Investigating the Effectiveness of Optimization with Modified Stability Boundary Locus Fitting for Approximation of α-order Fractional Filters

This paper presents a new approach for the rational approximation of fractional-order lowpass and highpass filters of order $\alpha$, where $\alpha \in(0, 1)$. The proposed approach considers the modified stability boundary locus (M-SBL) based filter approximants as an initial point for a classical optimizer to determine the model coefficients. The performance of the M-SBL fitting for the fractional-order filter approximation is compared with the proposed method to justify the effectiveness of the suggested scheme regarding both the magnitude and phase characteristics. The distinct advantage of the proposed approach is to avoid the incorporation of stability and minimum-phase constraints, thus reducing the computational burden. Comparisons with the published literature demonstrate the overall improved frequency-domain fitting performance for the proposed approximants.