Processing of large sets of stochastic signals: filtering based on piecewise interpolation technique
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Suppose K__Y and K__X are large sets of observed and reference signals, respectively, each containing N signals. Is it possible to construct a filter F that requires a priori information only on few signals, p≪ N, from K__X but performs better than the known filters based on a priori information on every reference signal from K__X? It is shown that the positive answer is achievable under quite unrestrictive assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of random signal sets. The proposed technique provides a single filter to process any signal from the arbitrarily large signal set. The filter is determined in terms of pseudo-inverse matrices so that it always exists.
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