Autocorrelation & PSD

Power Spectral Density — Wiener–Khinchin Theorem

Signal x(t)

Autocorrelation R(τ) = E[x(t)x(t+τ)]

Power Spectral Density S(f) = FFT{R(τ)}

Signal: f₁: f₂: Noise: Speed:

Wiener–Khinchin theorem: the power spectral density is the Fourier transform of the autocorrelation function. A periodic signal shows sharp PSD peaks; white noise has flat PSD and delta ACF. Autocorrelation reveals hidden periodicities even in noisy signals.