FIR prediction using Newton´s backward interpolation algorithm with smoothed successive differences

Two alternative extensions to Newton´s original backward interpolation algorithm that can be used to predict finite-order polynomials are proposed. In both approaches, the highest-order successive differences, corresponding to the constant nonzero derivatives, are smoothed before they are added to lower-order differences. The first smoother proposed is a linear lowpass filter, e.g. a moving averager that is optimal for attenuating white Gaussian and uniformly distributed noises, and the second one is a standard median filter that is optimal for double-exponentially distributed noise. These smoothers reduce the undesired gain of the entire predictor at the higher frequencies, thus making the modified Newton algorithms useful for real signal-processing applications