@inproceedings{c8851a44c52741088d01e1ab6cf111c5,
title = "Distributional time-domain system representations",
abstract = "In this paper we analyze the convergence behavior of convolution-type system representations for the Paley-Wiener space PWπ1. We completely characterize all stable linear time-invariant (LTI) systems for which we have convergence in the distributional sense by giving a necessary and sufficient condition for convergence. Furthermore, we prove that there are stable LTI systems and signals in PWπ1 for which the convolution integral and the convolution sum diverge even in a distributional sense. In signal processing, distributions are often used to show convergence. Surprisingly, here we are in a situation where distributions cannot be used to justify convergence.",
keywords = "Bandlimited signal, Convergence, Convolution, Distribution, System representation",
author = "M{\"o}nich, {Ullrich J.} and Holger Boche",
year = "2010",
doi = "10.1109/ICASSP.2010.5495782",
language = "English",
isbn = "9781424442966",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "3994--3997",
booktitle = "2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010 - Proceedings",
note = "2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010 ; Conference date: 14-03-2010 Through 19-03-2010",
}