Levin’s Transformation-based Continuous-Time Linear-Phase Selective Filters

Abstract

In this paper, authors derive a family of linear-phase selective filters based on Levin’s transformation. The approach consists of developing an approximation to the Laplace transform of impulse response of the chosen linear-phase selective filter using a sum of shifted and scaled causal splines. This approximation is then rationalized using Levin’s transformation to obtain a realizable medium-order transfer function which is then balanced and truncated to the required order. The magnitude and phase features of the filter derived are presented and discussed. It is shown that the closed-form solution obtained can act as a starting point for approximation methods that use local search routines.