Characterizations of Gabor systems via the Fourier transform
type: Item
instance of: scholarly article
title: Characterizations of Gabor systems via the Fourier transform
zbMATH Open document ID: 0966.42021
author: Wojciech Czaja
published in: Collectanea Mathematica
publication date: 2001-02-18T00:00:00Z
full work available at URL: https://eudml.org/doc/41507
review text: Consider a set of functions \(g^1,...,g^L \in L^2(R^d)\). Given nondegenerate \(d \times d\) matrices \(A,B\), the associated Gabor system is the set of functions \(\{e^{2\pi i Am \cdot x} g^k(x- Bn) \}_{m,n \in Z^d, k=1,..,L}\). The paper gives (in terms of the Fourier transform) equivalent conditions for the Gabor system to be an orthogonal system in \(L^2(R^d)\) or a tight frame.
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1526489
zbMATH Keywords: Gabor frame
zbMATH Keywords: tight frame
zbMATH Keywords: orthonormal basis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1526489