Genetic algorithm approach for the optimization of multiplierless sub-filters generated by the frequency-response masking technique

In this paper, the genetic algorithm (GA) is applied to optimize the discrete coefficient values of very sharp linear phase FIR digital filters generated by the frequency-response masking (FRM) technique. The discrete coefficient space is the signed power-of-two (SPT) space. Since the genetic algorithm optimizes all the sub-filters´ coefficients simultaneously, it overcomes the drawback existing in linear optimization technique that optimizes the sub-filters individually. If the genetic algorithm starts from the continuous solution obtained by using a non-linear joint optimization algorithm, the obtained overall ripple magnitude of the discrete solution is very close to that of the continuous solution. Great improvement is achieved compared to the discrete coefficient filters obtained by rounding the coefficient values of the continuous solutions.