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

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 approximatin...

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Veröffentlicht in:Circuits, systems, and signal processing Jg. 41; H. 6; S. 3415 - 3445
Hauptverfasser: Gupta, Anmol, Kumar, Sanjay
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.06.2022
Springer Nature B.V
Schlagworte:
Approximation
Circuits and Systems
Closed form solutions
Differential equations
Digital filters
Electrical Engineering
Electronics and Microelectronics
Engineering
Exact solutions
Finite difference method
FIR filters
Instrumentation
Interpolation
Kernels
MacLaurin series
Mathematical analysis
Medical imaging
Operators (mathematics)
Series expansion
Signal,Image and Speech Processing
Atangana–Baleanu (AB)
Finite impulse response (FIR)
MacLaurin series expansion
Fractional-order digital filter
Fractional-sample delay interpolation
ISSN:0278-081X, 1531-5878
Online-Zugang:Volltext
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Zusammenfassung: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.
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ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-021-01942-z