1,489 research outputs found
Stochastic Wiener Filter in the White Noise Space
In this paper we introduce a new approach to the study of filtering theory by
allowing the system's parameters to have a random character. We use Hida's
white noise space theory to give an alternative characterization and a proper
generalization to the Wiener filter over a suitable space of stochastic
distributions introduced by Kondratiev. The main idea throughout this paper is
to use the nuclearity of this spaces in order to view the random variables as
bounded multiplication operators (with respect to the Wick product) between
Hilbert spaces of stochastic distributions. This allows us to use operator
theory tools and properties of Wiener algebras over Banach spaces to proceed
and characterize the Wiener filter equations under the underlying randomness
assumptions
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. 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
Slanted matrices, Banach frames, and sampling
In this paper we present a rare combination of abstract results on the
spectral properties of slanted matrices and some of their very specific
applications to frame theory and sampling problems. We show that for a large
class of slanted matrices boundedness below of the corresponding operator in
for some implies boundedness below in for all . We use
the established resultto enrich our understanding of Banach frames and obtain
new results for irregular sampling problems. We also present a version of a
non-commutative Wiener's lemma for slanted matrices
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