Recursive allpass filter design using least-squares techniques

Three methods for the design of recursive allpass filters are presented. In one of these methods, a least-squares error based on the difference between the desired and actual frequency responses is formulated in a quadratic form. In the other methods, a least-squares error based on the difference between the desired and actual phase responses is formulated in a quadratic form. In all the methods, the coefficients of the allpass filters are obtained by solving a system of linear equations. By appropriately choosing the weighting function we are able to design allpass filters that are optimal in the least-squares sense as well as the minimax sense. Examples are provided to demonstrate the efficacy of the methods