Wiener–Khinchin Theorem

The Wiener-Khinchin theorem states that the power spectral density S(f) of a wide-sense stationary process is the Fourier transform of its autocorrelation function R(τ) = E[X(t)X(t+τ)]. This deep duality links time-domain correlations to frequency-domain power, with fundamental applications in signal processing, turbulence, and quantum noise.