Can every analog system be simulated on a digital computer?

Holger Boche, Volker Pohl

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

4 Scopus citations

Abstract

A Turing machine is a model describing the fundamental limits of any realizable computer, digital signal processor (DSP), or field programmable gate array (FPGA). This paper shows that there exist very simple linear time-invariant (LTI) systems which can not be simulated on a Turing machine. In particular, this paper considers the linear system described by the voltage-current relation of an ideal capacitor. For this system, it is shown that there exist continuously differentiable and computable input signals such that the output signal is a continuous function which is not computable. Moreover, for this particular system, we present sharp results characterizing computable input signals which guarantee that the output signal is computable. Additionally, it is shown that the computability of the step response of an LTI system does not necessarily imply that the impulse response is computable.

Original languageEnglish
Title of host publication2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1783-1787
Number of pages5
ISBN (Electronic)9781509066315
DOIs
StatePublished - May 2020
Event2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Barcelona, Spain
Duration: 4 May 20208 May 2020

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2020-May
ISSN (Print)1520-6149

Conference

Conference2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020
Country/TerritorySpain
CityBarcelona
Period4/05/208/05/20

Keywords

  • Computability
  • Linear time-invariant systems
  • Stable systems
  • Turing machines

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