# Difference between revisions of "Dictionary:Wiener filter"

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{{#category_index:W|Wiener filter}} | {{#category_index:W|Wiener filter}} | ||

− | (wē’ n∂r) A causal filter that will transform an input into a desired output as nearly as possible, subject to certain constraints. | + | <translate> |

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+ | (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 [[Special:MyLanguage/Dictionary:normal_equations|''normal equations'']] (q.v.). Each frequency is passed proportional to | ||

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+ | <center><math> \frac{[S(f)]^2}{[S(f)]^2+[N(f)]^2}</math>.</center> | ||

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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 | + | 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 ''[[Special:MyLanguage/Dictionary:least-squares_filter|least-squares filter]]''. See [[Special:MyLanguage/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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## Latest revision as of 18:09, 18 September 2018

(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

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.