Optimal design of IIR wideband digital differentiators and integrators using salp swarm algorithm

Abstract

This paper proposes an approach based on a weighted L1-norm optimization criterion and employs it in conjunction with salp swarm algorithm (SSA) to design 2nd- to 4th-order wideband infinite impulse response (IIR) digital differentiators (DDs). Integration of the proposed fitness function and SSA allows both the magnitude and phase responses to be improved. An extensive simulation is carried out to explore the performance of the proposed approach. First, a comparative study with widely used methods, namely, real-coded genetic algorithm (RCGA) and particle swarm optimization (PSO), is performed to examine accuracy, robustness, consistency and efficiency. Afterwards, the magnitude and phase responses of the proposed digital differentiators are compared with those of the existing designs in the literature. New wideband IIR digital integrators (DIs) are derived by inverting transfer functions of their respective digital differentiators and then compared with the existing designs in the literature in terms of the magnitude and phase responses. Simulation and statistical results reveal that the superiority of the proposed approach is statistically significant and demonstrate that the proposed digital differentiators and integrators significantly outperform all state-of-the-art designs in terms of the magnitude response as measured by the absolute relative error (ARE) with almost linear phase responses in wideband frequency regions.