Information Loss and Anti-Aliasing Filters in Multirate Systems

This work investigates the information loss in a decimation system, i.e., in a downsampler preceded by an anti-aliasing filter. It is shown that, without a specific signal model in mind, the anti-aliasing filter cannot reduce information loss, while, e.g., for a simple signal-plus-noise model it can...

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Bibliographic Details
Published inarXiv.org
Main Authors Geiger, Bernhard C, Kubin, Gernot
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 07.07.2014
Subjects
Aliasing
Digital cameras
Filter design (mathematics)
Information theory
Normal distribution
Random noise
Upper bounds
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Summary:This work investigates the information loss in a decimation system, i.e., in a downsampler preceded by an anti-aliasing filter. It is shown that, without a specific signal model in mind, the anti-aliasing filter cannot reduce information loss, while, e.g., for a simple signal-plus-noise model it can. For the Gaussian case, the optimal anti-aliasing filter is shown to coincide with the one obtained from energetic considerations. For a non-Gaussian signal corrupted by Gaussian noise, the Gaussian assumption yields an upper bound on the information loss, justifying filter design principles based on second-order statistics from an information-theoretic point-of-view.
ISSN:2331-8422