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An optimally concentrated Gabor transform for localized time-frequency components

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Abstract

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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Authors and Affiliations

  1. Signal Processing Laboratory 2, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 11, 1015, Lausanne, Switzerland

    Benjamin Ricaud

  2. Genesis, Domaine du Petit Arbois, BP 69, 13545, Aix-en-Provence, France

    Guillaume Stempfel & Hélène Lachambre

  3. Aix-Marseille Université, CNRS, Centrale Marseille, LATP, UMR7353, 13453, Marseille, France

    Bruno Torrésani

  4. Faculty of Mathematics, University of Vienna, NuHAG, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria

    Christoph Wiesmeyr

  5. Faculty of Engineering and Management, Department of Electrical Engineering and Industrial Informatics, Eftimie Murgu University, Resita, Romania

    Darian Onchis

Authors
  1. Benjamin Ricaud
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  2. Guillaume Stempfel
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  3. Bruno Torrésani
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  4. Christoph Wiesmeyr
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  5. Hélène Lachambre
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  6. Darian Onchis
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Corresponding author

Correspondence to Benjamin Ricaud.

Additional information

Communicated by: Peter Maass, Hans G. Feichtinger, Bruno Torresani, Darian M. Onchis, Benjamin Ricaud and David Shuman

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Ricaud, B., Stempfel, G., Torrésani, B. et al. An optimally concentrated Gabor transform for localized time-frequency components. Adv Comput Math 40, 683–702 (2014). https://doi.org/10.1007/s10444-013-9337-9

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  • DOI: https://doi.org/10.1007/s10444-013-9337-9

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