# [time-nuts] Allan variance by sine-wave fitting

Bob kb8tq kb8tq at n1k.org
Tue Nov 28 09:05:45 EST 2017

Hi

> On Nov 28, 2017, at 8:12 AM, Attila Kinali <attila at kinali.ch> wrote:
>
> On Tue, 28 Nov 2017 09:52:37 +0100
> Mattia Rizzi <mattia.rizzi at 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.

Coming back to ADEV, just as a SA has an upper frequency, lower frequency,
a couple of bandwidths, and persistence other devices have associated specs.
As these specs change, so do the readings you get. A noise floor measured with
a 100 KHz bandwidth is obviously different than one with a 1 KHz bandwidth.
That’s easy to spot looking at noise. If you are looking at a sine wave tone, it
may not be so obvious. Finding the “right” signal to show this or that with ADEV
is not always easy….. With some of these techniques, people have been
digging into this and that for decades.

Bob

>
>> 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
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