Algorithms for low power and high speed FIR filter realization using differential coefficients

Most realizations of FIR filters use the coefficients directly to compute the convolution with the input data. We present a set of new algorithms for low power and high-speed realization of FIR filters. The algorithms use various orders of differences between coefficients for computing the convolution. Also the results of computations are stored and reused, thus requiring more storage and storage accesses. These techniques result in a reduction in the net computations necessary per convolution as compared to directly using the coefficients. It is shown analytically that this computational reduction at the cost of more storage can result in a lower net computational energy dissipated and an enhanced speed. These algorithms are applied to an example FIR filter to quantify the energy savings and speedup.