Design of efficient generalized digital fractional order differentiators using an improved whale optimization...

This article proposes a new design and realization method for generalized digital fractional-order differentiator (GFOD) based on a composite structure of infinite impulse response (IIR) subfilters. The proposed method utilizes an improved whale optimization algorithm (IWOA) to compute the optimal coefficients of IIR subfilters of the realization structure. IWOA is developed by incorporating a piecewise linear chaotic mapping (PWLCM) and an adaptive inertia weight based on the hyperbolic tangent function (AIWHT) into the framework of original whale optimization algorithm (WOA). Simulation experiments are conducted to compare the performance of our method with that of well-known techniques, real-coded genetic algorithm (RCGA), particle swarm optimization (PSO), and original WOA. The results show that the new metaheuristic is superior to the other metaheuristics in terms of attaining the most accurate GFOD approximation. Moreover, the proposed IIR-based GFOD is compared with state-of-the-art GFOD, and observed to save about 50% of implementation complexity. Therefore, our method can be utilized in real-world digital signal processing applications.