Difference between revisions of "Dictionary:Wiener filter"

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If a desired output is specified, the Wiener filter will give the output for an actual input which comes closest to the desired output. Also called a ''[[Dictionary:least-squares_filter|least-squares filter]]''. See [[Dictionary:Wiener-Hopf_equations|''Wiener-Hopf equations'']] and Sheriff and Geldart (1995, 293, 295, 559–560). Named for Norbert Wiener (1894–1964), American mathematician.
 
If a desired output is specified, the Wiener filter will give the output for an actual input which comes closest to the desired output. Also called a ''[[Dictionary:least-squares_filter|least-squares filter]]''. See [[Dictionary:Wiener-Hopf_equations|''Wiener-Hopf equations'']] and Sheriff and Geldart (1995, 293, 295, 559–560). Named for Norbert Wiener (1894–1964), American mathematician.
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Revision as of 12:37, 28 May 2014

(wē’ n∂r) A causal filter that will transform an input into a desired output as nearly as possible, subject to certain constraints. ‘‘As nearly as possible’’ (in a least squares sense) implies that the sum of the squares of differences between the filter output and the desired result is minimized. The filter optimizes standout of a signal S (which is a function of frequency, f) in the presence of random noise N (also a function of frequency). The filter is given by the normal equations (q.v.). Each frequency is passed proportional to

([S(f)]2)/([S(f)]2+[N(f)]2).


If a desired output is specified, the Wiener filter will give the output for an actual input which comes closest to the desired output. Also called a least-squares filter. See Wiener-Hopf equations and Sheriff and Geldart (1995, 293, 295, 559–560). Named for Norbert Wiener (1894–1964), American mathematician.