System approximation with general measurement functionals

Holger Boche; Ullrich J. Monich

doi:10.1109/ICASSP.2014.6854389

System approximation with general measurement functionals

Holger Boche, Ullrich J. Monich

Chair of Theoretical Information Technology

Massachusetts Institute of Technology

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

2 Scopus citations

Abstract

The approximation of linear time-invariant (LTI) systems by sampling series is an important topic in signal processing. Recently, it was conjectured [1] and proved [2] that, for every sampling pattern that is a complete interpolating sequence, there exists a universal stable LTI system such that for every oversampling factor there exists a bandlimited input signal such that the approximation process, which is used to approximate the output signal of the LTI system, diverges. This instability of the approximation process shows a fundamental limit of sampling-based signals processing. However, as is shown in this paper, by using more general measurement functionals this divergence can be overcome.

Original language	English
Title of host publication	2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4180-4184
Number of pages	5
ISBN (Print)	9781479928927
DOIs	https://doi.org/10.1109/ICASSP.2014.6854389
State	Published - 2014
Event	2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 - Florence, Italy Duration: 4 May 2014 → 9 May 2014

Publication series

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

Conference

Conference	2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
Country/Territory	Italy
City	Florence
Period	4/05/14 → 9/05/14

Keywords

bandlimited signal
complete interpolating sequence
linear time-invariant system
measurement functional
sampling

Access to Document

10.1109/ICASSP.2014.6854389

Cite this

Boche, H., & Monich, U. J. (2014). System approximation with general measurement functionals. In 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 (pp. 4180-4184). Article 6854389 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2014.6854389

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year = "2014",

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booktitle = "2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014",

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Boche, H & Monich, UJ 2014, System approximation with general measurement functionals. in 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014., 6854389, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 4180-4184, 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014, Florence, Italy, 4/05/14. https://doi.org/10.1109/ICASSP.2014.6854389

System approximation with general measurement functionals. / Boche, Holger; Monich, Ullrich J.
2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 4180-4184 6854389 (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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AB - The approximation of linear time-invariant (LTI) systems by sampling series is an important topic in signal processing. Recently, it was conjectured [1] and proved [2] that, for every sampling pattern that is a complete interpolating sequence, there exists a universal stable LTI system such that for every oversampling factor there exists a bandlimited input signal such that the approximation process, which is used to approximate the output signal of the LTI system, diverges. This instability of the approximation process shows a fundamental limit of sampling-based signals processing. However, as is shown in this paper, by using more general measurement functionals this divergence can be overcome.

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Boche H, Monich UJ. System approximation with general measurement functionals. In 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 4180-4184. 6854389. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2014.6854389

System approximation with general measurement functionals

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