On Tue, 28 Nov 2017 09:52:37 +0100 Mattia Rizzi <mattia.ri...@gmail.com> wrote:
> >Well, any measurement is an estimate. > > It's not so simple. If you don't assume ergodicity, your spectrum analyzer > does not work, because: > 1) The spectrum analyzer takes several snapshots of your realization to > estimate the PSD. If it's not stationary, the estimate does not converge. I do not see how ergocidity has anything to do with a spectrum analyzer. You are measuring one single instance. Not multiple. And no, you do not need stationarity either. The spectrum analyzer has a lower cut of frequency, which is given by its update rate and the inner workings of the SA. > 2) It's just a single realization, therefore also a flat signal can be a > realization of 1/f flicker noise. Your measurement has *zero* statistical > significance. A flat signal cannot be the realization of a random variable with a PSD ~ 1/f. At least not for a statisticially significant number of time-samples. If it would be, then the random variable would not have a PSD of 1/f. If you go back to the definition of the PSD of a random variable X(ω,t), you will see it is independent of ω. And about statistical significance: yes, you will have zero statistical significance about the behaviour of the population of random variables, but you will have a statistically significant number of samples of *one* realization of the random variable. And that's what you work with. Attila Kinali -- It is upon moral qualities that a society is ultimately founded. All the prosperity and technological sophistication in the world is of no use without that foundation. -- Miss Matheson, The Diamond Age, Neil Stephenson _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.