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Title:
The wavelet transform, time-frequency localization and signal analysis
Authors:
Daubechies, Ingrid
Affiliation:
AA(AT&T Bell Laboratories, Murray Hill, NJ)
Publication:
IEEE Transactions on Information Theory (ISSN 0018-9448), vol. 36, Sept. 1990, p. 961-1005.
Publication Date:
09/1990
Category:
Communications and Radar
Origin:
STI
NASA/STI Keywords:
ORTHONORMAL FUNCTIONS, SIGNAL ANALYSIS, TIME DEPENDENCE, FOURIER TRANSFORMATION, PARAMETER IDENTIFICATION
Bibliographic Code:
1990ITIT...36..961D

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.
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Database: Astronomy
Physics
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