On the equivalence between classical and distributional convergence for Shannon type interpolation series and applications

Ezra Tampubolon, Holger Boche

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

Abstract

The distribution theory serves as an important theoretical foundation for some approaches arose from the engineering intuition. Particular examples are approaches based on the delta-”function”. We show that for the Shannon sampling/interpolation series (SSS/SIS) of continuous signals”vanishing” at infinity, the classical notion of convergence given in complex analysis is equivalent with the modern notion given by the distribution theory, in the sense that the SSS converges at a point on the real line, different from the sampling/interpolation point, if and only if it converges distributionally. This result is in spirit of Weyl's Lemma on the Laplace equation. As an extension, we give those results also for the sampling/interpolation series based on the sine-type function.

Original languageEnglish
Title of host publicationSCC 2017 - 11th International ITG Conference on Systems, Communications and Coding
PublisherVDE VERLAG GMBH
ISBN (Electronic)9783800743629
StatePublished - 2019
Event11th International ITG Conference on Systems, Communications and Coding, SCC 2017 - Hamburg, Germany
Duration: 6 Feb 20179 Feb 2017

Publication series

NameSCC 2017 - 11th International ITG Conference on Systems, Communications and Coding

Conference

Conference11th International ITG Conference on Systems, Communications and Coding, SCC 2017
Country/TerritoryGermany
CityHamburg
Period6/02/179/02/17

Keywords

  • Band-Limited interpolation
  • Convergence
  • Distribution Theory
  • Divergence
  • Shannon interpolation series
  • Shannon sampling series
  • Sine-type functions

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