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.Comment: 12 pages; a shorter version of this paper was published at the 2014
International Zurich Seminar on Communication
