Wiener-Chinchin theorem

Rather than measuring the time correlation function of the scattering amplitude, one can also use a monochromator and determine the spectral density. As stated by the Wiener-Chinchin theorem, the spectral density of a fluctuating quantity and its time correlation function are related by Fourier-transformations. Applied to our case we may write... 

Rather than characterizing the dynamics of a fluctuating state variable by the time-dependent correlation function (X (0)X (t)), one can also describe it by the spectral density Xy u ) ). The Wiener—Chinchin theorem, a fundamental theorem of statistical physics, states that these two functions represent a pair of Fourier transforms, i.e.. 

---