Design of optimal band-stop FIR filter using L1-norm based RCGA

In this paper, an optimal design of linear phase digital finite impulse response (FIR) band stop (BS) filter using the L1-norm based real-coded genetic algorithm (L1-RCGA) is presented. Although RCGA has proved its ability to overcome the drawbacks associated with conventional gradient-based optimization methods of filter design, it is applied here with a novel fitness function based on the L1-norm. This leads to a global optimal solution along with the improvement in filter design with same specifications. The designed filter pursues a better response in terms of flat passband, high stopband attenuation and fast convergence. The simulation results justify that the proposed FIR BS filter using L1-RCGA outperforms the existing optimization techniques, the L1-method and particle swarm optimization (PSO) and the conventional methods such as least-squares (LS) approach, Kaiser window method and the Parks McClellan (PM) algorithm. A detailed analysis is performed to evaluate the performance of the designed filters.