Enhanced colliding bodies optimisation-based optimal design of wideband digital integrators and differentiators

This paper presents an efficient approach to determine the optimal set of coefficients for the design of wideband infinite impulse response (IIR) digital integrators (DIs) and digital differentiators (DDs) of first, second, third, and fourth order, meeting the accurate magnitude response specification, using a recently proposed evolutionary optimisation algorithm called enhanced colliding bodies optimisation (ECBO). To demonstrate the effectiveness of the proposed approach, the results of the ECBO-based designs have been compared with those of eight other nature-inspired metaheuristic optimisation algorithms. Parametric and non-parametric statistical hypothesis tests are conducted to validate the consistency of the performance of the ECBO-based DIs and DDs. Simulation results demonstrate that ECBO-based designs achieve the least absolute magnitude error and demonstrate a competitive group delay response of the designed DIs and DDs of different orders as compared with the designs based on the competing algorithms. The proposed DIs and DDs also outperform those of the design approaches published in literature and achieve the best responses in terms of the maximum absolute magnitude error over a wide frequency range.