Abstract
In this paper, an optimal design method for stable IIR(Infinite Impulse Response) filters in a criterion of min-max sense is proposed. The design problem is considered one of the complex Chebyshev approximation for rational function including the stability constraint, we formulated such the problem as a real linear semi-infinite programming using the real rotation theorem. Then, the problem is solved by the three phase method that is one of the methods solving semi-infinite programming problem. The three phase method is composed of three operations. In the first operation, some candidates of active constraints are selected by the iterative simplex method. Next, the second operation integrates some degenerate constraints. In the third operation, the approximation solution obtained until second operation is adjusted so as to satisfy the optimality condition. As a result, the filters designed by the method are more precise than one designed by conventional method. Several design examples are shown to present effectiveness of the proposed method.
