A nonlinear filter is the filter whose output is a nonlinear function of the input. By definition, any filter that is not a linear filter is a nonlinear filter. One practical reason to use nonlinear filters instead of linear filters is that linear filters may be too sensitive to a small fraction of anomalously large observations at the input.
One of the most commonly used nonlinear filters is the median filter .
Linear Filter: http://www.statistics.com/resources/glossary/l/linfilt.php
A linear filter is the filter whose output is a linear function of the input. Any output value of a linear filter is the weighted mean of input values. In other words, to form one element 
of the output at time 
, it is necessary to multiply the input values for time moments adjacent to by coefficients and to sum up the products.
Mathematically, the output of a linear filter may be described by the expression
 |
where
- is the output of the filter (the result of filtering);
-
is the input of the filter (the original time series to be filtered); -
is the size of the "window" of the filter - the number of the input values affecting one output value; -
are "weights" that completely describe any linear filter.
In contrast to nonlinear filter , there is a well developed and conceptually rich mathematical theory of linear filters.
All the linear filters are subdivided into two broad categories - nonrecursive filters and recursive filters .
Examples of a linear filters are: the rectangular filter , the triangular filter , the Gaussian filter , the exponential filter , Kalman filter .
See also: Smoother (Smoothing Filter) , predicting filter
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