Work

Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning

Year: 2023

Type: article

Abstract: This article compares two methods of algorithmically processing bandlimited time-continuous signals in light of the general problem of finding “suitable” representations of analog information on digital hardware. Albeit abstract, we argue that this problem is fundamental in digital twinning, a signal-processing paradigm the upcoming 6G communication-technology standard relies on heavily. Using computable analysis, we formalize a general framework of machine-readable descriptions for representing analytic objects on Turing machines. Subsequently, we apply this framework to sampling and interpolation theory, providing a thoroughly formalized method for digitally processing the information carried by bandlimited analog signals. We investigate discrete-time descriptions, which form the implicit quasi-standard in digital signal processing, and establish continuous-time descriptions that take the signal’s continuous-time behavior into account. Motivated by an exemplary application of digital twinning, we analyze a textbook model of digital communication systems accordingly. We show that technologically fundamental properties, such as a signal’s (Banach-space) norm, can be computed from continuous-time, but not from discrete-time descriptions of the signal. Given the high trustworthiness requirements within 6G, e.g., employed software must satisfy assessment criteria in a provable manner, we conclude that the problem of “trustworthy” digital representations of analog information is indeed essential to near-future information technology.

Source: Algorithms

DOI: 10.3390/a16110514

Authors: Holger Boche, Yannik N. Böck, Ullrich J. Mönich, Frank H. P. Fitzek

Institutions: Technical University of Munich, Technische Universität Dresden

Language: English

Topic: Computability, Logic, AI Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,779

Funders: Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung