Fast Algorithms for Convolution

Abstract

The most important structure in digital signal processing is the nonrecur-sive digital filter known as the finite impulse response (FIR) filter. The FIR filter is simply a tapped delay line. It convolves the input datastream with the filter taps. An incoming datastream of digital samples enters the filter and an outgoing datastream of digital samples leaves the filter. The datastreams entering and leaving the filter are so long as to appear infinite. Perhaps thousands or even millions of samples pass through the filter per second, and this may continue indefinitely.