Design of recursive group-delay filters by autoregressive modeling

A new method of design of recursive group-delay filters is presented in this paper. The method uses autoregressive modeling to derive parameters of the filter. The design is based on the following line of argument. The desired group-delay characteristics are to be realized through a stable all-pass filter. The transfer function of an all-pass filter is completely determined by the coefficients of either the numerator or the denominator polynomial. For a stable all-pass filter, the denominator polynomial must be a minimum phase polynomial. For a minimum phase polynomial, the magnitude function and the group-delay function are related through cepstral coefficients. Therefore, from the given group-delay specification, the cepstral coefficients corresponding to the pole part (inverse of the denominator polynomial) of the desired filter are first determined. The magnitude spectrum corresponding to these cepstral coefficients is approximated using autoregressive modeling. A wide variety of group-delay filters can be realized by the proposed method, depending on the nature of approximation used and the accuracy desired. The design procedure is illustrated through examples.