Optimal design of linear phase FIR band stop filter using particle swarm optimization with improved inertia weight technique

Recently there has been a lot of research conducted on FIR filter design problem which involves multi-modal, multi-parameter optimization techniques that can be utilized to determine the impulse response coefficient of a filter and try to meet the ideal frequency response characteristics. In this paper a recently proposed multi-objective swarm optimization algorithm called particle swarm optimization with improved inertia weight (PSOIIW) is applied for the design of optimal linear phase digital band stop finite impulse response (FIR) filter. PSOIIW adopts a new definition for the velocity vector and swarm updating and hence the solution quality is improved. The inertia weight has been modified for the PSO to enhance its search capability to obtain the global optimal solution. The key feature of the applied modified inertia weight mechanism is to monitor the weights of particles, which linearly decrease in general applications. In the design process, the filter length, pass band and stop band frequencies, feasible pass band and stop band ripple sizes are specified. The simulation results obtained prove the superiority of the algorithm compared to the other prevailing optimization algorithms like real code genetic algorithm (RGA), particle swarm optimization (PSO), and differential evolution (DE) for the solution of the multimodal, non-differentiable, highly non-linear, and constrained FIR filter design problems.