Design of minimum multiplier fractional order differentiator based on lattice wave digital filter

Abstract

In this paper, a novel design of fractional order differentiator (FOD) based on lattice wave digital filter (LWDF) is proposed which requires minimum number of multiplier for its structural realization. Firstly, the FOD design problem is formulated as an optimization problem using the transfer function of lattice wave digital filter. Then, three optimization algorithms, namely, genetic algorithm (GA), particle swarm optimization (PSO) and cuckoo search algorithm (CSA) are applied to determine the optimal LWDF coefficients. The realization of FOD using LWD structure increases the design accuracy, as only N number of coefficients are to be optimized for Nth order FOD. Finally, two design examples of 3rd and 5th order lattice wave digital fractional order differentiator (LWDFOD) are demonstrated to justify the design accuracy. The performance analysis of the proposed design is carried out based on magnitude response, absolute magnitude error (dB), root mean square (RMS) magnitude error, arithmetic complexity, convergence profile and computation time. Simulation results are attained to show the comparison of the proposed LWDFOD with the published works and it is observed that an improvement of 29% is obtained in the proposed design. The proposed LWDFOD approximates the ideal FOD and surpasses the existing ones reasonably well in mid and high frequency range, thereby making the proposed LWDFOD a promising technique for the design of digital FODs.