On the Computability of System Approximations under Causality Constraints

Holger Boche, Volker Pohl

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragBegutachtung

Abstract

Approximating the transfer function of stable causal linear systems by a basis expansion is a common task in signal-and system theory. This paper characterizes a scale of signal spaces, containing stable causal transfer functions, with a very simple basis (the Fourier basis) but which is not computable. Thus it is not possible to determine the coefficients of this basis expansion on any digital computer such that the approximation converges to the desired function. Since the Fourier basis is not computable, the second part of the paper investigates whether there exist better bases. To this end, the notion of a computational basis is introduced and it is shown that there exists no computational basis in these spaces. The paper characterizes also subspaces on which computational bases do exist.

OriginalspracheEnglisch
Titel2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
Herausgeber (Verlag)Institute of Electrical and Electronics Engineers Inc.
Seiten4559-4563
Seitenumfang5
ISBN (Print)9781538646588
DOIs
PublikationsstatusVeröffentlicht - 10 Sept. 2018
Veranstaltung2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Calgary, Kanada
Dauer: 15 Apr. 201820 Apr. 2018

Publikationsreihe

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Band2018-April
ISSN (Print)1520-6149

Konferenz

Konferenz2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
Land/GebietKanada
OrtCalgary
Zeitraum15/04/1820/04/18

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