On the windowed Fourier transform and wavelet transform of almost periodic functions


Partington J., Unalmis B.

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, vol.10, no.1, pp.45-60, 2001 (SCI-Expanded) identifier identifier

Abstract

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. (C) 2001 Academic Press.