Article | REF: AF4510 V1

Time-frequency analysis. Wavelets - Theory

Authors: José MARTINEZ, Pierre GAJAN, Alain STRZELECKI

Publication date: April 10, 2002, Review date: February 4, 2020

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2. Signal laws

Determining the laws of a signal (amplitude and frequency modulations) is a problem we're trying to solve in many fields (acoustics, radar and sonar detection, etc.). The time-frequency methods mentioned (atomic decompositions or energy distributions) can be used to approximate these modulations. Energy distributions naturally find a privileged field of application here. We define here an equivalent for algorithms related to atomic decompositions, using wavelet analysis as a basic tool. The transposition to the case of FFGs is immediate and yields similar results.

2.1 Analytical signal

By analogy with the formalism of quantum mechanics, D. Gabor and then J. Ville

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Signal laws