Wiener–Khinchin theorem

The Wiener–Khinchin theorem states that energy spectral density of a function is the Fourier Transform of the corresponding autocorrelation sequence. The theorem is a special case of the correlation theorem.

Continous case:

${\displaystyle S_{xx}(f)=\int _{-\infty }^{\infty }r_{xx}(\tau )e^{-j2\pi f\tau }d\tau }$

Discrete case:

${\displaystyle S_{xx}(f)=\sum _{k=-\infty }^{\infty }r_{xx}(k)e^{-j2\pi kf}}$