Design of two-dimensional FIR filters using norm-preserving dilation

This paper develops two algorithms for the design of linear phase, two-dimensional (2-D) FIR digital filters. These algorithms belong to the class of indirect design methods where the desired frequency response itself is a (usually noncausal) transfer function of higher order that allows the use of powerful tools from systems theory to accomplish the design task. Specifically, we show how an optimal L₂ design can be derived as a matrix approximation problem in the Frobenius norm, and how a suboptimal L_∞ design can be obtained by solving a matrix approximation problem in the 2-norm using the Davis-Kahn-Weinberger theorem on norm-preserving dilations. A case study is included to demonstrate the usefulness of the proposed methods