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A Novel Genetic Algorithm for Optimization of FRM Digital Filters over DBNS Multiplier Coefficient Space Based on Correlative Roulette Selection

The use of double base number system (DBNS) multiplier coefficients reduces the complexity and power consumption in the hardware implementation of FIR digital filters. The use of genetic algorithms for optimization of the constituent DBNS multiplier coefficients can further reduce the complexity of the digital filter. This paper presents a novel genetic algorithm based on correlative roulette selection (CRS) for the optimization of frequency response-masking (FRM) FIR digital filters over the DBNS multiplier coefficient space. In this approach, the underlying operations of crossover and mutation automatically give rise to valid DBNS multiplier coefficients without any recourse to gene repair. An application example is given for the design of a FRM FIR lowpass digital filter employing DBNS multiplier coefficients. The resulting FIR digital filter outperforms a corresponding infinite-precision digital filter obtained by using the Parks-McClellan technique