# System theoretic perspectives of the sampling theorem

Gjerrit Meinsma, Leonid Mirkin

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

### Abstract

In this paper we study the (classical) problem of reconstructing a continuous-time signal from its samples. We adopt a system-theoretical viewpoint of this problem. Namely, we assume that the continuous-time signal is modeled as the output of a linear time-invariant system and then formulate the reconstruction problem as the (either $L^2$ or $L^\infty$) optimal model-matching problem in the lifted domain. This leads to an alternative proof of the celebrated Sampling Theorem and some interesting extensions.
Original language Undefined Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems Kyoto Elsevier 730-741 12 not assigned Published - Jul 2006 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006 - Kyoto, JapanDuration: 24 Jul 2006 → 28 Jul 2006Conference number: 17

### Publication series

Name Proceedings of the International Symposium on Mathematical Theory of Networks and Systems supplement 17

### Conference

Conference 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006 MTNS Japan Kyoto 24/07/06 → 28/07/06

• EWI-8185
• IR-66616
• METIS-237624

### Cite this

Meinsma, G., & Mirkin, L. (2006). System theoretic perspectives of the sampling theorem. In Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (pp. 730-741). (Proceedings of the International Symposium on Mathematical Theory of Networks and Systems; Vol. 17, No. supplement). Kyoto: Elsevier.
Meinsma, Gjerrit ; Mirkin, Leonid. / System theoretic perspectives of the sampling theorem. Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. Kyoto : Elsevier, 2006. pp. 730-741 (Proceedings of the International Symposium on Mathematical Theory of Networks and Systems; supplement).
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abstract = "In this paper we study the (classical) problem of reconstructing a continuous-time signal from its samples. We adopt a system-theoretical viewpoint of this problem. Namely, we assume that the continuous-time signal is modeled as the output of a linear time-invariant system and then formulate the reconstruction problem as the (either $L^2$ or $L^\infty$) optimal model-matching problem in the lifted domain. This leads to an alternative proof of the celebrated Sampling Theorem and some interesting extensions.",
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Meinsma, G & Mirkin, L 2006, System theoretic perspectives of the sampling theorem. in Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. Proceedings of the International Symposium on Mathematical Theory of Networks and Systems, no. supplement, vol. 17, Elsevier, Kyoto, pp. 730-741, 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006, Kyoto, Japan, 24/07/06.

System theoretic perspectives of the sampling theorem. / Meinsma, Gjerrit; Mirkin, Leonid.

Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. Kyoto : Elsevier, 2006. p. 730-741 (Proceedings of the International Symposium on Mathematical Theory of Networks and Systems; Vol. 17, No. supplement).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

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AU - Mirkin, Leonid

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N2 - In this paper we study the (classical) problem of reconstructing a continuous-time signal from its samples. We adopt a system-theoretical viewpoint of this problem. Namely, we assume that the continuous-time signal is modeled as the output of a linear time-invariant system and then formulate the reconstruction problem as the (either $L^2$ or $L^\infty$) optimal model-matching problem in the lifted domain. This leads to an alternative proof of the celebrated Sampling Theorem and some interesting extensions.

AB - In this paper we study the (classical) problem of reconstructing a continuous-time signal from its samples. We adopt a system-theoretical viewpoint of this problem. Namely, we assume that the continuous-time signal is modeled as the output of a linear time-invariant system and then formulate the reconstruction problem as the (either $L^2$ or $L^\infty$) optimal model-matching problem in the lifted domain. This leads to an alternative proof of the celebrated Sampling Theorem and some interesting extensions.

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KW - IR-66616

KW - METIS-237624

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BT - Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems

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Meinsma G, Mirkin L. System theoretic perspectives of the sampling theorem. In Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. Kyoto: Elsevier. 2006. p. 730-741. (Proceedings of the International Symposium on Mathematical Theory of Networks and Systems; supplement).