access icon free Accurate integer-order rational approximation of fractional-order low-pass Butterworth filter using a metaheuristic optimisation approach

© The Institution of Engineering and Technology
Received 20/05/2017, Accepted 03/01/2018, Revised 28/11/2017, Published 16/01/2018

This study presents a new approach to design fractional-order low-pass Butterworth filters (FOLPBF) in terms of integer-order rational approximations meeting an accurate magnitude response. A parameter-independent, metaheuristic optimisation algorithm called colliding bodies optimisation (CBO) is used for this purpose. The CBO-based optimisation routine determines the optimal values of the coefficients for the proposed integer-order models for the (1 + α), where, 0 < α < 1, order FOLPBFs. The performance of the proposed filter is examined concerning the passband and the stopband characteristics, solution quality robustness, and the convergence rate. The generic nature of the proposed design approach is also demonstrated. The roll-off characteristics of the proposed higher orders of FOLPBFs exhibit accurate stopband attenuation behaviour. The proposed designs also achieve the best magnitude responses as compared with state-of-the-art designs published in the recent literature. The proposed models can be practically implemented without using any fractance devices.

Inspec keywords: approximation theory; optimisation; convergence of numerical methods; low-pass filters; band-pass filters; Butterworth filters

Other keywords: stopband characteristics; colliding bodies optimisation; accurate stopband attenuation behaviour; solution quality robustness; accurate integer-order rational approximation; parameter-independent optimisation algorithm; CBO-based optimisation routine; metaheuristic optimisation approach; integer-order models; FOLPBF; accurate magnitude response; fractional-order low-pass Butterworth filters; passband characteristics; convergence rate

Subjects: Interpolation and function approximation (numerical analysis); Optimisation techniques; Filtering methods in signal processing; Interpolation and function approximation (numerical analysis); Signal processing theory; Optimisation techniques

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