# Difference between revisions of "Dictionary:Wiener filter"

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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 normal equations (q.v.). Each frequency is passed proportional to

${\displaystyle {\frac {[S(f)]^{2}}{[S(f)]^{2}+[N(f)]^{2}}}}$.

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.