Complex frequency response FIR filter design

This paper provides an algorithm for designing FIR filters that approximate both the magnitude and phase of the frequency response. The new algorithm produces a filter optimized under the weighted Chebyshev norm. The algorithm starts from a first stage unoptimized filter designed by a Remez-like algorithm and then uses shifted Dirichlet kernel functions to reduce large error peaks and converge to an equiripple set of peaks. The error function is modified at each iteration by subtracting a best-fit linear combination of kernel functions due to the large error peak(s). For one length-100 example, the computation of this algorithm was less than that of the complex Remez by two orders of magnitude