Recall the definition of the Autocorrelation function of a function ,

(1) 
Also recall that the Fourier Transform of is defined by

(2) 
giving a Complex Conjugate of

(3) 
Plugging and into the Autocorrelation function therefore gives
so, amazingly, the Autocorrelation is simply given by the Fourier Transform of the Absolute Square
of ,

(5) 
The WienerKhintchine theorem is a special case of the CrossCorrelation Theorem with .
See also Autocorrelation, CrossCorrelation Theorem, Fourier Transform
© 19969 Eric W. Weisstein
19990526