An Etymological Dictionary of Astronomy and Astrophysics
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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.

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.

In → magnetohydrodynamics, in the limit of zero → resistivity, the → magnetic field  B satisfies the → induction equation  ∂B/∂t = ∇ x (v x B), then for a → plasma confined by a perfectly conducting boundary, the → magnetic helicity is conserved. If the normal field is fixed on the boundary, the minimum-energy state is the linear → force-free magnetic field that conserves the total magnetic helicity.

Named after the Dutch astrophysicist Lodewijk Woltjer (1930-2019), who discovered the phenomenon in 1958 while studying the → Crab Nebula; → theorem.