A Recursive Digital Filter Design using Global Optimization Technique

Close form analytical techniques for the design of a certain class of recursive digital filters such as the elliptic filter have appeared. Such close form analytical techniques are suitable for designing filters with piece-wise constant magnitude response. The design of recursive digital filters with arbitrary frequency response is a nonlinear optimization problem. Specifically, it belongs to the class of global bi-lever programming problem. Optimal solution for a global bi-lever programming problem is notoriously difficult to obtain. In this paper, the bi-lever programming problem is first converted into a differentiate one-lever problem. Consequently we not only prove that the global minimizer of the converted one-lever problem is an approximate global minimizer of the original bi-lever problem, but also a novel filled function method for the design of recursive digital filters meeting arbitrary frequency response specifications is proposed. Several design examples are presented to illustrate our new technique