Difference between revisions of "Dictionary:Wiener filter"

From SEG Wiki
Jump to: navigation, search
(Categorizing pages with HTML math)
(Marked this version for translation)
 
(3 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 +
<languages/>
 +
<translate>
 +
</translate>
 
{{#category_index:W|Wiener filter}}
 
{{#category_index:W|Wiener filter}}
(w&#x0113;&#x2019; n&#x2202;r) A causal filter that will transform an input into a desired output as nearly as possible, subject to certain constraints. &#x2018;&#x2018;As nearly as possible&#x2019;&#x2019; (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  
+
<translate>
 +
<!--T:1-->
 +
(w&#x0113;&#x2019; n&#x2202;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  
  
<center>(&#x005B;''S''(''f'')&#x005D;<sup>2</sup>)/(&#x005B;''S''(''f'')&#x005D;<sup>2</sup>+&#x005B;''N''(''f'')&#x005D;<sup>2</sup>).</center>
+
<!--T:2-->
 +
<center><math> \frac{[S(f)]^2}{[S(f)]^2+[N(f)]^2}</math>.</center>
  
  
 
+
<!--T:3-->
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.
+
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.
 
+
</translate>
[[Category:Pages with unformatted equations]]
 

Latest revision as of 19:09, 18 September 2018

Other languages:
English • ‎español


(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.