Smoothing problem (stochastic processes): Difference between revisions

Revision as of 04:03, 13 March 2019

Revision as of 01:35, 22 August 2019

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Note that initially, the Wiener's filter was just a convolution, but the later developments were different: one was estimation and the other one was filter design in the sense of design of a convolution filter. This is a source of confusion.

Both the smoothing problem (in sense of estimation) and the filtering problem (in sense of estimation) are often confused with smoothing and filtering in other contexts (especially non-stochastic signal processing, often a name of various types of convolution). These names are used in the context of World War 2 with problems framed by people like [[Norbert Wiener]].<ref name="wiener-report"/><ref name="wiener-book" /> One source of confusion is the [[Wiener Filter]] is in form of a simple convolution. However, in Wiener's filter, two time-series are given. When the filter is defined, a straigtforwardstraightforward convolution is the answer. However, in later developments such as Kalman filtering, the nature of filtering is different to convolution and it deserves a different name.

The distinction is described in the following two senses: