Filtering and compression for infinite sets of stochastic signals

Authors:
Anatoli Torokhti;Phil Howlett
Affiliations:
Centre for Industrial and Applied Mathematics, School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095, Australia;Centre for Industrial and Applied Mathematics, School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095, Australia
Venue:
Signal Processing
Year:
2009

Citing 5
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Abstract

We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the scheme concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.