Rapid optimization of FRM digital filters over CSD multiplier coefficient space using a diversity controlled genetic algorithm

In a preceding paper, it was shown that the canonical signed-digit (CSD) representation of the multiplier coefficients in frequency response-masking (FRM) FIR digital filters leads to a substantial reduction in the hardware complexity of the FIR digital filter. However, a direct approximation of the infinite-precision multiplier coefficients to their CSD counterparts may cause the FIR digital filter to cease to satisfy the given filter design specifications. This paper presents a novel technique based on diversity controlled (DC) genetic algorithm (GA) for the discrete optimization of FRM FIR digital filters over the CSD multiplier coefficient space. The salient feature of the DCGA technique is that it permits external control over population diversity and parent selection pressure, giving rise to a rapid convergence to an optimal solution. It is shown that the application of the proposed DCGA technique to the optimization of a benchmark low-pass FRM digital filter over CSD multiplier coefficient space leads to an order of magnitude speed-up factor as compared to that associated with a conventional GA. Moreover, the optimized CSD FRM digital filter outperforms the corresponding infinite-precision digital filter obtained by the classical Parks-Mclellan approach.