Spectral Power Density

$\begin{displaymath} P_y(\nu)\equiv\lim_{T\to\infty} {2\over T} \left\vert{\int_{-T/2}^{T/2} [y(t)-\bar y]e^{-2\pi i\nu t}\,dt}\right\vert^2, \end{displaymath}$

$\displaystyle \int_0^\infty P_y(\nu)\,d\nu$	$\textstyle =$	$\displaystyle \lim_{T\to\infty} {1\over T}\int_{-T/2}^{T/2} [y(t)-\bar y]^2\,dt$
	$\textstyle =$	$\displaystyle \left\langle{(y-\bar y)^2}\right\rangle{}={\sigma_y}^2.$

See also Power Spectrum