Wideband digital integrators and differentiators designed using particle swarm optimisation

Digital integrators (DIs) and digital differentiators (DDs) of second, third and fourth-order based on particle swarm optimisation (PSO) algorithm are presented. A modified particle swarm optimisation (MPSO) algorithm with reducing maximum velocity has been used to optimise the mean square error of the digital operators. Statistical and simulation results have been presented for comparing quality of optimal operators obtained by MPSO, genetic algorithm (GA), two variants of PSO and PSO-GA hybrid techniques. The results obtained for best solutions by the proposed algorithm are either superior or at par with the basic PSO variants and hybrid techniques. The proposed digital operators have also been simulated using MATLAB, and the results have been compared with that of existing DIs and DDs derived by different optimisation algorithms, to demonstrate the effectiveness of the use of proposed MPSO. The relative magnitude errors (dB) obtained for digital integrators and differentiators are as low as -40 and -35 dB, respectively, which are valid for almost the full band of normalised frequency.