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

Abstract

In this paper, we present a novel method for designing polynomial FIR predictors and polynomial-predictive FIR differentiators for fixed-point environments. Our method yields filters that perform exact prediction and differentiation even with short coefficient word lengths. Under ordinary coefficient truncation or rounding, prediction and differentiation capabilities of these filters degrade considerably or may even be totally lost. With the proposed method, the filters are designed so that the prediction and differentiation properties are exactly preserved in fixed-point implementations. The presented filter design method is based on integer programming and can be directly applied to fixed-point FIR design specifications, which can be formulated in a form of linear constraints on the filter coefficients.