Effective Approximation of Bandlimited Signals and Their Samples

Holger Boche; Ullrich J. Monich

doi:10.1109/ICASSP40776.2020.9053196

Effective Approximation of Bandlimited Signals and Their Samples

Holger Boche, Ullrich J. Monich

Chair of Theoretical Information Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 Scopus citations

Abstract

Shannon's sampling theorem is of high importance in signal processing, because it links the continuous-time and discrete-time worlds. For bandlimited signals we can switch from one domain into the other without loosing information. In this paper we analyze if and how this transition affects the computability of the signal. Computability is important in order that the approximation error can be controlled. We show that the computability of the signal is not always preserved. Further, we provide a simple necessary and sufficient condition for the computability of the continuous-time signal, and a simple canonical algorithm that can be used for the computation.

Original language	English
Title of host publication	2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5590-5594
Number of pages	5
ISBN (Electronic)	9781509066315
DOIs	https://doi.org/10.1109/ICASSP40776.2020.9053196
State	Published - May 2020
Event	2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Barcelona, Spain Duration: 4 May 2020 → 8 May 2020

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	2020-May
ISSN (Print)	1520-6149

Conference

Conference	2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020
Country/Territory	Spain
City	Barcelona
Period	4/05/20 → 8/05/20

Keywords

Effective approximation
approximation error
computability
continuous-time signal
discrete-time signal

Access to Document

10.1109/ICASSP40776.2020.9053196

Cite this

Boche, H., & Monich, U. J. (2020). Effective Approximation of Bandlimited Signals and Their Samples. In 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings (pp. 5590-5594). Article 9053196 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2020-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP40776.2020.9053196

Boche, Holger ; Monich, Ullrich J. / Effective Approximation of Bandlimited Signals and Their Samples. 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2020. pp. 5590-5594 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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abstract = "Shannon's sampling theorem is of high importance in signal processing, because it links the continuous-time and discrete-time worlds. For bandlimited signals we can switch from one domain into the other without loosing information. In this paper we analyze if and how this transition affects the computability of the signal. Computability is important in order that the approximation error can be controlled. We show that the computability of the signal is not always preserved. Further, we provide a simple necessary and sufficient condition for the computability of the continuous-time signal, and a simple canonical algorithm that can be used for the computation.",

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Boche, H & Monich, UJ 2020, Effective Approximation of Bandlimited Signals and Their Samples. in 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings., 9053196, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2020-May, Institute of Electrical and Electronics Engineers Inc., pp. 5590-5594, 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020, Barcelona, Spain, 4/05/20. https://doi.org/10.1109/ICASSP40776.2020.9053196

Effective Approximation of Bandlimited Signals and Their Samples. / Boche, Holger; Monich, Ullrich J.
2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2020. p. 5590-5594 9053196 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2020-May).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Shannon's sampling theorem is of high importance in signal processing, because it links the continuous-time and discrete-time worlds. For bandlimited signals we can switch from one domain into the other without loosing information. In this paper we analyze if and how this transition affects the computability of the signal. Computability is important in order that the approximation error can be controlled. We show that the computability of the signal is not always preserved. Further, we provide a simple necessary and sufficient condition for the computability of the continuous-time signal, and a simple canonical algorithm that can be used for the computation.

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KW - approximation error

KW - computability

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KW - discrete-time signal

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Boche H, Monich UJ. Effective Approximation of Bandlimited Signals and Their Samples. In 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2020. p. 5590-5594. 9053196. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP40776.2020.9053196

Effective Approximation of Bandlimited Signals and Their Samples

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