be chosen from an infinite number of possible duals provide different synthesis operations could be constructed satisfying important properties Nathanaël …
Resources:	[PDF] from academia.edu

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Frame multipliers-invertibility and representation for the inverse

Diana T Stoeva, Peter Balazs
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Authors:	Diana T Stoeva, Peter Balazs
Description:	In modern life, applications of signal processing can be found in numerous technical items, for example in wireless communication or medical imaging. In the last decade time-variant filters have found more and more applications. A particular way to implement such filters are Gabor multipliers [4], also known as Gabor filters [6]. Such operators find application for example in psychoacoustics [2] or measurement of acoustical systems [5]. In [1] the concept of Bessel multipliers, ie operators of the form
Resources:	[PDF] from researchgate.net

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Bessel, Frame and Riesz Multipliers

Peter Balazs
arXiv preprint math/0510091
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Authors:	Peter Balazs
Journal:	arXiv preprint math/0510091
Description:	This paper introduces the concept of Bessel and frame multipliers. These operators are defined by a fixed pattern, called the symbol, which is used after analysis, before synthesis. This concept is a generalization of Gabor multipliers. It allows specialization to any analysis/synthesis systems, that form Bessel sequences, like eg wavelet frames. Basic properties of this general class of operators are investigated in this paper. In particular the connection of the class of the symbol to the class of the operators is specified. The question, how the operator depends on a perturbation of the frames or the symbol, is also treated. As a special case the multipliers for Riesz bases are examined.

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New Concepts in Frame Theory Motivated by Acoustical Applications

Peter Balazs
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Authors:	Peter Balazs
Description:	Application-oriented mathematics develops theoretical results and new mathematical concepts, motivated by application, in contrast to “applied mathematics” focusing just on providing and applying mathematical tools for the applied sciences. The application-oriented approach produces results significant both for mathematics and the applied sciences. In this context we developed new concepts in frame theory motivated by signal processing and acoustical applications. Frames are generalizations of bases, and give more freedom for the analysis and modification of information. The concept of frames is a theoretical background for signal processing. On the other hand, signal processing algorithms and processes are essential for application in audio and acoustics. Linking the mathematical frame theory, the signal processing algorithms, their implementations and finally acoustical applications leads to a very promising, synergetic combination of research in different fields, which has not been fully exploited yet. To establish that link a thorough investigation of the theory is important. So we have investigated topics in frame theory, extending the standard mathematical concepts. As a particular case of analysis and synthesis systems we have researched mathematical topics in time-frequency analysis. Furthermore a big focus was the mathematical theory of multipliers, which are operators created by combining frame analysis, multiplication and resynthesis. To show that frame theory is important for applications we have included two applied topics, which both apply Gabor frame multipliers in acoustical projects.
Resources:	[PDF] from balazs.at

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The Interplay of Frames and Operators

Peter Balazs
arXiv preprint math/0510146
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Authors:	Peter Balazs
Journal:	arXiv preprint math/0510146
Description:	This paper will look at the connection of operators and frames respectively related sequences from different viewpoints. We will give a survey of the classification of frames and similar sequences by the properties of the associated operators. Furthermore an important part will be the investigation of how to find a matrix representation of operators with Bessel sequences, frames and Riesz bases. Apart from that we will extend the well-known fact, that frames are exactly the images of orthonormal bases using surjective bounded operators. We will also shortly investigate which operator keep the properties of these kind of sequences.

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Peter Balazs

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