The wavelet transform, time-frequency localization and signal analysis

Author

Daubechies, Ingrid

Author_Institution

Math. Dept., Michigan Univ., Ann Arbor, MI, USA

Volume

36

Issue

5

fYear

1990

fDate

9/1/1990 12:00:00 AM

Firstpage

961

Lastpage

1005

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

Keywords

Fourier transforms; signal processing; transforms; frequency analysis; reconstruction method; short time Fourier transform; signal analysis; stability; time-dependent signal; time-frequency density; time-frequency localization; wavelet transform; windowed Fourier transform; Fourier transforms; Lattices; Physics; Proposals; Reconstruction algorithms; Signal analysis; Signal resolution; Time frequency analysis; Wavelet analysis; Wavelet transforms;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.57199

Filename

57199