Discrete Gabor transforms: The Gabor-Gram matrix approach
type: Item
instance of: scholarly article
title: Discrete Gabor transforms: The Gabor-Gram matrix approach
zbMATH Open document ID: 0915.65145
DOI: 10.1007/BF02475925
author: Sigang Qiu
published in: The Journal of Fourier Analysis and Applications
publication date: 1999-06-15T00:00:00Z
full work available at URL: https://eudml.org/doc/59550
review text: The author develops efficient algorithms for the computation of Gabor coefficients and dual Gabor windows. In contrast to the matrix of the frame operator \(\text{GG}^*\) considered by \textit{S. Qiu} [Optical Eng. 34, No. 10, 2872-2878 (1995)], he studies the matrix \(\text{GM}= \text{G}^*\text{G}\). He shows that GM consists of circulant blocks. Further, if \(n\) divides \(ab\), then these blocks are arranged in a circulant manner. Consequently, matrix-vector multiplication with GM can be performed in an efficient way by using fast Fourier transforms. Applying this fact, the author proposes an efficient iterative algorithm (conjugate gradient algorithm) to compute the Gabor coefficients and the dual Gabor window. Numerical examples are included.
Mathematics Subject Classification ID: 65T50
zbMATH DE Number: 1220784
zbMATH Keywords: discrete Gabor transform
zbMATH Keywords: Gabor-Gram matrix
zbMATH Keywords: conjugate gradient algorithm
zbMATH Keywords: numerical examples
zbMATH Keywords: Gabor coefficients
zbMATH Keywords: dual Gabor windows
zbMATH Keywords: fast Fourier transforms
zbMATH Keywords: iterative algorithm
reviewed by: Gabriele Steidl
MaRDI profile type: Publication
cites work: Q4365111
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description: scientific article; zbMATH DE number 1220784