On fast FIR filters implemented as tail-canceling IIR filters

We have developed an algorithm based on synthetic division for deriving the transfer function which cancels the tail of a given arbitrary rational (IIR) transfer function after a desired number of time steps. Our method applies to transfer functions with repeated poles, whereas previous methods of tail-subtraction cannot [1]. We use a parallel state-variable technique with periodic refreshing to induce nite memory in order to prevent accumulation of quantization error in cases where the given transfer function has unstable modes. We present two methods for designing linear-phase Truncated IIR (TIIR) lters: one based on the addition and the other on the cascading of anti-phase lters. We explore nite-register e ects for unstable modes and provide bounds on the maximum TIIR lter length. In particular, we show that for unstable systems the available dynamic range of the registers must be three times that of the data. Considerable computational savings over conventional FIR lters are attainable for a given speci cation of linear-phase lter. We provide examples of lter design. We show how to generate nite-length polynomial impulse responses using TIIR lters. We list some applications of TIIR lters, including uses in digital audio and an algorithm for e ciently implementing Kay's optimal high-resolution frequency estimator [2].