Characterization of the pointwise and the peak value behavior of system approximation under thresholding

Holger Boche, Ullrich J. Mönich

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

Abstract

In this paper we study the system approximation process, which naturally emerges when a stable linear timeinvariant (LTI) system is applied on the Shannon sampling series, for the case that the samples of the signal are disturbed by the non-linear threshold operator, which sets all samples that are below some threshold to zero. We analyze its behavior for signals in the Paley-Wiener space PW1π of bandlimited signals with absolutely integrable Fourier transform as the threshold tends to zero. We treat the pointwise as well as the global behavior and characterize the systems for which there exist signals such that the approximation error diverges as the threshold tends to zero. We further show that for those systems in a certain topological sense almost all signals lead to divergence and that the divergence can be arbitrarily fast.

Original languageEnglish
Title of host publication2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2013
Pages759-763
Number of pages5
DOIs
StatePublished - 2013
Event2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2013 - Darmstadt, Germany
Duration: 16 Jun 201319 Jun 2013

Publication series

NameIEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC

Conference

Conference2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2013
Country/TerritoryGermany
CityDarmstadt
Period16/06/1319/06/13

Keywords

  • Paley-Wiener space
  • divergence speed
  • linear time invariant system
  • sampling series
  • threshold operator

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