%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