Anatoli Torokhti and Phil Howlett Optimal Data Compression and Filtering The Case of Infinite Signal Sets
2604 - 2615
2008
2
11
International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering http://waset.org/publications/11167
http://waset.org/publications/23
World Academy of Science, Engineering and Technology
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 rankconstrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.
International Science Index 23, 2008