A Genetic Algorithm Employing Correlative Roulette Selection for Optimization of FRM Digital Filters over CSD Multiplier Coefficient Space

It is well known that canonical signed digit (CSD) multiplier coefficients reduce the complexity and power consumption requirements in the hardware implementation of FIR digital filters. Optimization of the constituent CSD multiplier coefficients using genetic algorithms can further reduce this complexity by constantly evolving from generation to generation based on the minimization of an objective fitness function modeled on the magnitude response characteristics of the digital filter. This paper presents a new genetic algorithm based on correlative roulette selection (CRS) for the optimization of frequency response-masking (FRM) FIR digital filters over the CSD multiplier coefficient space. Based on genetic operations such as crossover and mutation, valid CSD multiplier coefficients are generated without any recourse to gene repair. An application example is given for the design of a FRM FIR lowpass digital filter employing CSD multiplier coefficients. The resulting FIR digital filter outperforms a corresponding infinite-precision digital filter obtained by using the Parks-McClellan technique