Design of recursive differentiators using quadratic programming

A method for the design of first and higher-degree recursive differentiators with constant group-delay characteristics using a least-squares approach is presented. In this method, a mean-square error based on the difference between the desired and actual frequency response is formulated in a quadratic form. Quadratic programming is employed wherein the constraint on stability is accommodated to design stable differentiators. Our method is compared with the linear programming (LP) approach in terms of the computational complexity and the variation of magnitude and group-delay errors with frequency. It is shown that the differentiators designed using our method have a much lower computational complexity and smaller variation of the magnitude and group-delay error with frequency than those designed using the LP approach