Improved power-of-two sharpening filter design by genetic algorithm

For high-speed low-complexity filter design, it is common practice to constrain the filters' coefficients to be a power-of-two or a sum of powers-of-two terms (P2), avoiding the full multiplication. Tapped interconnection of different sub-filters are sometimes used to enhance the ripple and stop-band attenuation performances. An extension of the simple cascade architectures, suitable for hardware implementation, is the polynomial sharpening technique. Firstly proposed by Kaiser-Hamming, it allows the use of identical sub-filters with a small hardware overhead. We propose a new approach to the design of P2 sharpening filters based on a specific genetic algorithm which optimizes both the FIR sub-filter and the sharpening polynomial coefficients expressed as P2 terms. This allows one to obtain better performances than the classical P2 design techniques when FIR filters with long impulse responses are involved.