Local and global convergence behavior of non-equidistant sampling series

Holger Boche, Ullrich J. Mönich

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations

Abstract

In this paper we analyze the local and global convergence behavior of sampling series with non-equidistant sampling points for the Paley-Wiener space PWπ1 and sampling patterns that are made of the zeros of sine-type functions. It is proven that the sampling series are locally uniformly convergent if no oversampling is used and globally uniformly convergent if oversampling is used. Furthermore, we show that oversampling is indeed necessary for global uniform convergence, because for every sampling pattern there exists a signal such that the peak value of the approximation error grows arbitrarily large if no oversampling is used. Finally, we use these findings to obtain similar results for the mean-square convergence behavior of sampling series for bandlimited wide-sense stationary stochastic processes.

Original languageEnglish
Title of host publication2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009
Pages2945-2948
Number of pages4
DOIs
StatePublished - 2009
Externally publishedYes
Event2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009 - Taipei, Taiwan, Province of China
Duration: 19 Apr 200924 Apr 2009

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Conference

Conference2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009
Country/TerritoryTaiwan, Province of China
CityTaipei
Period19/04/0924/04/09

Keywords

  • Non-equidistant sampling
  • Reconstruction
  • Sampling series
  • Sine type
  • Stochastic process

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