Optimal Data Compression and Filtering: The Case of Infinite Signal Sets
The authors present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, they 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.