Spaceability for sets of bandlimited input functions and stable linear time-invariant systems with finite time blowup behavior

Spaceability for sets of bandlimited input functions and stable linear time-invariant systems... The approximation of linear time-invariant systems by sampling series is studied for bandlimited input functions in the Paley–Wiener space PW π 1 , i.e., bandlimited signals with absolutely integrable Fourier transform. It has been known that there exist functions and systems such that the approximation process diverges. In this paper we identify a signal set and a system set with divergence, i.e., a finite time blowup of the Shannon sampling expression. We analyze the structure of these sets and prove that they are jointly spaceable, i.e., each of them contains an infinite-dimensional closed subspace such that for any function and system pair from these subspaces, except for the zero elements, we have divergence. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Spaceability for sets of bandlimited input functions and stable linear time-invariant systems with finite time blowup behavior

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946017020053
Publisher site
See Article on Publisher Site

Abstract

The approximation of linear time-invariant systems by sampling series is studied for bandlimited input functions in the Paley–Wiener space PW π 1 , i.e., bandlimited signals with absolutely integrable Fourier transform. It has been known that there exist functions and systems such that the approximation process diverges. In this paper we identify a signal set and a system set with divergence, i.e., a finite time blowup of the Shannon sampling expression. We analyze the structure of these sets and prove that they are jointly spaceable, i.e., each of them contains an infinite-dimensional closed subspace such that for any function and system pair from these subspaces, except for the zero elements, we have divergence.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 13, 2017

References

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