On the Fixed-Point Implementation of Fractional-Delay Filters Based on the Farrow Structure

In this paper, the fixed-point implementation of adjustable fractional-delay filters using the Farrow structure is considered. Based on the observation that the sub-filters approximate differentiators, closed-form expressions for the $L_2$ -norm scaling values at the outputs of each sub-filter as well as at the inputs of each delay multiplier are derived. The scaling values can then be used to derive suitable word lengths by also considering the round-off noise analysis and optimization. Different approaches are proposed to derive suitable word lengths including one based on integer linear programming, which always gives an optimal allocation. Finally, a new approach for multiplierless implementation of the sub-filters in the Farrow structure is suggested. This is shown to reduce register complexity and, for most word lengths, require less number of adders and subtracters when compared to existing approaches.