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Proceedings Paper

Structural properties of Gabor transforms and numerical algorithms
Author(s): Sigang Qiu
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Paper Abstract

Let g be a Gabor window of length N, (a,b) be a pair of lattice constants. The time and frequency translates {MmbTnag} of g forms so-called Gabor family (or Weyl-Heisenberg wavelet system). In this note, we present the structural properties of the discrete Gabor transforms, and determine the best approximation of a signal (chi) (epsilon) $CBARN in a very general case by linear combinations from a given Gabor family (we do not assume here whether this family forms a frame or not). For this task, we are determining the (generalized) dual Gabor atom. We propose the conjugate-gradient (CG)- method with O(N) complexity for fixed lattice constants (a,b) to solve the problem.

Paper Details

Date Published: 6 April 1995
PDF: 12 pages
Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); doi: 10.1117/12.205457
Show Author Affiliations
Sigang Qiu, Univ. of Connecticut (United States)

Published in SPIE Proceedings Vol. 2491:
Wavelet Applications II
Harold H. Szu, Editor(s)

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