2021/11/11 by Anatoli Torokhti, Torokhti, Anatoli
Computer Science · Engineering · Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Signal Processing (eess.SP) #cs.NA #eess.SP #electronic engineering #information engineering #math.NA
paper · pdf · doi:10.48550/arxiv.2111.06041
arxiv created 2021/11/11 · arxiv updated 2021/11/12
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 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.