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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Vydáno v:Applied and computational harmonic analysis Ročník 10; číslo 1; s. 45 - 60
Hlavní autoři: Partington, J.R., Ünalmış, Banu
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 2001
Témata:
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
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Shrnutí: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