Revisiting the use of squared magnitude function for the optimal approximation of (1 + α)-order Butterworth filter

Abstract

Optimal rational approximation of the fractional-order Butterworth filter (FBF) based on a two-step design procedure is proposed. Firstly, the coefficients of the squared magnitude function of an approximant which matches the squared magnitude response of the ideal (1 + α)-order FBF, where 0<α<1, are determined using the Genetic Algorithm (GA). Then, the stable model is used as an initial point for Powell’s conjugate direction algorithm (PCDA). The computational efficiency and the robustness of the suggested strategy are justified using illustrative examples. The proposed designs show a marked improvement in solution quality compared to the state-of-the-art. PSPICE responses for the FBFs realized using current feedback operational amplifiers (CFOA) confirm a close match with the theoretical characteristic. Python code for implementing the proposed designs using the Powell’s method is also provided.