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Time-Frequency/Time-Scale Reassignment

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Wavelets and Signal Processing

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

This chapter reviews the reassignment principle, which aims at “sharpening” time-frequency and time-scale representations in order to improve their readability.

The basic idea, which simply consists in moving the time-frequency contributions from the point where they are computed to a more appropriate one, is presented first for the simple cases of the spectrogram and scalogram and then extended to general classes of time-frequency and time-scale energy distributions.

We further consider how the reassignment idea can be implemented efficiently and how it actually operates. Cases (with both deterministic and random signals) where closed-form expressions can be obtained offer the opportunity to better understand how reassignment works. We also give a geometrical characterization of the transform of the time-frequency plane made by the reassignment.

Finally, with two examples (signal de-noising and detection) we illustrate how the reassignment can be useful in practical signal processing applications.

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Authors
  1. Eric Chassande-Mottin
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  2. Francois Auger
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  3. Patrick Flandrin
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Editors and Affiliations

  1. Department of Mathematics, The University of Texas-Pan American, Edinburg, TX, 78539-2999, USA

    Lokenath Debnath

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Chassande-Mottin, E., Auger, F., Flandrin, P. (2003). Time-Frequency/Time-Scale Reassignment. In: Debnath, L. (eds) Wavelets and Signal Processing. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0025-3_8

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  • DOI: https://doi.org/10.1007/978-1-4612-0025-3_8

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6578-8

  • Online ISBN: 978-1-4612-0025-3

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