Recursive linear smoothed Newton predictors for polynomial extrapolation

Abstract

Newton predictors have considerable gain at the higher frequencies, which reduces their applicability to practical signal processing where the narrowband primary signal is often corrupted by additive wideband noise. Two modifications that can be used to extrapolate low-order polynomials have been proposed. 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, reducing the undesired noise gain. The linear smoothed Newton (LSN) predictor is extended in this work by including a recursive term in 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 computationally efficient IIR predictors with significantly lowered gain at the higher frequencies. The recursive predictor is analyzed in the time and frequency domains and compared to the other predictors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>