Probabilistic Error Free Design of Long Fixed-Point Polynomial FIR Predictors

In this paper, a method for designing long fixed-point polynomial FIR predictors (FPFPs) is proposed. Our method yields filters that perform exact prediction even with short coefficient word lengths. Under ordinary coefficient quantization, prediction capabilities degrade, or may be totally lost. Here, the filters are designed so that the prediction properties are exactly preserved in fixed-point implementations. The algorithm is derived for second degree polynomial prediction using any filter length and integer prediction step. Also some non-integer prediction steps are possible.