Sampling of bandlimited functions on unions of shifted lattices
type: Item
instance of: scholarly article
title: Sampling of bandlimited functions on unions of shifted lattices
zbMATH Open document ID: 1001.94013
author: Hamid Behmard
author: Adel Faridani
published in: The Journal of Fourier Analysis and Applications
publication date: 2002-07-08T00:00:00Z
review text: The authors consider the Shannon sampling theory for (multidimensional, not necessarily periodic) sampling sets that are unions of shifted lattices. This theory is presented in the general framework of Fourier transforms on a locally compact abelian group \(G\). Then a continuous function \(f\in L^2(G)\) is reconstructed from its samples if the sampling set and the support of the Fourier transform of \(f\) satisfy certain compatibility conditions. An explicit reconstruction formula of \(f\) is given for sampling sets that are unions of 2 shifted lattices. Several examples are given, including a numerical example implemented in MATLAB. These methods provide a new tool for designing sampling sets of minimal density.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 94C10
Mathematics Subject Classification ID: 43A25
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 42B10
zbMATH DE Number: 1757471
zbMATH Keywords: multidimensional sampling
zbMATH Keywords: nonuniform sampling
zbMATH Keywords: nonperiodic sampling
zbMATH Keywords: Shannon sampling theory
zbMATH Keywords: Fourier transforms
zbMATH Keywords: locally compact abelian group
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: s00041-002-0003-8
OpenAlex ID: W2150633517
DOI: 10.1007/S00041-002-0003-8
description: scientific article; zbMATH DE number 1757471