# Energy Blowup for Truncated Stable LTI Systems

Abstract:

In this paper we analyze the convergence behavior of a sampling based system approximation process, where the time variable is in the argument of the signal and not in the argument of the bandlimited impulse response. We consider the Paley-Wiener space $PW_\pi^2$ of bandlimited signals with finite energy and stable linear time-invariant (LTI) systems, and show that there are signals and systems such that the approximation process diverges in the $L^2$-norm, i.e., the norm of the signal space. We prove that the sets of signals and systems creating divergence are jointly spaceable, i.e., there exists an infinite dimensional closed subspace of $PW_\pi^2$ and an infinite dimensional closed subspace of the space of all stable LTI systems, such that the approximation process diverges for any non-zero pair of signal and system from these subspaces.

## icassp2017_energy_poster.pdf

### Paper Details

Authors:
Holger Boche, Ullrich Mönich
Submitted On:
2 March 2017 - 5:57am
Type:
Poster
Event:
Presenter's Name:
Ullrich Mönich
Document Year:
2017

(271)

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[1] Holger Boche, Ullrich Mönich, "Energy Blowup for Truncated Stable LTI Systems", IEEE SigPort, 2017. [Online]. Available: http://sigport.org/1580. Accessed: Jun. 16, 2019.
@article{1580-17,
url = {http://sigport.org/1580},
author = {Holger Boche; Ullrich Mönich },
publisher = {IEEE SigPort},
title = {Energy Blowup for Truncated Stable LTI Systems},
year = {2017} }
TY - EJOUR
T1 - Energy Blowup for Truncated Stable LTI Systems
AU - Holger Boche; Ullrich Mönich
PY - 2017
PB - IEEE SigPort
UR - http://sigport.org/1580
ER -
Holger Boche, Ullrich Mönich. (2017). Energy Blowup for Truncated Stable LTI Systems. IEEE SigPort. http://sigport.org/1580
Holger Boche, Ullrich Mönich, 2017. Energy Blowup for Truncated Stable LTI Systems. Available at: http://sigport.org/1580.
Holger Boche, Ullrich Mönich. (2017). "Energy Blowup for Truncated Stable LTI Systems." Web.
1. Holger Boche, Ullrich Mönich. Energy Blowup for Truncated Stable LTI Systems [Internet]. IEEE SigPort; 2017. Available from : http://sigport.org/1580