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The formula you quote, Sxx(ω):=limT→∞E[|1T−−√∫T0x(t)e−iωtdt|2], is not correct. I have never seen a reliable source that proves (or even asserts) that it converges. I see it a lot on the internet and in engineering textbooks: they never bother to assert that it converges.

There are many different ways to look at degrees of freedom. I wanted to provide a rigorous answer that starts from a concrete definition of degrees of freedom for a statistical estimator as this may be useful/satisfying to some readers:

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sxx|probability

Sxx in linear regression Sxx in linear regression
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How do I find Sxx in a Simple linear regression model? How do I find Sxx in a Simple linear regression model?
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What does SXX mean in statistics? What does SXX mean in statistics?
Find Sxx, Sxy, Syy, B1, B0, SST, SSR, SSE, R^2, R, Se for the。 Find Sxx, Sxy, Syy, B1, B0, SST, SSR, SSE, R^2, R, Se for the。
sxx|probability

sxx|probability

Form of the spectral density in Wiener Khinchin theorem? Form of the spectral density in Wiener Khinchin theorem? Form of the spectral density in Wiener Khinchin theorem? Form of the spectral density in Wiener Khinchin theorem? Form of the spectral density in Wiener Khinchin theorem?
Linear regression: degrees of freedom of SST, SSR, and RSS Linear regression: degrees of freedom of SST, SSR, and RSS Linear regression: degrees of freedom of SST, SSR, and RSS Linear regression: degrees of freedom of SST, SSR, and RSS Linear regression: degrees of freedom of SST, SSR, and RSS
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Showing that Showing that Showing that Showing that Showing that
Sxx in linear regression Sxx in linear regression Sxx in linear regression Sxx in linear regression Sxx in linear regression
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How do I find Sxx in a Simple linear regression model? How do I find Sxx in a Simple linear regression model? How do I find Sxx in a Simple linear regression model? How do I find Sxx in a Simple linear regression model? How do I find Sxx in a Simple linear regression model?
statistics statistics statistics statistics statistics
What does SXX mean in statistics? What does SXX mean in statistics? What does SXX mean in statistics? What does SXX mean in statistics? What does SXX mean in statistics?
Find Sxx, Sxy, Syy, B1, B0, SST, SSR, SSE, R^2, R, Se for the。 Find Sxx, Sxy, Syy, B1, B0, SST, SSR, SSE, R^2, R, Se for the。 Find Sxx, Sxy, Syy, B1, B0, SST, SSR, SSE, R^2, R, Se for the。 Find Sxx, Sxy, Syy, B1, B0, SST, SSR, SSE, R^2, R, Se for the。 Find Sxx, Sxy, Syy, B1, B0, SST, SSR, SSE, R^2, R, Se for the。

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