The uniformity of non-uniform Gabor bases
type: Item
instance of: scholarly article
title: The uniformity of non-uniform Gabor bases
zbMATH Open document ID: 1019.42023
DOI: 10.1023/A:1021350103925
author: Yang Wang
author: Youming Liu
published in: Advances in Computational Mathematics
publication date: 2003-04-10T00:00:00Z
review text: It is well known that the 1-dimensional regular Gabor system \(\{e^{2\pi imx}g(x-n) \}_{m,n\in\mathbb{Z}}\) forms an orthonormal basis for \(L^2(\mathbb{R})\) if \(g=\chi_{[0,1]}\). The authors prove some kind of inverse statement related to irregular Gabor systems of the form \(\{e^{2\pi i\lambda x}g(x-p) \}_{\lambda\in F,p\in I}\), where \(F,I\) are discrete subsets of \(\mathbb{R}\): if such a system is an orthonormal basis and the support of \(g\) is an interval \(\Omega\), then the time-frequency shifts necessarily forms a lattice and \(|g|=c\chi_\Omega\). However, for just compactly supported generator functions, irregular Gabor orthonormal bases are proven to exist (also in higher dimensions).
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1896708
zbMATH Keywords: orthonormal basis
zbMATH Keywords: irregular Gabor systems
MaRDI profile type: Publication
full work available at URL: a:1021350103925
OpenAlex ID: W154532047
description: scientific article; zbMATH DE number 1896708