Adaptive signal and system approximation and strong divergence

Holger Boche, Ullrich J. Monich

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

2 Scopus citations

Abstract

Many divergence results for sampling series are in terms of the limit superior and not the limit. This leaves the possibility of a convergent subsequence. If there exists a convergent subsequence, adaptive signal processing techniques can be used. In this paper we study sampling-based signal reconstruction and system approximation processes for the space PWπ1 of bandlimited signals with absolutely integrable Fourier transform. For all analyzed examples, which include the peak value of the Shannon and the conjugated Shannon sampling series, we prove strong divergence, i.e., divergence for all subsequences. Hence, adaptive signal processing techniques do not help in these cases. We further analyze whether an adaptive choice of the reconstruction functions in the oversampling case can improve the behavior.

Original languageEnglish
Title of host publication2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3616-3620
Number of pages5
ISBN (Electronic)9781467369978
DOIs
StatePublished - 4 Aug 2015
Event40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia
Duration: 19 Apr 201424 Apr 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2015-August
ISSN (Print)1520-6149

Conference

Conference40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
Country/TerritoryAustralia
CityBrisbane
Period19/04/1424/04/14

Keywords

  • Hilbert transform
  • Paley-Wiener space
  • linear time-invariant system
  • reconstruction
  • strong divergence

Fingerprint

Dive into the research topics of 'Adaptive signal and system approximation and strong divergence'. Together they form a unique fingerprint.

Cite this