SYSTEMS AND METHODS FOR A PARTIAL SUM DIGITAL FIR FILTER

A digital FIR filter is provided that inputs a series of data samples x[0] . . . x[n] and generates a partial sum output PS[i], where i≦n. The partial sum output is a weighted version of the a difference between a partial sum of the previous i−1 data samples, PS[i−1], and the current data sample x[n] added to the current data sample x[n]. The filter includes a plurality of weighting stages. Each weighting stage includes a first adder for subtracting the current data sample x[n] from the previous partial sum PS[i−1], a multiplier that multiplies the difference by a weighting coefficient, and a second adder that sums the weighted difference with the current data sample. The filter also includes a plurality of delay elements, each of which inputs a partial sum and imposes a unit delay on the partial sum before supplying it to a weighting stage.