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Advances in Computational Mathematics

, Volume 40, Issue 3, pp 683–702 | Cite as

An optimally concentrated Gabor transform for localized time-frequency components

  • Benjamin Ricaud
  • Guillaume Stempfel
  • Bruno Torrésani
  • Christoph Wiesmeyr
  • Hélène Lachambre
  • Darian Onchis
Article

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.

Keywords

Gabor transform Time-frequency analysis Optimization Sparsity Signal processing Audio 

Mathematics Subject Classifications (2010)

65K10 65T99 42C15 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Benjamin Ricaud
    • 1
  • Guillaume Stempfel
    • 2
  • Bruno Torrésani
    • 3
  • Christoph Wiesmeyr
    • 4
  • Hélène Lachambre
    • 2
  • Darian Onchis
    • 5
  1. 1.Signal Processing Laboratory 2Ecole Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  2. 2.GenesisAix-en-ProvenceFrance
  3. 3.Aix-Marseille Université, CNRSCentrale Marseille, LATP, UMR7353MarseilleFrance
  4. 4.Faculty of MathematicsUniversity of Vienna, NuHAGWienAustria
  5. 5.Faculty of Engineering and ManagementDepartment of Electrical Engineering and Industrial Informatics, Eftimie Murgu UniversityResitaRomania

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