Adaptive Signal Models

Goodwin, Michael M.

doi:10.1007/978-1-4419-8628-3

Cited by 41 publications

(6 citation statements)

References 179 publications

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“…This fact brings the convergence problem in the process of approximation. In order to solve this problem, one can use the orthogonal matching pursuit (OMP) algorithm [ 12 ].…”

Section: Basic Matching Pursuit Algorithmmentioning

confidence: 99%

Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm

Kaplun

Voznesenskiy

Romanov

et al. 2019

Entropy

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In this paper, we consider the application of the matching pursuit algorithm (MPA) for spectral analysis of non-stationary signals. First, we estimate the approximation error and the performance time for various MPA modifications and parameters using central processor unit and graphics processing unit (GPU) to identify possible ways to improve the algorithm. Next, we propose the modifications of discrete wavelet transform (DWT) and package wavelet decomposition (PWD) for further use in MPA. We explicitly show that the optimal decomposition level, defined as a level with minimum entropy, in DWT and PWD provides the minimum approximation error and the smallest execution time when applied in MPA as a rough estimate in the case of using wavelets as basis functions (atoms). We provide an example of entropy-based estimation for optimal decomposition level in spectral analysis of seismic signals. The proposed modification of the algorithm significantly reduces its computational costs. Results of spectral analysis obtained with MPA can be used for various signal processing applications, including denoising, clustering, classification, and parameter estimation.

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“…This fact brings the convergence problem in the process of approximation. In order to solve this problem, one can use the orthogonal matching pursuit (OMP) algorithm [ 12 ].…”

Section: Basic Matching Pursuit Algorithmmentioning

confidence: 99%

Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm

Kaplun

Voznesenskiy

Romanov

et al. 2019

Entropy

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“…Taken together, the coefficients and the functions build the complete representation (expansion) of a signal: the more compact (sparse) this representation is, the more the functions are correlated to the signal (see (Goodwin 1998)).…”

Section: Basic Signal Modelsmentioning

confidence: 99%

Symbolic Representations for Music

Marsden¹

1996

New Technologies for the Humanities

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I first would like to thank to my supervisor, Prof. Fabio Bellissima, for his careful guidance during my study years and for his friendship. I'll never forget our meetings in Siena. I also would like to thank my co-advisor, Prof. G. Corsi, for the continuous support given during these years. I am extremely grateful to Moreno Andreatta, Carlos Agon and Gerard Assyag, for hosting me at the Musical representations team at IRCAM and to Ichiro Fujinaga for hosting me at McGill University. Thanks to Juan Josè Burred, Philippe Esling, Arnaud Dessein and Niels Bogaards for reviewing and discussing the manuscripts and for their great friendship. Finally, I am really thankful to my great family: Bernardino, Ornella, Leonardo and Sara. Without them my life is completely meaningless; this work is dedicated to them.

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“…The strong onset is taken into account by the introduction in the model of the delay parameters {t m }. Other approaches to handle this problem can be found in [8], [10], [16], [17], [21].…”

Section: B Damping Factor Sign and Compact Representationmentioning

confidence: 99%

Damped and delayed sinusoidal model for transient signals

Boyer

Abed-Meraim

2005

IEEE Trans. Signal Process.

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Abstract-In this work, we present the Damped and Delayed Sinusoidal (DDS) model, a generalization of the sinusoidal model. This model takes into account an angular frequency, a damping factor, a phase, an amplitude and a timedelay parameter for each component. Two algorithms are introduced for the DDS parameter estimation using a subband processing approach. Finally, we derive the CramerRao Bound (CRB) expression for the DDS model and a simulation-based performance analysis in the context of a noisy fast time-varying synthetic signal and in the audio transient signal modeling context.

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Adaptive Signal Models

Cited by 41 publications

References 179 publications

Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm

Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm

Symbolic Representations for Music

Damped and delayed sinusoidal model for transient signals

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