%0 Journal Article %A Anatoli Torokhti and Stanley Miklavcic %D 2012 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 67, 2012 %T Piecewise Interpolation Filter for Effective Processing of Large Signal Sets %U https://publications.waset.org/pdf/12739 %V 67 %X 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. %P 770 - 777