Finite wordlength implementation of IIR polynomial predictive filters

Polynomial Predictive Filters (PPFs) are capable of predicting future values of a signal that can be approximated as a piecewise polynomial. In addition to prediction, the magnitude response of PPFs can be shaped to block additive noise present in the signal. In this paper, we discuss the implementation of IIR PPFs using fixed point arithmetic. If turns out to be possible to choose the filter length so that the predictive capabilities of the infinite precision filter are preserved exactly. Furthermore, for such filter lengths, the magnitude response is robust to coefficient quantization errors, and very low number of bits can be used to represent the coefficients while maintaining a close match to the original magnitude response shape. Based on these results, we suggest a straightforward method for designing IIR PPFs for fixed point implementations.