The elliptic function in graph filters

Abstract

This paper applies the elliptic function to design graph filters, which can obtain arbitrary precision for step graph spectral responses. This method takes the mathematical form of the traditional elliptic analog filter, and its zero-pole points are recalculated. The approach obtains the coefficients of graph filters at a low computation cost by the polynomial multiplication rather than solving a nonlinear problem. Elliptic graph filters can control the ripples in the pass- and stop-band and width of transition band. Numerical experiments show the proposed approach outperformances the compared methods in designing the desired graph frequency responses.