Minimax Design of IIR Digital Filters Using Iterative SOCP

In this paper, a novel method for IIR digital filter design using iterative second-order cone programming (SOCP) is proposed under the minimax criterion. The convex relaxation technique is utilized to transform the original nonconvex design problem into an SOCP problem. By solving the relaxed problem, the lower and upper bounds on the optimal value of the original problem can be obtained. In order to reduce the discrepancy between the original and relaxed design problems, an iterative procedure is developed. At each iteration, a linear constraint is further incorporated to guarantee the convergence of the iterative procedure. In practice, the convergence speed can be further improved by introducing a soft threshold variable in this linear constraint. Accordingly, a regularization term is incorporated in the objective function of the design problem at each iteration. The stability of the designed filters can be ensured by a new positive realness based linear constraint. Several examples are presented to demonstrate the effectiveness of the proposed method.