Some properties of tail-canceling IIR filters

Infinite impulse response (IIR) recursive linear digital filters are widely used because of their low computational cost and low storage overhead requirements. Finite impulse response (FIR) filters, on the other hand, allow the possibility of implementing linear-phase linear digital filters which have constant group delay across all frequencies. The tradeoff is that to achieve similar magnitude transfer functions, FIR filters usually require much larger filter orders than their IIR counterparts. We describe an algorithm for the efficient implementation of certain classes of FIR filters. We introduce an extension of the truncated IIR (TIIR) algorithm which allows the truncation of arbitrary IIR filter tails. Our algorithm allows the possibility of implementing polynomial impulse responses. Additionally, we present an analysis of the effects of limited numerical precision and provide design guidelines for designing systems with acceptable noise tolerance.