Is this a universal relation between signal power and period (frequency)?

I am Fourier analyzing at a bunch of signals of equal length and find that $$\frac{d\ln({E[P]})}{d\ln({PT'})}$$ is constant across the dataset, where $T$ is a vector of the periods (inverse of frequencies) of each signal, and $P$ is the vector of the power corresponding to each of those periods. $E[P]$ is the mean power of the given signal. I include a graph to illustrate.

Should I expect this relation in any signal? Or does this point to something unique about the signals I am dealing with?

• Can you be a bit clearer about the make up of the "bunch of signals" you are using? Also, what is the length of the signals you are using are you taking the FFT of the whole signal? – tobassist Oct 4 '13 at 7:15