TY - JFULL AU - Anatoli Torokhti and Phil Howlett PY - 2008/12/ TI - Optimal Data Compression and Filtering: The Case of Infinite Signal Sets T2 - International Journal of Electronics and Communication Engineering SP - 2603 EP - 2615 VL - 2 SN - 1307-6892 UR - https://publications.waset.org/pdf/11167 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 23, 2008 N2 - We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter. ER -