RECURSIVE LINEAR SMOOTHED NEWTON PREDICTORS FOR POLYNOMIAL EXTRAPOLATION

Newton predictors have been used by mathematicians to extrapolate tables of polynomials and transcendental functions. However, the predictors based on this computationally efficient algorithm have considerable gain at the higher frequencies. This property reduces their applicability to practical signal processing where the narrow-band primary signal is often corrupted by additive wide-band noise. In a recent paper, two alternative modifications were proposed to the original algorithm that can be used to extrapolate low-order polynomials. In both approaches, the highest order difference of successive input samples, approximating the constant nonzero derivative, is smoothed before it is added to the lower order differences. The additional smoothers reduce the undesired noise gain of Newton predictors. In this paper, we extend the Linear Smoothed Newton (LSN) predictor by including a recursive term into the basic transfer function and cascading the rest of the successive difference paths with appropriately delayed extrapolation filters of corresponding polynomial orders. This leads to a new class of computationally efficient IIR predictors with significantly lowered gain at the higher frequencies. The introduced Recursive Linear Smoothed Newton predictor is analyzed in the time and frequency domains, and compared to the original Newton predictor, the LSN predictor, and the optimal Heinonen-Neuvo FIR predictor.