Fractional-order Lowpass Elliptic Responses of (1+α)-order Transfer Functions

Abstract

In this paper a least squares fitting is applied to determine the coefficients of a fractional-order transfer function that approximates the passband and stopband ripple characteristics of a second-order Elliptic lowpass filter. These fittings are applied to three different frequency ranges to evaluate the impact of the selection of approximated frequency band on the determined coefficients and the transfer function magnitude characteristics. MATLAB simulations of (1+ɑ) order lowpass magnitude responses with fractional steps from ɑ=0.1 to ɑ=0.9 are given as examples to highlight the fractional-step compared to the second-order Elliptic response. Further, MATLAB simulations of the (1+ɑ)=1.25 and 1.75 using all three sets of coefficients determined using different frequency bands are given as examples to highlight their differences.