I have read several times that the variance for time domain data with a zero mean is equal to the integral of the power spectral density divided by N.
From wikipedia, the discrete form of Parseval's theorem is:
To my eye, the term on the left can only be called the variance of the time domain data if that data has a mean of zero. However, as I follow derivations of Parseval's theorem (poorly), I don't see any indication that the mean value of the time domain needs to be zero for the theorem to be applicable. Can anyone knowledgeable confirm this?