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TIME-DOMAIN CONCENTRATION AND APPROXIMATION OF COMPUTABLE BANDLIMITED SIGNALS

Citation Author(s):
Holger Boche, Ullrich J. Mönich
Submitted by:
Ullrich Moenich
Last updated:
22 June 2021 - 4:08am
Document Type:
Poster
Document Year:
2021
Event:
Presenters Name:
Ullrich J. Mönich

Abstract 

Abstract: 

Turing computability deals with the question of what is theoretically computable on a digital computer, and hence is relevant whenever digital hardware is used. In this paper we study different possibilities to define computable bandlimited signals and systems. We consider a definition that uses finite Shannon sampling series as approximating functions and another that employs computable continuous functions together with an effectively computable time concentration. We discuss the advantages and drawbacks of both definitions and analyze the connections and differences. In particular, we show that both definitions are equivalent for many practically relevant signal classes, e.g. for bandlimited signals with finite energy, but also that there are important differences, such as for the impulse responses of BIBO stable LTI systems.

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Poster of the ICASSP 2021 presentation

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