Design of multidimensional spherically symmetric and constant group delay recursive digital filters with sum of powers-of-two coefficients

A method is presented for the design of multidimensional, spherically symmetric, separable-denominator recursive digital filters with sum-of-powers-of-two coefficients satisfying both predetermined magnitude and constant group delay specifications. This method has two stages. In the first stage the denominator of the specific transfer function is designed to satisfy the constant group delay specification. In the second stage the corresponding constant group delay numerator is designed along with the designed denominator in order to meet the magnitude specification. Both stages are carried out by successive quantizations and reoptimizations of precomputed continuous coefficients. The optimization algorithm used is continuous, unconstrained, and nonlinear. Since such an M-dimensional recursive transfer function possesses symmetry, the number of unknown coefficients and the number of frequency samples for optimization can be greatly reduced; this method is computationally efficient. The results of three design examples are given for illustration