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In the context of signal averaging to reduce uncorrelated noise:

Is it possible to perform signal averaging from just the magnitude spectrum of certain signals? Or that would only work if we know also the phase information of those signals. In that case, what would be the requirement for the signals to average, regarding phase information? I guess they both have to be somehow "related" to the same "starting point".

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The short and most common answer is that you can average without phase but there are cases where you can average phase as well.

Cross correlation between 2 sigmals where one has a delayed component of the other that is of a "long" duration can exploit complex averaging.

Spectral analysis using the periodogram averages magnitude or magnitude squared.

There are numerous examples of where you do or don't use complex averaging. It depends on the problem being solved and is typically going to be relatively obvious if you should or shouldn't. If you expect the phase to evolve in a predictable way over your observations, you can use that to your advantage.

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  • $\begingroup$ Thanks for the answer @Stanley Pawlukiewicz . And what if the information is given in frequency bands (like octave bands let's say). Would averaging help in reducing noise as well in this case? I guess so, and I feel is kind of an stupid question but I just want to be sure. $\endgroup$ – sdiabr Nov 19 '18 at 22:16
  • $\begingroup$ In most circumstances that I can envision, yes averaging magnitude would make sense. Experimenting would settle the issue $\endgroup$ – Stanley Pawlukiewicz Nov 19 '18 at 22:54

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