A WEIGHTED LEAST-SQUARES ALGORITHM FOR QUASI-EQUIRIPPLE FIR AND IIR DIGITAL-FILTER DESIGN

It has been demonstrated by several authors that if a suitable frequency response weighting function is used in the design of an FIR filter, the weighted least squares solution is equiripple. The crux of the problem in the design of equiripple filters using the weighted least squares technique lies in the determination of the necessary least squares frequency response weighting function. In this paper, a novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi-equiripple design is presented. The algorithm converges very rapidly. From our experience, it typically produces a design which is only about 1 dB away from the minimax optimum solution in two iterations and converges to within 0.1 dB in six iterations. Convergence speed is independent of the order of the filter. It can be used to design filters with arbitrarily prescribed phase and amplitude response.