Optimal design of fir filters in complex Chebyshev sense using semi-infinite programming method

The purpose of this paper is to propose a novel method of an optimal Chebyshev design for FIR filters in a complex domain using a linear semi-infinite optimization technique. One of difficulties of such the design problem is to assure an optimality of the obtained solution because of a nonlinearity of the problem and an ambiguity of a number of extremal frequencies. In the proposed method, the nonlinear optimization problem is transformed to the linear semi-infinite optimization problem, and can be solved by the three phase method, which is based on an optimality condition strictly. Some design examples are shown to illustrate a performance of the proposed method.