Accurate integer‐order rational approximation of fractional‐order low‐pass Butterworth filter using a metaheuristic optimisation approach

Abstract

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.