A new method for designing equiripple group delay filters

A new method for designing all-pass filters with arbitrary group delay characteristics is presented. The design method is based on the recursive relationship between the filter coefficients of a minimum phase all-po1e filter and the corresponding cepstral coefficients. It is shown that by splitting the actual group delay response into the primary approximating function, being a finite cosine series, and into the truncation error function, the approximation problem can be solved using an iterative procedure. At each iteration, the truncation error of the previous iteration is included in the desired function and the primary approximating function is optimized using the Remez multiple exchange algorithm. This algorithm is continued until both the primary approximating function and the truncation error function remain the same. The new method does not require any initial values and yields in an equiripple error solution in most practical cases.