{"title":"Piecewise Interpolation Filter for Effective Processing of Large Signal Sets","authors":"Anatoli Torokhti, Stanley Miklavcic","country":null,"institution":"","volume":67,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":770,"pagesEnd":778,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12739","abstract":"Suppose KY and KX are large sets of observed and\r\nreference signals, respectively, each containing N signals. Is it possible to construct a filter F : KY \u2192 KX that requires a priori\r\ninformation only on few signals, p \u0003 N, from KX but performs better than the known filters based on a priori information on every\r\nreference signal from KX? It is shown that the positive answer is\r\nachievable under quite unrestrictive assumptions. The device behind\r\nthe proposed method is based on a special extension of the piecewise\r\nlinear interpolation technique to the case of random signal sets. The proposed technique provides a single filter to process any signal from\r\nthe arbitrarily large signal set. The filter is determined in terms of pseudo-inverse matrices so that it always exists.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 67, 2012"}