OK, I have been banging my head for quite a while trying to make sense of this simple equation:
The $1/T$ is what is causing me all the grief. I assume that the square of the Fourier transform of the signal $X$ is a finite function. So won't the $T$ in the denominator mean that the PSD, $S_x$, will always tend toward zero? If $X$ does increase to infinity with time, can someone explain this to me? I am thinking that $X$ is a measure of the frequency content of the random time signal, and that shouldn't change appreciably with the time taken to measure it.