Generalized IIR polynomial predictive filters
Konsta Koppinen, Jaakko T. Astola · 2000
The transfer functions of all polynomial predictors are derived. Previously proposed IIR polynomial predictive filters based on the feedback extension of FIR predictors are shown to be a special case of this general class. 1. INTRODUCTION Polynomial predictors refer to linear filters capable of unbiased extrapolation of polynomial signals. A motivation for polynomial predictors is that polynomial signal models are useful in several applications, e.g. control systems [1], signal smoothing [2] and noise reduction [3]. Recursive predictor structures and iterative algorithms for their optimization have been proposed in [4]. These are based on augmenting a FIR predictor by adding the delayed output of the filter to the input, resulting in unbiased estimation of polynomial signals while adding more degrees of freedom to the filter. In this paper, we show that the feedback extension method is a special case of a more general class of predictive IIR filters by deriving the possible transfer f...