Design of digital FIR filters using differential evolution algorithm based on reserved genes

Filtering has been an enabling technology and has found ever-increasing applications. There are two main classes of digital filters: finite impulse response (FIR) filters and infinite impulse response (IIR) filters. FIR filter can be guaranteed to have linear phase and are always stable filters, so FIR filters is widely applicable. The differential evolution (DE) algorithm, which has been proposed particularly for numeric optimization problems, is a population-based algorithm like the genetic algorithms. In this work, the new DE algorithm based on reserved genes has been applied to the design of digital finite impulse response filters. In this new algorithm, the new vectors can be produced by the combination of genes of the selected chromosomes. These new vectors as the new individuals are evolved with other individuals in the population. It can increase the diversity of population and the algorithm is effective to avoid the local optimal solution. It can get more accurate solution. Its performance has been compared to other method. Examples are illustrated to demonstrate the effectiveness of the proposed design method.