Efficient design of recursive filters satisfying prescribed magnitude and phase specifications

A method for the design of recursive filters satisfying prescribed specifications using a least-squares approach is presented. In this method, a weighted mean-square error based on the difference between desired and actual frequency responses is formulated in a quadratic form. Quadratic programming is employed wherein the constraint on stability is accommodated. The proposed method is compared with the linear programming approach in terms of the computational complexity, mean-square error, and group delay error. It is shown that the proposed method has a much lower computational complexity and yields filters that have lower mean-square and group delay errors compared to those obtained using the linear programming approach