Design of stable, causal 2-D digital filters using real coefficient 2-D all-pass building blocks

Presented here is a method for the design of 2-D causal quarter-plane recursive digital filters with real coefficients and arbitrary magnitude with/without linear phase characteristics, by using all-pass building blocks. It is shown that in general, cascades of sum or difference of two 2-D all-pass filters with appropriate delay elements are required to guarantee the arbitrary shape of the cutoff boundary of the desired filters. To design a 2-D filter satisfying given specifications the binary parameters of the cascaded all-pass structure are adapted from the given table, and the coefficients of the 2-D all-pass filters are obtained via an iterative technique by using a nonlinear optimization method. Design examples are given to illustrate the usefulness of the proposed technique.