Talk:Wiener–Khinchin theorem

The second equation in this article defines the autocovariance of a stationary process, not the autocorrelation; it's needs to be normalized by dividing by the time 0 autocovariance, or just the variance of the process.

Autocovariance vs. Autocorrelation

Autocovariance and autocorrelation are not the same thing.
A previous commenter got it wrong, too.
Call the first one C(τ) and call the second R(τ).
Now, the first one is set up so that C(0) = 0, or in electronics engineering terninology, this means that C(τ) does not have a "DC" value, and when we take the Fourier transform of C(τ), we DO NOT get a Dirac delta function in the spectral density S(f) at frequency f = 0.

In contrast, R(τ) CAN have a positive value, or in electronics engineering terminology, it can have a positive "DC" value. (Negative DC values cause other problems.) When we take the Fourier transform of R(τ) in that case, we DO get a Dirac delta function in the spectral density S(f) at frequency f = 0. Hence, S(f) is discontinuous at f = 0, and the derivative of S(f) does not exist at f = 0.

To summarize the relationship between C(τ) and R(τ), we have a simple equation: R(τ) = C(τ) + K, where K is a positive number or possibly zero.98.81.0.222 (talk) 01:12, 9 July 2012 (UTC)