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An optimally concentrated Gabor transform for localized time-frequency components

Ricaud, Benjamin ; Stempfel, Guillaume ; Torrésani, Bruno ; Wiesmeyr, Christoph ; Lachambre, Hélène ; Onchis, Darian

In: Advances in Computational Mathematics, 2014, vol. 40, no. 3, p. 683-702

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    Titre
    • An optimally concentrated Gabor transform for localized time-frequency components
    Auteur
    • Ricaud, Benjamin. Signal Processing Laboratory 2, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 11, 1015, Lausanne, Switzerland
    • Stempfel, Guillaume. Genesis, Domaine du Petit Arbois, BP 69, 13545, Aix-en-Provence, France
    • Torrésani, Bruno. Aix-Marseille Université, CNRS, Centrale Marseille, LATP, UMR7353, 13453, Marseille, France
    • Wiesmeyr, Christoph. Faculty of Mathematics, University of Vienna, NuHAG, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria
    • Lachambre, Hélène. Genesis, Domaine du Petit Arbois, BP 69, 13545, Aix-en-Provence, France
    • Onchis, Darian. Faculty of Engineering and Management, Department of Electrical Engineering and Industrial Informatics, Eftimie Murgu University, Resita, Romania
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Advances in Computational Mathematics, 2014, vol. 40, no. 3, p. 683-702. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:326524
    Summary
    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.