Two-dimensional FIR filter design using matrix dilation approach

This paper develops an approach for the optimal design of two-dimensional (2-D) finite impulse response (FIR) filters based on the minimization of a new performance index. The approach gives analytical expressions for the optimal solution and offers a two-parameter family of suboptimal filters. It is shown that the conventional least square solutions is a member of this family. The approach is based on a result in linear algebra, and used in robust control theory known as the dilation equation. An efficient numerical algorithm for solving the filter design problem using the dilation equation is proposed, and some techniques for choosing the design parameters are discussed. Finally, same examples are shown illustrating the flexibility of the design using the new approach.