Design of recursive digital filters with linear phase using two all-pass filters with/without integer coefficients

The performance of filters with linear phase in the domain of interest which are realized as a parallel of two allpass filters is investigated. The method uses unconstrained optimization to approximate both the group delay and the magnitude response of the desired filter simultaneously, if the constant group delay characteristic is required. A Hurwitz polynomial is generated, discretized, and assigned to the denominator of the filter transfer function to ensure the stability of the filter. Integer programming based on the branch-and-bound or tree search method is proposed. With this algorithm the error caused by truncating the filter coefficients is minimized. Examples to illustrate the usefulness of the proposed techniques are given