Design and application of allpass filters with equiripple group delay errors

Allpass filters have found many applications in signal processing areas. In this paper, an iterative linear programming (LP) algorithm is first presented to solve the minimax phase error design of allpass filters. Then an iterative weighted minimax (WMM) method is presented to design allpass filters with equi-ripple group delay errors. Finally, the iterative WMM method is applied to the design of allpass-filter-based halfband filters with equiripple constant group delays. Design examples demonstrate that the new iterative LP algorithm is very efficient for the minimax allpass filter design, and the iterative WMM method is very effective for the equiripple constant group delay designs of allpass filters and allpass-filter-based halfband filters.