Optimal polynomial predictors with application specific fixed prefilters

A prefiltering approach for optimal prediction of polynomial signals is proposed. The new scheme enables the use of an arbitrary prefilter for which a finite impulse response (FIR) postfilter is optimized. The FIR postfilter is designed such that polynomial signals of given order are predicted unchanged, with additional degrees of freedom used for minimization of the noise gain. It is shown with examples that by providing an FIR predictor with a simple first-order recursive prefilter the noise gain can be greatly reduced at minimal additional implementation cost