Open AccessApproximation of fractional‐order low‐pass filter
Author(s) -
Mahata Shibendu,
Saha Suman Kumar,
Kar Rajib,
Mandal Durbadal
Publication year - 2019
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2018.5128
Subject(s) - transfer function , integer (computer science) , filter (signal processing) , mathematics , ideal (ethics) , function (biology) , order (exchange) , operator (biology) , low pass filter , algorithm , mathematical optimization , computer science , finance , economics , computer vision , philosophy , biochemistry , chemistry , epistemology , repressor , evolutionary biology , transcription factor , gene , electrical engineering , biology , programming language , engineering
Optimal integer‐order transfer function approximations to model the single fractance element‐based fractional‐order low‐pass filter (FLF) for any arbitrary order α , where, 0 < α < 1, is proposed here. First of all, the integer‐order filter coefficients for FLFs, with α varying from 0.01 to 0.99 in steps of 0.01, are directly obtained by using a metaheuristic algorithm called colliding bodies optimisation. For practical usability, the approximated FLF coefficients are explicitly provided in the form of analytical equations by employing a curve fitting on the optimised coefficients in the second step. The proposed approach provides a simpler design procedure in comparison to the reported literature which approximates the FLF by substituting an integer‐order rational approximation of the s α operator in the transfer function of the ideal FLF. Simulations confirm the superior modelling accuracy of the proposed design over the recent literature.