Recursive filter design using differential correction

Recent work by Thajchayapong and Rayner [1] demonstrated a technique for designing recursive infinite impulse response (IIR) digital filters by linear programming. By using an algorithm, described by Barrodale et al. [2], the differential correction algorithm, we will show how one may obtain optimum rational approximations to a given magnitude-squared frequency response in the Chebyshev norm. This optimization may be carried out on disjoint sets of frequency points obviating specification of the given magnitude-squared frequency response in transition bands. In addition, it will be shown how the differential correction algorithm is easily generalized to include weighted Chebyshev approximation.