Approximation of group delay response of allpass filters using weighted least square method

Allpass filters with prescribed group-delay response are useful in compensating such response. In general, the approximation of group-delay response is formulated as a nonlinear problem; thus, its approximation becomes difficult. The design methods with nonlinear optimization have the problem that initial values of filter coefficients are needed and heavy computation is required. The design method is simplified in the conventional method where magnitude response is approximated instead of group-delay response, but the approximation error is increased in the indirect methods. This paper proposes a method in which group-delay response is approximated by a linear function and optimal solution is obtained in the least square sense by iteratively solving the linear equations. This method has the merit that the error of group-delay response is directly evaluated. Moreover, applying Lawson's algorithm to this method, an equiripple solution can be obtained and maximum value of error can be decreased.