Piecewise Interpolation Filter For Effective Processing Of Large Signal Sets
Anatoli Torokhti, Stanley J. Miklavcic · Zenodo (CERN European Organization for Nuclear Research) · 2012
Suppose KY and KX are large sets of observed and reference signals, respectively, each containing N signals. Is it possible to construct a filter F : KY → KX that requires a priori information only on few signals, p N, from KX but performs better than the known filters based on a priori information on every reference signal from KX? 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.