On the Windowed Fourier Transform and Wavelet Transform of Almost Periodic Functions

We present the windowed Fourier transform and wavelet transform as tools for analyzing persistent signals, such as bounded power signals and almost periodic functions. We establish the analogous Parseval-type identities. We consider discretized versions of these transforms and construct generalized...

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Bibliographic Details
Published in:Applied and computational harmonic analysis Vol. 10; no. 1; pp. 45 - 60
Main Authors: Partington, J.R., Ünalmış, Banu
Format: Journal Article
Language:English
Published: Elsevier Inc 2001
Subjects:
almost periodic function
bounded power signal
convolution
frame
generalized harmonic analysis
Parseval identity
shift-invariant operator
wavelet transform
windowed Fourier transform
almost periodic function
bounded power signal
windowed Fourier transform
wavelet transform
convolution
shift-invariant operator
generalized harmonic analysis
Parseval identity
frame
ISSN:1063-5203, 1096-603X
Online Access:Get full text
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Summary:We present the windowed Fourier transform and wavelet transform as tools for analyzing persistent signals, such as bounded power signals and almost periodic functions. We establish the analogous Parseval-type identities. We consider discretized versions of these transforms and construct generalized frame decompositions. Finally, we bring out some relations with shift-invariant operators and linear systems.
ISSN:1063-5203
1096-603X
DOI:10.1006/acha.2000.0326