Smoothing problem (stochastic processes): Difference between revisions

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Both smoothing problems and filtering problems are often confused with smoothing and filtering in other contexts (especially non-stochastic signal processing). These names are used in the context of World War 2 defined by people like Norbert Wiener <ref name="wiener-report"/><ref name="wiener-book" />.
 
Smoothing in the sense of convolution, means low-pass filtering, convolution with a kernel or blurring (image processing).
In the Filtering Problem the information from observation up to the time of the current sample is used. In smoothing all observation samples are used (from future). Filtering is causal but smoothing is batch processing of the same problem, namely, estimation of a time-series process based on serial incremental observations.
 
In the Filtering Problemproblem the information from observation up to the time of the current sample is used. In smoothing all observation samples are used (from future). Filtering is causal but smoothing is batch processing of the same problem, namely, estimation of a time-series process based on serial incremental observations.
 
== See Also==