Minimum number of operations under a general number representation for digital filter synthesis

In this work, we introduce an algorithm for the optimization of the number of operations in the multiplier block of a digital filter based on a general number representation for the coefficients. In common subexpression elimination algorithms, constants are generally represented with the minimum number of non-zero digits based on their CSD, or MSD representations. We observe that these representations may yield a solution far from the minimum. The general number representation used in our algorithm considers a much larger set of alternative implementations of a constant, which includes the CSD and MSD representations. To cope with the increased search space, we propose model simplification and problem reduction techniques. In this paper, we show that the proposed exact algorithm using general number representation achieves a significant reduction in the number of operations, which can be up to 15 % with respect to the solutions obtained under MSD representation.