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Some Aspects of Non-Stationary Signal Processing with Emphasis on Time-Frequency and Time-Scale Methods

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Wavelets

Part of the book series: Inverse Problems and Theoretical Imaging ((IPTI))

Abstract

The analysis and the processing of nonstationary signals call for specific tools which go beyond Fourier analysis. This paper is intended to review most of the Signal Processing methods which have been proposed in this direction. Emphasis is put on time-frequency representations and on their time-scale versions which implicitly make use of “wavelet” concepts. Relationships between Gabor expansion, wavelet transform and ambiguity functions are detailed by considering signal decomposition as a detection-estimation problem. This permits one to make more precise some of the links which exist between time-frequency and time-scale.

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  1. Laboratoire de Traitement du Signal, UA 346 CNRS, ICPI, 25, Rue du Plat, F-69288, Lyon Cedex 02, France

    P. Flandrin

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  1. Centre National de la Recherche Scientifique, Luminy - Case 907, F-13288, Marseille Cedex 9, France

    Jean-Michel Combes , Alexander Grossmann  & Philippe Tchamitchian ,  & 

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Flandrin, P. (1989). Some Aspects of Non-Stationary Signal Processing with Emphasis on Time-Frequency and Time-Scale Methods. In: Combes, JM., Grossmann, A., Tchamitchian, P. (eds) Wavelets. Inverse Problems and Theoretical Imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97177-8_4

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