Ruhr-Uni-Bochum

Computable Time Concentration of Bandlimited Signals and Systems

2021

Conference / Medium

Authors

Ullrich J. Mönich Holger Boche

Research Hub

Research Hub A: Kryptographie der Zukunft
Research Hub B: Eingebettete Sicherheit

Research Challenges

RC 2: Quantum-Resistant Cryptography
RC 5: Physical-Layer Security

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.

Tags

Coding Theory
Complexity Theory
Implementation Attacks
Information Theory
Post-Quantum Cryptography