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Periodogram
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==Definition== There are at least two different definitions in use today.<ref name="Comparison"/> One of them involves time-averaging,<ref name="Wolfram"/> and one does not.<ref name="Matlab"/> Time-averaging is also the purview of other articles ([[Bartlett's method]] and [[Welch's method]]). This article is not about time-averaging. The definition of interest here is that the power spectral density of a continuous function, <math>x(t),</math> is the [[Fourier transform]] of its auto-correlation function (see [[Fourier transform#Cross-correlation theorem|Cross-correlation theorem]], [[Spectral density#Power spectral density|Spectral density]], and [[Wiener–Khinchin theorem]]): <math display="block">\mathcal{F}\{x(t)\circledast x^*(-t)\} = X(f)\cdot X^*(f) = \left| X(f) \right|^2.</math>
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