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Recursive Filter

Recursive Filter:

In recursive filters , the output Math image at the moment Math image is a function of the output values Math image at the previous moments and, probably, of the input values.

A major advantage of recursive filters over nonrecursive filters is that they are computationally simpler. For example, for any recursive linear filter , there is a functionally equivalent non-recursive linear filter. But the non-recursive variant may be characterized by an infinitely large window size and, hence, be difficult for practical implementation. (See, for example, explanations on the exponential filter ).

Mathematically, a recursive filter may be described by the following general expression:


  • Math image is an arbitrary function of the previous output values Math image and input values Math image , linear or nonlinear.

Some examples of recursive filters are the exponential filter , the Kalman filter .

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