A NOVEL-APPROACH TO THE DESIGN OF 2-D RECURSIVE DIGITAL-FILTERS

An efficient method is presented for the design of 2-D circular symmetric recursive digital filters satisfying prescribed magnitude and constant group-delay responses. The transfer function of this class of 2-D filters has a zero-phase non-separable numerator and separable denominator 2-variable polynomials in z1 and z2. In the proposed technique the coefficients of the 2-D filters are calculated in two steps. In the first step the parameters of two 1-D all pole filters 1/D1(z1) and 1/D2(z2) are calculated by minimizing a multicriterion objective function using a suitable optimization technique so that the magnitude and group-delay responses of the desired 2-D filter along the omega-1, omega-2 axes are obtained. Essentially, the first step of the proposed design method yields a 2-D all pole separable product filter with rectangular cutoff boundaries with or without constant group-delay responses in the passband of the above filter. In the second step, the parameters of the zero-phase 2-variable non-separable polynomial in z1 and z2 in the numerator can be determined through minimization of a cost function using a linear programming approach. Note that the second step acts as a magnitude equalizer to convert a rectangular cutoff boundary to a circular one. An example illustrates the usefulness of the proposed algorithm.