If you get into the computation of the Fourier Transform of the auto correlation funciton, you will find that you can do a 2-sided or a 1-sided Fourier Transform and they both give different results. The 2-sided Fourier Transform of the ACF is called a correlogram and the 1-sided Fourier Transform of the ACF is periodogram.
Usually, the correlogram is more accurate than the periodogram. A good book to learn the applications of this would be Spectral Analysis of Signals by Petre Stoica and Randolph Moses. Usually the EEG of nerve signals gives strong cross-correlations during neural activity and weak cross-correlations during lack of neural activity. This property is used in prosthetic devices to identify the activity the brain wishes to perform.