Filter Function Synthesis by Gegenbauer Generating Function

Abstract

Low-pass all-pole transfer functions with non-monotonic amplitude characteristic in the pass-band and at least (n −1) flatness conditions for ω = 0 are considered in this paper. A new class of filters in explicit form with one free parameter is obtained by applying generating functions of Gegenbauer polynomials. This class of filters has good selectivity and good shape of amplitude characteristics in the pass-band. The amplitude characteristics of these transfer functions have gain in the upper part of pass-band with respect to the gain for ω = 0. This way we have greater margin of attenuation in the upper part of the pass-band. This means a greater tolerance of elements or for elements with given tolerances, greater ambient temperature changes. The appropriate choice of the free parameter enables us to generate filter functions obtained with CHEBYSHEV polynomials of the first and second kind and LEGENDRE polynomials.