Wiener-Khinchin Theorem

S(f) = FT[C(τ)] — autocorrelation and power spectral density are Fourier pairs




Wiener-Khinchin: C(τ) = ∫x(t)x(t+τ)dt, S(f) = ∫C(τ)e^{-2πifτ}dτ. Peaks in S(f) correspond to oscillations in C(τ). Colored noise: S(f)∝f^{-α}.