3D parametric adjustment of the Gegenbauer's continuous filter function

Abstract

The paper proposes a precise analytical method for finding the explicit expression for the characteristic function of filters applicable to the design of double terminated ladder LC filter and RC active filters. Recently introduced new class of continual filter function generated by the extremal Christoffel-Darboux formula for the orthogonal Gegenbauer polynomials has two parameters, the filter order, n, and the real free parameter, ν. In this paper, a detailed analysis of attenuation in the bandwidth and insertion loss around the stop-band cut-off frequency, ωcs, is carried out using 3D plots on the example of the filter function of the 13-th order.