NDLI: Generalized Gabor expansions of discrete-time signals in l/sup 2/(Z) via biorthogonal-like sequences

Content Provider	IEEE Xplore Digital Library
Author	Morris, J.M. Youhong Lu
Copyright Year	1991
Abstract	In this paper, a biorthogonal-like sequences (BLS) theory and its application to the generalized Gabor expansions (equivalently, the generalized short-time Fourier transform/filterbank summation) are presented. A pair of BLS's are defined to be two sequences satisfying a biorthogonal-like condition (BLC), which is a moment equation and equivalent to a linear difference equation. We show that two collections in a Hilbert space generated by a pair of BLS's in the joint time-frequency domain are complete, either can be used as an analysis filter, and the other can be used as a synthesis filter for a generalized Gabor expansion of discrete-time signals. A sufficient and necessary condition on the existence of BLS's based on the moment equation is presented, which is simpler to use than frame theory. Given a filter generating a frame, its BLS's also generate frames. The dual frame is one of them. Given a FIR analysis/synthesis filter, there is a FIR synthesis/analysis filter if BLS's exist. The algorithm to compute FIR analysis and synthesis filters based on the linear difference equation is presented in this paper, which is simpler than frame operator.
Sponsorship	IEEE Signal Processing Society
Starting Page	1378
Ending Page	1391
Page Count	14
File Size	1345526
File Format	PDF
ISSN	1053587X
Volume Number	44
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1996-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Finite impulse response filter Difference equations Gabor filters Signal synthesis Fourier transforms Filter bank Hilbert space Signal generators Time frequency analysis Signal analysis
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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