Equiripple and minimax (Chebyshev) approximations for recursive digital filters

Abstract

The problem of designing recursive digital filters whose frequency response approximates an arbitrarily prescribed function in the Chebyshev sense on a single interval is considered. Certain degenerate cases where the best Chebyshev approximation is not equiripple are studied in detail, and an algorithm is given for determining the best Chebyshev as well as the best equiripple approximation. Finally, a number of examples illustrating applications of this algorithm are given.