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I'm trying to estimate the spectrum of a noisy time series and considering two approaches and their relative correctness.

Let's say the time series is 800s long. Option 1 is to do a Welch spectrum with samples of 20s length with 50% overlap with each sample. Option 2 is, I pick 20s samples at random 100 times (ideally, should cover the full time series), produce the PSD of each sample, and average them to produce an estimate. So this would be like a Bartlett estimate using random sampling instead of systematic non-overlapping samples. Is there one of the above that's more correct? It seems to me that the random sampling may produce snippets that are more statistically independent. They certainly don't give the same answer. The PSD produced by the random sampling is consistently giving lower values than the Welch spectrum. Any thoughts are appreciated.

Thanks!

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