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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.

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Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack sxx.Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

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