Wiener filter is a MMSE estimator. The thing I am concerned about is whether it works in any type of additive noise? Does the expression of WF $H_{wf}(f)={S_{xy}(f)}/{S_{xx}(f)+N(f)}$ fits for arbitrary type of signal and noise? (y=x+n). Thanks,
The wiener filter is a linear filter and it is an MMSE estimator only if both the signal and the additive noise are Gaussian otherwise there might be better nonlinear estimators to estimate the signal.
However, if one restrict oneself to the class of linear estimators, the wiener filter still gives the best linear estimator provided that the signal and additive noise are both WSS (wide sense stationary).
I believe in the derivation of the Wiener filter we assume that the noise is uncorrelated with the signal.
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