Allpass transfer functions with prescribed group delay

This paper presents a method for the design of discrete-time allpass transfer functions with prescribed group delay. The design procedure consists in computing the unit pulse response of an associated stable and minimal phase system using coefficients from the Fourier series expansion of the specified group delay. The allpass coefficients are computed from the unit pulse response using Prony's method. The procedure allows the design of allpass functions with prescribed number of stable and unstable poles. It is useful as an approximation method by itself but the major motivation for developing it was to systematically obtain initial solutions for the design of digital filters consisting of the parallel connection of two allpass filters.<>