Design of IIR filters with constraints using multi-swarm PSO

Abstract

In this study, IIR (Infinite Impulse Response) filters having a null and the specified error in a stop band are designed using PSO (Particle Swarm Optimization). A new penalty function is introduced to an objective function in addition to the conventional penalty function that ensures the stability of IIR filters. Furthermore, the specified error is restricted in the objective function. A design problem based on the minimax criteria is formulated as the non-linear optimization problem and cannot be solved easily. In addition, local minima are brought to the objective function because of adding such constraints. PSO is applicable to solve such non-linear optimization problems. However, it is reported that a local minimum stagnation occurs due to the strong intensification characteristic. Therefore, it is important to avoid the local minimum stagnation. In our method, a particle reallocation strategy is applied when the stagnation occurs. The effectiveness of our method is verified through several design examples.