Design of Mittag–Leffler Kernel-Based Fractional-Order Digital Filter Using Fractional Delay Interpolation - Gupta, Anmol; Kumar, Sanjay (Circuits, systems, and signal processing, 2022)
In this paper, a novel closed-form analytical expression for the design of recently introduced non-singular and non-local Mittag–Leffler kernel-based Atangana–Baleanu–Caputo (ABC) fractional-order digital filter (FODF) has been proposed. The design has been obtained by first numerically approximating the ABC fractional differential operator using backward finite difference approach. Then, MacLaurin series expansion-based fractional delay interpolation formula is applied to obtain closed-form FIR filter approximation of ABC-FODF (herein, specified as ML-ABC-FODF). Various design examples are presented to show the performance of the proposed ML-ABC-FODF. From simulation and analytical study conducted, it has been seen that ML-ABC-FODF yields better performance over the entire Nyquist band of frequencies. Furthermore, an exact approximation to the first-order digital differentiator has been obtained when fractional-order α → 1 , which highlights the efficacy of the proposed method. Finally, 1-D and 2-D applications of the proposed ML-ABC-FODF are established and comparison is made with conventional approaches for accurate delineation of R-peaks in ECG signals as well as sharpening of medical images.