Abstract
In this paper, we present an algorithm for the design of an optimal recursive digital filter with a specified magnitude frequency response. The method requires O(N super(2)) computations to design a filter of size N, and exhibits numerical stability and quadratic convergence to the optimum within five iterations. The multiple exchange iterative algorithm uses the Chebyshev error criterion in the magnitude-squared frequency response domain, and has been developed using the interpolation theory and the alternation theorem for rational function approximation.