Continuous linear decompositions
Time-frequency analysis. Wavelets - Theory
Article REF: AF4510 V1
Continuous linear decompositions
Time-frequency analysis. Wavelets - Theory

Authors : José MARTINEZ, Pierre GAJAN, Alain STRZELECKI

Publication date: April 10, 2002, Review date: February 4, 2020 | Lire en français

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1. Continuous linear decompositions

1.1 Fourier with sliding window

To carry out a local spectral analysis of a signal s(t) around an arbitrary time t0 , we need to calculate a Fourier transform (FT) of the immediate vicinity of this point. Since the Fourier integral requires an infinite integration time, this implies that the local aspect is introduced by looking at the signal only within a certain interval T close to

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