On causal band-limited mean square approximation
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We study causal dynamic approximation of non-bandlimited processes by band-limited processes such that a part of the historical path of the underlying process is approximated in $L_2$-norm by the trace of a band-limited process. This allows to cover the case of irregular non-smooth processes. We show that this problem has an unique optimal solution. The approximating band-limited process is obtained in time domain in a form of sinc series. To accommodate the current flow of observations, the coefficients of this series and the related band-limited process have to be changed dynamically. This can be interpreted as a causal and linear filter that is not time invariant.
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Dokuchaev, Nikolai (2012)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 ...
Dokuchaev, Nikolai (2013)We study causal dynamic smoothing of discrete time processes via approximation by band-limited discrete time processes. More precisely, a part of the historical path of the underlying process is approximated in Euclidean ...
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 ...