The Wiener-Khinchin Theorem states that the power spectral density of a wide-sense stationary random process equals the Fourier transform of that process's autocorrelation function. Named for Norbert Wiener and Aleksandr Khinchin, it is the foundational result connecting the time-domain statistics of a random signal to its frequency-domain behavior, underlying spectral analysis throughout signal processing and time series statistics.
Facts
Partially Attested
Proof YearWikipedia dates the deterministic case to Wiener in 1930 and the stochastic version to Khinchin in 1934; no single proof year applies to both namesakes. StatementThe power spectral density of a wide sense stationary random process is equal to the Fourier transform of that process's autocorrelation function. 2 Classification
Statement Form Sources
1. Wikipedia: Wiener-Khinchin theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
In applied mathematics and statistics, the Wiener-Khinchin theorem or Wiener-Khintchine theorem, also known as the Wiener-Khinchin-Einstein theorem or the Khinchin-Kolmogorov theorem, states that the power spectral density of a wide-sense-stationary random process is equal to the Fourier transform of that process's autocorrelation function.
2. Wiener-Khinchin theorem (Wikipedia)
Lead section
the power spectral density of a wide-sense-stationary random process is equal to the Fourier transform of that process's autocorrelation function
History section
Khinchin published that probabilistic analogue in 1934
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