“Wiener-Khintchine Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Wiener-Khintchine Theorem

释义

Wiener-Khintchine Theorem

Recall the definition of the Autocorrelation function of a function ,

(1)

Also recall that the Fourier Transform of

is defined by

(2)

giving a Complex Conjugate of

(3)

Plugging

and

into the Autocorrelation function therefore gives

so, amazingly, the Autocorrelation is simply given by the Fourier Transform of the Absolute Squareof

(5)

The Wiener-Khintchine theorem is a special case of the Cross-Correlation Theorem with

See also Autocorrelation, Cross-Correlation Theorem, Fourier Transform

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