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Design of Mittag–Leffler Kernel-Based Fractional-Order Digital Filter Using Fractional Delay Interpolation

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Abstract

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 \(\alpha \rightarrow 1\), 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.

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Acknowledgements

The authors would like to thank the Science and Engineering Research Board (SERB) [Grant Number SB/S3/EECE/0149/2016], Department of Science and Technology (DST), Government of India, India, for providing the research facilities. The author is grateful for being financially supported by the CSIR, New Delhi, India (File no. 09/0677(11165)/2021-EMR-I).

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  1. Biomedical Signal Analysis and Interpretation Laboratory (BioSAIL), Department of Electronics and Communication Engineering, Thapar Institute of Engineering and Technology, Patiala, India

    Anmol Gupta & Sanjay Kumar

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Gupta, A., Kumar, S. Design of Mittag–Leffler Kernel-Based Fractional-Order Digital Filter Using Fractional Delay Interpolation. Circuits Syst Signal Process 41, 3415–3445 (2022). https://doi.org/10.1007/s00034-021-01942-z

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