Analytic Properties of Downsampling for Bandlimited Signals
Holger Boche, Ullrich J. Mönich
Abstract
In this paper we study downsampling for bandlimited signals. Downsampling in the discrete-time domain corresponds to a removal of samples. For any downsampled signal that was created from a bandlimited signal with finite energy, we can always compute a bandlimited continuous-time signal such that the samples of this signal, taken at Nyquist rate, are equal to the downsampled discrete-time signal. However, as we show, this is no longer true for the space of bounded bandlimited signals that vanish at infinity. We explicitly construct a signal in this space, which after downsampling does not have a bounded bandlimited interpolation. This shows that downsampling in this signal space is an operation that can lead out of the set of discrete-time signals for which we have a one-to-one correspondence with continuous-time signals.
BibTeX
@inproceedings{icassp2019_analyticproperti,
title = {Analytic Properties of Downsampling for Bandlimited Signals},
author = {Holger Boche and Ullrich J. Mönich},
booktitle = {ICASSP 2019},
year = {2019}
}