[time-nuts] Re: Can ADEV of a frequency source be correctly determined using a continuous time-stamping frequency counter?

[Magnus Danielson]

Hi Erik,

On 2021-11-09 18:26, Erik Kaashoek wrote:
> As far as I understood the ADEV at a Tau of 1 second is a statement 
> about the amount of variation to be expected over a one second interval.
Rather, the variation of readings of a frequency estimation done over a 
span over 1 second.
> It would be nice if we would be able to measure a frequency in an 
> infinite short interval but any frequency measurement takes time.
Turn out that basic white noise and systematic noise will limit our 
frequency resolution to form a 1/tau limit slope, so infinite short 
interval will bury it well into that noise whatever we do.
> What if the frequency counter does a complete measurement of a 
> frequency source every second and all the variation within that second 
> is hidden because of the "integration" that happens over the second?

That is what happens, but that is not what the ADEV is about, it's about 
the variations of these measures as we look for a bunch of them. So if 
we now have say 1000 of these frequency estimates, how much variations 
in these can be contributed to the random noise of the source, and to 
analyse that, we need at least a tool like ADEV since standard deviation 
will not even converge for white and flicker phase noise modulation.

What ADEV actually aims to do is to provide a low-frequency spectroscopy 
method at a time when time-interval counters was about the only tool at 
hand, and even those where very rare. We now have a much wider palette 
of tools, but ADEV is relevant for how we measure frequency stability 
and a few other applications.

> This is specially the case with continuous time-stamping counters.
> They can provide a precise number by applying statistical methods on 
> many measurements done during one second but they can not provide 
> information exactly at the end of a second.
> Is this kind of statistical measurement over a period of a second 
> still valid for determining the ADEV at the Tau of one second of a 
> frequency source?
Not for ADEV, but if you use averaging counter you get the result of 
MDEV and for linear regression / least square counter you get the 
response of PDEV. That is the result of various statistical measures and 
then applying the ADEV processing on these frequency estimates. The 
upcoming IEEE Std 1139 revision, which is in approval process now 
include language to reflect that.
> Or should there be a correction factor depending on the method used in 
> the frequency counter?

Yes, you then need to use the appropriate bias function for ADEV/MDEV 
and ADEV/PDEV to convert between these scales. Knowing the response of 
ADEV, MDEV and PDEV for a particular noise-type which is dominant at the 
tau of interest, you can readily convert between them by forming the 
bias functions.

You may find NIST SP-1065 a useful and handy tool, even if it does not 
cover the more recent work such as PDEV.

https://www.nist.gov/publications/handbook-frequency-stability-analysis

> I tried to read some scientific studies on this subject but I am not 
> smart enough to understand.
> Hope one of you can provide some information.

It is scattered over a large number of articles, and quite a lot of 
folks get confused. Hopefully the updated IEEE Std 1139 will be of aid 
to you. It also has lots of useful references.

Cheers,
Magnus