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Wiener–Khinchin theorem
In applied mathematics, the Wiener–Khinchin theorem, also known as the Wiener–Khintchine theorem and sometimes as the Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem, states that the autocorrelation function of a wide-sense-stationary random process has a spectral decomposition given by the power spectrum of that process.〔Hannan, E.J., "Stationary Time Series", in: John Eatwell, Murray Milgate, and Peter Newman, editors, ''The New Palgrave: A Dictionary of Economics. Time Series and Statistics'', Macmillan, London, 1990, p. 271.〕
==History==
Norbert Wiener proved this theorem for the case of a deterministic function in 1930;. Aleksandr Khinchin later 〔″Wiener's basic theory of 'generalised harmonic analysis' is in no way probabilistic, and the theorems apply to single well defined functions rather than to ensembles of functions.″ "A further development of these ideas occurs in the work of A. I. Khintchine (1894—1959) on stationary random processes (or stochastic processes)..." "...in contexts in which it is not important to distinguish the two aproaches the theory is often referred to as the Wiener—Khintchine theory."〕 formulated an analogous result for stationary stochastic processes and published that probabilistic analogue in 1934. Albert Einstein explained, without proofs, the idea in a brief two-page memo in 1914.
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