Efficient recursive realizations of FIR filters

A class of efficient filter structures is proposed which uses a recursive realization of an FIR filter. The structures are in some sense a generalization of the frequency sampling structure, but they are more versatile and arise from a time-domain rather than frequency-domain argument. The new structure has a tap out of every block delay, and the length of the block delay is the length of each piecewise section of the time-domain approximation. The number of taps, filter coefficients, and the amount of arithmetic are proportional to the number of piecewise sections, not to the actual filter length or order. This filter is particularly efficient when a long-length filter can be approximated by a few piecewise sections, which is the case for many practical filters.This research was supported by NSF grant ECS 81-00453.