Exponential approximation of multivariate bandlimited functions from average oversampling. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Chen, Wenjian; Zhang, Haizhang
• Is Part Of: Applicable analysis. Volume 101:Issue 1(2022)
• Page Start: 63
• Page End: 80
• Publication Date: 2022-01-02
• Subjects: Average sampling -- exponential decayness -- multivariate bandlimited functions -- the Shannon sampling theorem; 41A25 -- 62D05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1728258
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an exponentially-decaying approximation error to reconstruct a multivariate bandlimited function from its finite average oversampling data. The key problem in our analysis is how to extend a function so that its inverse Fourier transform decays at an optimal rate to zero at infinity.