Design of IIR filters in the complex domain

The problem of IIR (infinite impulse response) digital filter design in the complex domain is formulated in a way such that the existence of the best approximation is guaranteed. An efficient algorithm based on the Ellacott-Williams method is proposed to solve the problem. The algorithm separately designs the numerator and denominator, and uses a linear programming method to solve the linear complex approximation problem. For each iteration, it requires only half the computations of the Ellacott-Williams algorithm. The locally best approximation is usually found in five iterations and has an exactly equiripple error. Two ways to establish good initial points are presented. IIR filters are designed which have nearly linear phase in the passbands. Degenerate design can be detected and is shown by an example. Comparisons among several kinds of the optimal digital filters are given