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Noise reduction in unevenly sampling polynomial predictors

An efficient noise reduction technique for unevenly sampling polynomial predictors is introduced. Our prediction procedure is based on Newton's classical divided-difference interpolation formula. The optimal smoothing filter is derived for the linear Newton predictor, and it is shown to perform well also in nonlinear prediction. The improved algorithm finds applications, for example, in predictive upsampling or synchronization of unevenly spaced samples.