Wavelets and applications : Time-frequency and time-scale analysis

Time-frequency and time-scale analysis
Wavelets and applications

Authors : Béatrice PESQUET-POPESCU, Jean-Christophe PESQUET

Review date: November 1, 2015 | Lire en français

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1. Time-frequency and time-scale analysis

Consider a continuous-time signal s (t ) of finite energy: ${‖ s ‖}^{2} = \int_{- \infty}^{\infty} {| s (t) |}^{2} d t$

A traditional tool for analyzing this signal is its Fourier transform[38], defined by : $S (f) =$

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Time-frequency and time-scale analysis

(1) - ABRAMOVICH (F.), SAPATINAS (T.), SILVERMAN (B.W.) - Wavelet thresholding via a bayesian approach. - J.R. Statist. Soc. B, 60, p. 725-749, 1998.
(2) - ABRY (P.) - Ondelettes et Turbulences. Multirésolutions, algorithmes de décompositions, invariance d'échelle et signaux de pression. - Diderot,...

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