Design of two-dimensional digital filters using integer coefficient 2-D all-pass filters

Presented here is a method for the design of 2-D causal quarter-plane recursive digital filters with integer coefficients and arbitrary magnitude characteristics, by using all-pass building blocks. It is shown that in general, cascade 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 coupled with discretization and re-optimization method. An example is given to illustrate the usefulness of the proposed technique.