Design of recursive digital integrators and differentiators using particle swarm optimization

This paper presents a new method for designing digital recursive integrators and differentiators by using nonlinear stochastic global optimization based on particle swarm optimization PSO. A modified PSO is used to optimize the unknown coefficients of second-order and third-order recursive integrators in order to obtain a better magnitude response closer to the ideal integrator. The coefficients of the state-of-the-art available filters in the literature are chosen as initial points in the PSO process. By choosing a good starting point, convergence to an optimal solution is greatly facilitated. A dynamic modification of the fitness function used in the PSO process leads to the design of a set of digital integrators each optimized for a specific frequency range. Then, second-order and third-order recursive digital differentiators are designed by inverting and stabilizing the transfer functions of the designed recursive integrators. The obtained stabilized differentiators are further optimized using PSO to further improve their performance. The magnitude responses of the designed filters outperform the existing integrators and differentiators. Copyright © 2015 John Wiley & Sons, Ltd.