[time-nuts] Is there a good web page introducing ADEV?

[Magnus Danielson]

On 2020-09-24 22:11, Richard (Rick) Karlquist wrote:
> Another great post, Tom.
>
> Amplifying Tom's last paragraph:
>
> 1.  The statistics of clocks are (take your pick)
>
> a.  Not gaussian, central limit theorem doesn't apply
> b.  Not stochastic
> c.  Not stationary
> d.  Not ergodic
> e.  Contain flicker of frequency processes that do not
> average to zero; AKA 1/f noise.

Actually flicker noise is a border-case of average to zero or not. Seems
to, but cannot be shown, but it has great deviations from this.

f. Integrated white and flicker noise. These will for sure not average
to zero.

>
> IOW, most of what you think you know about statistics doesn't
> apply.  For example, "variance" is undefined because "mean" is
> undefined.  It is important to get inside Dave Allan's head in
> terms of why he invented this in the first place.
This is all true, except for the last part, since you really need to
consider the duo of Jim Barnes and David Allan. If you look at the early
work, their work and contribution overlap. Some of the important math
was actually discovered by Jim Barnes. They had to work hard to figure
out a way to overcome the lack of a meaningful mean value, and they did
that by reducing the mean to a minimum, over 2 frequency values and then
average over that.
>
> 2.  Many poorly informed practitioners are in denial about the
> above and resort the measures known as "jitter" or "wander".
> These further muddy the water.  They are IMHO, even more difficult
> to understand than ADEV.  They have their place (a very narrow one)
> but should be disregarded if you want to understand ADEV.
>
Well, there is a context where these terms have a very clear and
practical meaning, and the narrow place they have is wide scale telecom
and broadcast use, and anything else falling into that category, which
is more and more. Using these terms where they are not meant to is
however just asking for trouble. However, in their telecom context they
have a very useful meaning with very practical and important implications.
> 3.  Unlike phase noise, ADEV is a fairly non-intuitive concept.
> While there are methods to convert phase noise to ADEV, you
> can't go in the other direction.
>
> You sometimes hear the phrase "this is not rocket science".
> Well in the case of ADEV, it IS rocket science (or at least
> rocket statistics).

ADEV is poorly explained many times, I did try at one point in time to
make the Wikipedia article fairly clear, and I think it may need to be
revisited because of many edits later things may have been lost. ADEV is
really the very specific estimation of two-point frequency estimation
stability as measured over two points of frequency measures. If this is
the type of measurement you want to do, it's meaningful. You can
understand some properties in those terms. At the time, measuring this
way was the only meaningful way they felt they had, they had counters to
handle the "long term stability", so they had to make sense of the
statistics that came out of those counters, that's how we ended up with
the ADEV, that was what was on David Allans mind at the time.

Cheers,
Magnus