The wavelet transform, time-frequency localization and signal analysis

Authors:
I. Daubechies
Affiliations:
Math. Dept., Michigan Univ., Ann Arbor, MI
Venue:
IEEE Transactions on Information Theory
Year:
2006

Citing 0
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Abstract

Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied. The first procedure is the short-time or windowed Fourier transform; the second is the wavelet transform, in which high-frequency components are studied with sharper time resolution than low-frequency components. The similarities and the differences between these two methods are discussed. For both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time-frequency density. Finally, the notion of time-frequency localization is made precise, within this framework, by two localization theorems