| Abstract: |
Predictive signal processing aims at producing estimates of future values of a signal,based on previous values and some knowledge on the characteristics of the signal.Prediction is useful for overcoming signal delays, which is important especially inreal-time control systems, and for optimizing the allocation of system resources, e.g.,communication channels. In practical measurement and instrumentation systems, thesignal is delayed by the nonidealities of the equipment used, e.g., in performing Ana-log-to-Digital conversions and messaging over communication buses and networks.Additionally, many signal processing algorithms, such as median filtering and blockalgorithms like the Fast Fourier Transform, cause algorithmic delay to the signal. Incontrol applications, signal prediction can be used to prepare the system for futureevents, e.g., the increased need for power.In engineering literature, several approaches to signal prediction have beenproposed, including Autoregressive Moving Average (ARMA) models, the Kalmanfilter, Artificial Neural Networks, and methods based on time-domain modeling. Theapplicability of each method on a given problem depends on the nature of the signal tobe predicted, the amount of a priori knowledge available on the signal, the predictionaccuracy required, and the computational resources available.Polynomial prediction is based on modeling the signal as a polynomial of alow degree over short intervals of time and extrapolating that model to the near future.This polynomial model is applicable to signals that change only slowly over time andcontain little additive noise. If these conditions are met by the signal, polynomial pre-dictors, very light to implement in comparison to most other prediction algorithms,become available. Finite Impulse Response (FIR) and Infinite Impulse Response (IIR)filters with fixed coefficients can be used for producing predictions of a polynomialsignal.In this work, the existing theory of FIR polynomial predictive filters (PPFs) isextended by considering complex-valued signals, with two independent polynomialcomponents, and the case where arbitrary input samples may be missing. These theo-
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