Design of Atangana-Baleanu-Caputo fractional-order digital filter.

Atangana-Baleanu-Caputo (ABC) fractional differential operator based upon Mittag-Leffler kernel exhibits all the advantages of conventional Riemann-Liouville and Caputo fractional differential operators; in addition, the kernel associated is non-singular. Therefore, this paper puts forward a closed-form analytical formulation for the design of an ABC-based fractional-order FIR filter for various signal processing and filtering applications. The closed-form expression is derived by utilizing backward finite difference method and fractional sample delay interpolation techniques. Furthermore, several design examples are considered to illustrate the effectiveness of the proposed method. From the analytical and simulation studies done, it is observed that the proposed design efficiently approximates the ideal frequency response of ABC-fractional differential operator. Finally, one-dimensional and two-dimensional applications of the proposed method are validated and compared against state-of-the-art methods for electrocardiogram (ECG) R-peak detection as well as for digital image sharpening.