Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning
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 signa...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-11-01
|
| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/16/11/514 |
| _version_ | 1827640837107875840 |
|---|---|
| author | Holger Boche Yannik N. Böck Ullrich J. Mönich Frank H. P. Fitzek |
| author_facet | Holger Boche Yannik N. Böck Ullrich J. Mönich Frank H. P. Fitzek |
| author_sort | Holger Boche |
| collection | DOAJ |
| description | 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 <i>not</i> 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. |
| first_indexed | 2024-03-09T17:05:11Z |
| format | Article |
| id | doaj.art-1ba67325ebff4ce380130bb7c211cd85 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-09T17:05:11Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-1ba67325ebff4ce380130bb7c211cd852023-11-24T14:24:24ZengMDPI AGAlgorithms1999-48932023-11-01161151410.3390/a16110514Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital TwinningHolger Boche0Yannik N. Böck1Ullrich J. Mönich2Frank H. P. Fitzek3Chair of Theoretical Information Technology, Technical University of Munich, 80333 Munich, GermanyChair of Theoretical Information Technology, Technical University of Munich, 80333 Munich, GermanyChair of Theoretical Information Technology, Technical University of Munich, 80333 Munich, GermanyDeutsche Telekom Chair of Communication Networks, Technical University of Dresden, 01187 Dresden, GermanyThis 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 <i>not</i> 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.https://www.mdpi.com/1999-4893/16/11/514digital twinningsamplinginterpolationShannon seriesbandlimited signalsTuring machines |
| spellingShingle | Holger Boche Yannik N. Böck Ullrich J. Mönich Frank H. P. Fitzek Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning Algorithms digital twinning sampling interpolation Shannon series bandlimited signals Turing machines |
| title | Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning |
| title_full | Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning |
| title_fullStr | Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning |
| title_full_unstemmed | Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning |
| title_short | Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning |
| title_sort | trustworthy digital representations of analog information an application guided analysis of a fundamental theoretical problem in digital twinning |
| topic | digital twinning sampling interpolation Shannon series bandlimited signals Turing machines |
| url | https://www.mdpi.com/1999-4893/16/11/514 |
| work_keys_str_mv | AT holgerboche trustworthydigitalrepresentationsofanaloginformationanapplicationguidedanalysisofafundamentaltheoreticalproblemindigitaltwinning AT yanniknbock trustworthydigitalrepresentationsofanaloginformationanapplicationguidedanalysisofafundamentaltheoreticalproblemindigitaltwinning AT ullrichjmonich trustworthydigitalrepresentationsofanaloginformationanapplicationguidedanalysisofafundamentaltheoreticalproblemindigitaltwinning AT frankhpfitzek trustworthydigitalrepresentationsofanaloginformationanapplicationguidedanalysisofafundamentaltheoreticalproblemindigitaltwinning |