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research article

An optimally concentrated Gabor transform for localized time-frequency components

Ricaud, Benjamin  
•
Stempfel, Guillaume
•
Torresani, Bruno
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2014
Advances In Computational Mathematics

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on l (p) -norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples.

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Type
research article
DOI
10.1007/s10444-013-9337-9
Web of Science ID

WOS:000337080800006

Author(s)
Ricaud, Benjamin  
Stempfel, Guillaume
Torresani, Bruno
Wiesmeyr, Christoph
Lachambre, Helene
Onchis, Darian
Date Issued

2014

Publisher

Springer

Published in
Advances In Computational Mathematics
Volume

40

Issue

3

Start page

683

End page

702

Subjects

Gabor transform

•

Time-frequency analysis

•

Optimization

•

Sparsity

•

Signal processing

•

Audio

Note

National Licences

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LTS2  
Available on Infoscience
August 29, 2014
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/106503
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