Structure of the set of signals with strong divergence of the Shannon sampling series

Holger Boche; Ullrich J. Monich; Ezra Tampubolon

doi:10.1109/ICASSP.2017.7953020

Structure of the set of signals with strong divergence of the Shannon sampling series

Holger Boche, Ullrich J. Monich, Ezra Tampubolon

Chair of Theoretical Information Technology

Technical University of Munich

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

1 Scopus citations

Abstract

It is known that there exist signals in Paley-Wiener space PW_π¹ of bandlimited signals with absolutely integrable Fourier transform, for which the peak value of the Shannon sampling series diverges unboundedly. In this paper we analyze the structure of the set of signals which lead to strong divergence. Strong divergence is closely linked to the existence of adaptive methods. We prove that there exists an infinite dimensional closed subspace of PW1_π¹, all signals of which, except the zero signal, lead to strong divergence of the peak value of the Shannon sampling series.

Original language	English
Title of host publication	2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4561-4565
Number of pages	5
ISBN (Electronic)	9781509041176
DOIs	https://doi.org/10.1109/ICASSP.2017.7953020
State	Published - 16 Jun 2017
Event	2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States Duration: 5 Mar 2017 → 9 Mar 2017

Publication series

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

Conference

Conference	2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Country/Territory	United States
City	New Orleans
Period	5/03/17 → 9/03/17

Keywords

Paley-Wiener space
Shannon sampling series
reconstruction process
spaceability
strong divergence

Access to Document

10.1109/ICASSP.2017.7953020

Cite this

Boche, H., Monich, U. J., & Tampubolon, E. (2017). Structure of the set of signals with strong divergence of the Shannon sampling series. In 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings (pp. 4561-4565). Article 7953020 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2017.7953020

Boche, Holger ; Monich, Ullrich J. ; Tampubolon, Ezra. / Structure of the set of signals with strong divergence of the Shannon sampling series. 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 4561-4565 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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abstract = "It is known that there exist signals in Paley-Wiener space PWπ1 of bandlimited signals with absolutely integrable Fourier transform, for which the peak value of the Shannon sampling series diverges unboundedly. In this paper we analyze the structure of the set of signals which lead to strong divergence. Strong divergence is closely linked to the existence of adaptive methods. We prove that there exists an infinite dimensional closed subspace of PW1π1, all signals of which, except the zero signal, lead to strong divergence of the peak value of the Shannon sampling series.",

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Boche, H, Monich, UJ & Tampubolon, E 2017, Structure of the set of signals with strong divergence of the Shannon sampling series. in 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings., 7953020, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 4561-4565, 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017, New Orleans, United States, 5/03/17. https://doi.org/10.1109/ICASSP.2017.7953020

Structure of the set of signals with strong divergence of the Shannon sampling series. / Boche, Holger; Monich, Ullrich J.; Tampubolon, Ezra.
2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. p. 4561-4565 7953020 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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

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N2 - It is known that there exist signals in Paley-Wiener space PWπ1 of bandlimited signals with absolutely integrable Fourier transform, for which the peak value of the Shannon sampling series diverges unboundedly. In this paper we analyze the structure of the set of signals which lead to strong divergence. Strong divergence is closely linked to the existence of adaptive methods. We prove that there exists an infinite dimensional closed subspace of PW1π1, all signals of which, except the zero signal, lead to strong divergence of the peak value of the Shannon sampling series.

AB - It is known that there exist signals in Paley-Wiener space PWπ1 of bandlimited signals with absolutely integrable Fourier transform, for which the peak value of the Shannon sampling series diverges unboundedly. In this paper we analyze the structure of the set of signals which lead to strong divergence. Strong divergence is closely linked to the existence of adaptive methods. We prove that there exists an infinite dimensional closed subspace of PW1π1, all signals of which, except the zero signal, lead to strong divergence of the peak value of the Shannon sampling series.

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Boche H, Monich UJ, Tampubolon E. Structure of the set of signals with strong divergence of the Shannon sampling series. In 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2017. p. 4561-4565. 7953020. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2017.7953020

Structure of the set of signals with strong divergence of the Shannon sampling series

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