## Biorthogonal-like sequences and generalized Gabor expansions of discrete-time signals in l/sup 2/(Z)

Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers (1994)

Pacific Grove, CA, USA

Oct. 31, 1994 to Nov. 2, 1994

ISSN: 1058-6393

ISBN: 0-8186-6405-3

pp: 1100-1104

Youhong Lu , Dept. of Electr. Eng., Maryland Univ., Baltimore, MD, USA

J.M. Morris , Dept. of Electr. Eng., Maryland Univ., Baltimore, MD, USA

ABSTRACT

A biorthogonal-like sequence (BLS) theory and its application to the generalized Gabor (1946) expansion (equivalently, the generalized short-time Fourier transform/filterbank summation) are presented. A pair of BLSs are defined to be two sequences satisfying a biorthogonal-like condition (BLC). We show that two collections in a Hilbert space generated by a pair of BLSs in the joint time-frequency domain are complete, and either can be used as an analysis filter, and the other as a synthesis filter, for a generalized Gabor expansion of discrete-time signals. An efficient algorithm for computation of BLSs is addressed in detail, and examples are presented to illustrate our results.<>

INDEX TERMS

sequences, filtering theory, time-frequency analysis, Fourier transforms, band-pass filters, signal representation

CITATION

Youhong Lu and J. Morris, "Biorthogonal-like sequences and generalized Gabor expansions of discrete-time signals in l/sup 2/(Z),"

*Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers(ACSSC)*, Pacific Grove, CA, USA, 1995, pp. 1100-1104.

doi:10.1109/ACSSC.1994.471629

CITATIONS