On the design of allpasses with prescribed group delay

The design of allpasses with group delays approximating a desired function is discussed. The method is based on a representation of the group delay of an allpass as a Fourier-series expansion and on a calculation of the transfer function of the allpass using a finite number of the corresponding coefficients. As a result, a Fourier-series expansion of the desired function can be used as a starting point. The result can be used either directly or as an initial solution for a Remez-like algorithm for the Chebyshev approximation of a desired group delay or phase response