Analysis of multiwindow Gabor-type schemes by frame methods
type: Item
instance of: scholarly article
title: Analysis of multiwindow Gabor-type schemes by frame methods
zbMATH Open document ID: 0885.42024
author: O. Diekmann
published in: Applied and Computational Harmonic Analysis
publication date: 1998-03-17T00:00:00Z
review text: The authors generalize the Gabor scheme by using several windows instead of a single window, i.e., \[ f(k)= \sum^R_{r= 0} c_{r,m,n} g_{r,m,n}(x),\quad g_{r,m,n}= g_r(x- na)e^{2\pi imbx}. \] Combining the Zak transform with the concept of frames, they characterize properties of the expansion coefficients \(g_{r,m,n}\) for the case where the product \(ab\) is a rational number. They consider the use of different sampling rates for each window as well as the application of nonexponential kernels. The authors examine the Balian-Low phenomenon in their context of multiwindows.
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 1038810
zbMATH Keywords: Gabor transform
zbMATH Keywords: Zak transform
zbMATH Keywords: frames
zbMATH Keywords: Balian-Low phenomenon
zbMATH Keywords: multiwindows
reviewed by: Gabriele Steidl
MaRDI profile type: Publication
full work available at URL: acha.1997.0209
OpenAlex ID: W1979303800
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DOI: 10.1006/ACHA.1997.0209
description: scientific article; zbMATH DE number 1038810