Decreasing the Minimal Sample Period for Recursive Filters Implemented Using Distributed Arithmetic

For distributed arithmetic the latency is proportional to the maximal number of fractional bits for any coefficient. When implementing recursive filters this is a disadvantage as the resulting minimal sample period may be longer compared with an implementation using separate multiplications and additions. In this paper we propose a method to decrease the latency for inputs where the corresponding coefficient has less fractional bits than the maximal of that distributed arithmetic unit. Further, we show how to utilize this technique to decrease the minimal sample period (iteration period) and how to schedule the distributed arithmetic operations to achieve this lower bound.