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. ‘‘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 [[Dictionary:normal_equations|''normal equations'']] (q.v.). Each frequency is passed proportional to  
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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 [[Dictionary:normal_equations|''normal equations'']] (q.v.). Each frequency is passed proportional to  
  
<center>(&#x005B;''S''(''f'')&#x005D;<sup>2</sup>)/(&#x005B;''S''(''f'')&#x005D;<sup>2</sup>+&#x005B;''N''(''f'')&#x005D;<sup>2</sup>).</center>
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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, 559-560). 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&#x2013;560). Named for Norbert Wiener (1894&#x2013;1964), American mathematician.
 
  
 
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[[Category:Pages with unformatted equations]]

Revision as of 02:06, 23 February 2015

(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

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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 least-squares filter. See Wiener-Hopf equations and Sheriff and Geldart (1995, 293, 295, 559-560). Named for Norbert Wiener (1894-1964), American mathematician.