{"title":"Generic Filtering of Infinite Sets of Stochastic Signals","authors":"Anatoli Torokhti, Phil Howlett","country":null,"institution":"","volume":30,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":427,"pagesEnd":440,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/2205","abstract":"A theory for optimal filtering of infinite sets of random\r\nsignals is presented. There are several new distinctive features of the\r\nproposed approach. First, a single optimal filter for processing any\r\nsignal from a given infinite signal set is provided. Second, the filter is\r\npresented in the special form of a sum with p terms where each term\r\nis represented as a combination of three operations. Each operation\r\nis a special stage of the filtering aimed at facilitating the associated\r\nnumerical work. Third, an iterative scheme is implemented into the\r\nfilter structure to provide an improvement in the filter performance at\r\neach step of the scheme. The final step of the scheme concerns signal\r\ncompression and decompression. This step is based on the solution of\r\na new rank-constrained matrix approximation problem. The solution\r\nto the matrix problem is described in this paper. A rigorous error\r\nanalysis is given for the new filter.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 30, 2009"}