Hi > On Nov 30, 2017, at 11:10 AM, Magnus Danielson <mag...@rubidium.dyndns.org> > wrote: > > > > On 11/30/2017 03:40 PM, Attila Kinali wrote: >> On Thu, 30 Nov 2017 12:44:13 +0100 >> Mattia Rizzi <mattia.ri...@gmail.com> wrote: >>> Let me emphasize your sentence: "you will have a statistically significant >>> number of samples of *one* realization of the random variable.". >>> This sentence is the meaning of ergodic process [ >>> https://en.wikipedia.org/wiki/Ergodic_process] >>> If it's ergodic, you can characterize the stochastic process using only one >>> realization. >>> If it's not, your measurement is worthless, because there's no guarantee >>> that it contains all the statistical information. >> You are mixing up ergodicity and reproducability. >> Also, you are moving the goalpost. >> We usually want to characterize a single clock or oscillator. >> Not a production lot. As such the we only care about the statistical >> properties of that single instance. If you want to verify that your >> production lot has consistent performance metrics, then this is a >> completely different goal and requires a different methodology. But >> in the end it will boil down to measuring each clock/oscillator >> individualy to make sure it fullfils the specs. >>>> 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 >>> >>> Without ergodicity you cannot claim it. You have to suppose ergodicity. >> If you demand ergodicity, you cannot have 1/f. >> You can have only one or the other. Not both. >> And if you choose ergodicity, you will not faithfully model a clock. >> >>> If it's not stationary, it can change over time, therefore you are not >>> authorized to use a SA. It's like measuring the transfer function of a >>> time-varying filter (e.g. LTV system), the estimate doesn't converge. >> Please take one of the SA's you have at CERN, measure an oscillator >> for a long time and note down the center frequency with each measurement. >> I promise you, you will be astonished. > > After tons of measurements and attempts on theory a model was formed that was > sufficiently consistent with measurements. > > The model that fits observation makes much of the traditional statistical > measures and definitions "tricky" to apply. > > Flicker, that is PSD of 1/f, still is tricky to hunt down the real root and > model it, so we just use approximation in it's place because we need to have > something to work with.
I believe that was roughly the third thing the prof said when he introduced 1/F noise back when I was in school. It *might* have been the fourth thing …. that was a long time ago …. Bob > Even without flicker, the white frequency noise messes with us. > > This thread seems to lost contact with these aspects. > > Cheers, > Magnus > _______________________________________________ > 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. _______________________________________________ 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.