Automated Digital Filter Synthesis with Canonical Signed Digit via Genetic Algorithms

Finite Impulse Response (FIR) digital filters are widely used in signal processing to remove noise and extract frequency-domain features. Genetic Algorithms (GAs) have been employed to synthesize FIR filters by optimizing the coefficients in their transfer function. A notable approach is to evolve FIR filter coefficients in the Canonical Signed Digit (CSD) representation, which simplifies hardware implementation by replacing multipliers with shifts and additions. However, its crossover and mutation operators frequently produce offspring that violate CSD constraints, requiring repeated retries or coefficient resets. We propose modified crossover and mutation operators that guarantee CSD-compliant offspring by construction. We compare our method against the original CSD-based GA and a real-valued GA baseline across five low-pass filter design problems, varying filter order and coefficient word length. Results show that our method consistently outperforms the original CSD-based approach.