Design of FIR filters with sum of power-of-two representation using simulated annealing

This work presents an efficient optimization method to design FIR filters with sum of power-of-two coefficients. The optimization problem is first formulated to minimize the number of nonzero digits in the whole set of filter coefficients. Then, a simplified Simulated Annealing algorithm is used to solve the problem. This method allows dealing with classical in-band ripple and stop-band rejection constraints, but also allows adding uncommon constraints, like transition band or stop-band shape constraints. For moderate long FIR filters, the proposed approach achieves comparable or better results than previous algorithms. Moreover, the method enables designing longer filters (~ 1500 coefficients) in a few hours, with a 30 to 50% reduction in the number of nonzero digits.