[time-nuts] Question about noisetypes and ADEV

Magnus Danielson magnus at rubidium.dyndns.org
Sun Oct 28 13:35:47 EDT 2018

Hej Anders!

On 10/28/18 1:14 PM, Anders Wallin wrote:
> I made a revised figure with a few improvements:
> - the PSDs now cross at 1Hz
> - the theoretical ADEV/MDEV pre-factors are now explicitly stated
> http://www.anderswallin.net/2018/10/noise-colours-again/
> source:
> https://github.com/aewallin/colorednoise/blob/master/example_noise_slopes2.py

This is a great illustration of what we have been discussing.

Notice that while the phase and frequency power densities neatly cross
at 1 Hz, the Allan Deviation and Modified Allan Deviation does not cross
at 1 s, in fact the cross-point between two noise-types is unique for
that pair, but around the same point.

The scale factors is due to how the details of the integration comes out.

> I forget where the MDEV-coefficients come from - maybe the Dawkins et al.
> paper? (worth adding to wikipedia also?)

Let me dig into that. I did that for ADEV and biases, and there is a
fair amount of copy from someone else, with some minor reformulations.
The biases for instance ended up with a rarely mentioned NIST publication.

> Also for flicker-PM there seems to be (slightly) different versions of the
> ADEV pre-factor in different references.

Yes, I've seen that too. For the Wikipedia I chose the more accurate
one, where as various forms of short-hands have been used. They are all
consistent as I recall it, but the difference is how they express the
value. Some combine the two constants into a single number, where as if
you do the integration you get three numbers, of which one depends on
tau and f_H.

It is worth mentioning that for WPM and FPM the integral does not
converge if allowed to go to infinite frequency, so the integral needs
to stop at the highest frequency f_H. The others do converge for
infinite frequency so the integrals continue to infinity rather than
stopping at f_H. So, the factors is not even created under the same
circumstances. On the other hand, for all practical matters I expect
them to be fairly close.


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