On the Fourier Representation of Computable Continuous Signals

Holger Boche, Ullrich J. Monich

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

9 Scopus citations

Abstract

In this paper we study whether it is possible to decide algorithmically if the Fourier series of a continuous function converges uniformly. We show that this decision cannot be made algorithmically, because there exists no Turing machine that can decide for each and every continuous functions whether its Fourier series converges uniformly. Turing computability describes the theoretical feasible that can be implemented on a digital computer, hence the result shows that there exists no algorithm that can perform this decision.

Original languageEnglish
Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5013-5017
Number of pages5
ISBN (Electronic)9781479981311
DOIs
StatePublished - May 2019
Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: 12 May 201917 May 2019

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2019-May
ISSN (Print)1520-6149

Conference

Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
Country/TerritoryUnited Kingdom
CityBrighton
Period12/05/1917/05/19

Keywords

  • Fourier series
  • Turing computability
  • continuous function
  • uniform convergence

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