Recall the definition of the autocorrelation function C(t) of a function E(t), C(t) congruent integral_(-∞)^∞ E^_(τ) E(t + τ) d τ. Also recall that the Fourier transform of E(t) is defined by E(τ) = integral_(-∞)^∞ E_ν e^(-2 π i ντ) d ν, giving a complex conjugate of E^_(τ) = integral_(-∞)^∞ E^__ν e^(2π i ντ) d ν.

autocorrelation | cross-correlation theorem | Fourier transform | Plancherel's theorem | power spectrum

Aleksandr Yakovlevich Khinchin | Norbert Wiener