Simplified design of high-order recursive group-delay filters

A new, simplified method is presented for the design of group-delay filters. The method is derived assuming that the filter order is large and that the filter group-delay function is smooth. Satisfactory results, however, are achieved even if both of these assumptions do not apply. The method permits the realization of filters that are equal ripple approximations to the smooth portions of given group-delay characteristics. The filters are constructed from second-order all-pass sections in cascade. Examples of linear group-delay, quadratic group-delay, and "stair step" group-delay filters are presented. The design method is simple enough to be implemented with dedicated hardware.