Autocorrelation of frequency-domain functions

Hi,

http://upload.wikimedia.org/math/d/d...2f2f619606.png is a signal, and http://upload.wikimedia.org/math/d/3...8c1793a733.png is signal-independent random noise.

I am reading a proof on Wikipedia (link), which says:

Quote:

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Originally Posted by Wikipedia

[...]we are assuming that the noise is independent of the signal, therefore:

http://upload.wikimedia.org/math/2/a...4601baaa1e.png

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What is the equivalent statement of this in terms of http://upload.wikimedia.org/math/d/d...2f2f619606.png and http://upload.wikimedia.org/math/d/3...8c1793a733.png?

Thanks.