An Etymological Dictionary of Astronomy and Astrophysics

A theorem used in signal processing whereby the → spectral density of a random signal is the → Fourier transform of the corresponding → autocorrelation function. In other words, the autocorrelation function and the spectral density function constitute a → Fourier transform pair. The Wiener-Khinchin theorem allows one to estimate the spectral density function from the Fourier transform of the autocorrelation function, which is easier to handle. The theorem has an important application particularly
in radio astronomy. The two following → Fourier integrals are called the Wiener-Khinchin relations: K(τ) = ∫ J(f)e^-iωτdf and J(f) = ∫ K(τ)e^iωτdτ (both summed over -∞ to +∞), where K(τ) is the autocorrelation function and J(f) is the spectral density.

See also: Named after Norbert Wiener (1894-1964), American mathematician, who
first published this theorem in 1930, and Aleksandr Khinchin (1894-1959), Russian mathematician, who did so independently in 1934; → theorem.