# Dictionary: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 *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.