On one sided band-limitness and extrapolation of sequences
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The paper suggests a notion of left band-limitness for one-sided semi-infinite sequences representing traces of two-sided band-limited sequences. A method of detecting these sequences is obtained. For more general one-sided sequences without this feature, a method for calculation of the projections on the subspace formed by the left band-limited sequences is developed. These projections represent mean-square optimal causal band-limited approximations of one-sided sequences; the procedure can be interpreted as causal smoothing. The corresponding smoothed left band-limited processes allow unique extrapolations to future times that can be interpreted as optimal forecasts.
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Dokuchaev, Nikolai (2018)This paper suggests a method of optimal extension of one-sided semi-infinite sequences of a general type by traces of band-limited sequences in deterministic setting, i.e., without probabilistic assumptions. The method ...
Dokuchaev, Nikolai (2014)The paper studies frequency characteristics and predictability of real sequences, i.e., discrete time processes in deterministic setting. We consider band-limitness and predictability of one-sided sequences. We establish ...
Dokuchaev, Nikolai (2017)The paper suggests a method of recovering of missing values based on optimal approximation by band-limited processes for sequences, i.e. discrete time processes, that are not necessarily band-limited. The problem is ...