Equiripple Approximation of Low-Pass FIR Filters

Abstract

For the first time, the existence and the nature of a generating polynomial of an equiripple low-pass finite impulse response (FIR) filter is presented. In terms of approximation theory, this achievement represents a polynomial approximation of two constants in two disjoint intervals in the equiripple sense which was missing in the approximation theory. In opposite to numerical solutions, the novel generating polynomial provides an insight into the nature of the approximation problem. Two demonstrations of approximating polynomials of equiripple low-pass FIR filters are included.