DESIGN OF MULTIDIMENSIONAL SPHERICALLY SYMMETRICAL AND CONSTANT GROUP DELAY RECURSIVE DIGITAL-FILTERS WITH SUM OF POWERS-OF-2 COEFFICIENTS

A method for the design of multidimensional spherically symmetric and separable denominator recursive digital filters with sum of powers-of-two coefficients satisfying both predetermined magnitude and constant group delay specifications is presented. The procedure of this method is divided into two stages. The first stage is to design the denominator of our specified transfer function so as to satisfy the constant group delay specification. The second stage is to design the corresponding constant group delay numerator along with the designed denominator in order to meet the magnitude specification. Both stages are carried out by successive quantizations and re-optimizations of pre-computed continuous coefficients. The optimization algorithm used is a continuous and unconstrained non-linear one. Since such a M-dimensional recursive transfer function possesses (2MA/!)-hedral symmetry, the number of unknown coefficients and the number of frequency samples for optimization can be greatly reduced. Consequently, this method is computationally efficient. The results of three design examples are given for illustration. © 1990 IEEE