Round-off error free fixed-point design of polynomial FIR predictors

We present a novel method for designing polynomial FIR predictors for fixed-point environments. Our method yields filters that perform exact prediction of polynomial signals even with short coefficient word lengths. Under ordinary coefficient truncation or rounding, the prediction capability degrades, or may be totally lost. With the proposed method, the filters are designed so that the predictive properties are exactly preserved in fixed-point implementations. The proposed filter design method is based on integer programming (IP) and can be directly applied to any fixed-point FIR design specifications which can be formulated in a form of linear constraints on the filter coefficients.