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 Connections
Has Statement Form
In Branch
Source Wiener-Khinchin theorem (Wikipedia)
Proved By
Source Wiener-Khinchin theorem (Wikipedia)
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
Norbert Wiener proved this theorem for the case of a deterministic function in 1930; Aleksandr Khinchin later formulated an analogous result for stationary stochastic processes and published that probabilistic analogue in 1934.
- In Branch: Probability and Statistics, Lead sentence
Proved By: Aleksandr Khinchin, Lead
Norbert Wiener proved this theorem for the case of a deterministic function in 1930; Aleksandr Khinchin later formulated an analogous result for stationary stochastic processes and published that probabilistic analogue in 1934
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.