Title :
Biorthogonal-like sequences and generalized Gabor expansions of discrete-time signals in l2(Z)
Author :
Lu, Youhong ; Morris, Joel M.
Author_Institution :
Dept. of Electr. Eng., Maryland Univ., Baltimore, MD, USA
fDate :
31 Oct-2 Nov 1994
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
Keywords :
Fourier transforms; band-pass filters; filtering theory; sequences; signal representation; time-frequency analysis; Hilbert space; algorithm; analysis filter; biorthogonal-like condition; biorthogonal-like sequences; discrete-time signals; filterbank summation; generalized Gabor expansions; generalized short-time Fourier transform; joint time-frequency domain; signal representation; synthesis filter; Band pass filters; Equations; Filter bank; Gabor filters; Hilbert space; Signal analysis; Signal generators; Signal synthesis; Stability; Time frequency analysis;
Conference_Titel :
Signals, Systems and Computers, 1994. 1994 Conference Record of the Twenty-Eighth Asilomar Conference on
Conference_Location :
Pacific Grove, CA
Print_ISBN :
0-8186-6405-3
DOI :
10.1109/ACSSC.1994.471629
