Structural properties of Gabor transforms and numerical algorithms

Sigang Qiu

doi:10.1117/12.205457

6 April 1995 Structural properties of Gabor transforms and numerical algorithms

Sigang Qiu

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205457
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

Let g be a Gabor window of length N, (a,b) be a pair of lattice constants. The time and frequency translates {M_mbT_nag} 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) $CBAR^N 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.

Citation Download Citation

Sigang Qiu "Structural properties of Gabor transforms and numerical algorithms", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205457

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