[time-nuts] Modified Allan Deviation and counter averaging

Bob Camp kb8tq at n1k.org
Sat Aug 1 17:17:59 EDT 2015


> On Aug 1, 2015, at 4:32 PM, Poul-Henning Kamp <phk at phk.freebsd.dk> wrote:
> --------
> In message <49C4CCD3-09CE-48A4-82B8-9285A43814E3 at n1k.org>, Bob Camp writes:
>> The approach you are using is still a discrete time sampling
>> approach. As such it does not directly violate the data requirements
>> for ADEV or MADEV.  As long as the sample burst is much shorter
>> than the Tau you are after, this will be true. If the samples cover < 1%
>> of the Tau, it is very hard to demonstrate a noise spectrum that
>> this process messes up.
> So this is where it gets interesting, because I suspect that your
> 1% "lets play it safe" threshold is overly pessimistic.

I completely agree with that. It’s more a limit that lets you do *some* sampling but steers clear
of any real challenge to the method. 

> I agree that there are other error processes than white PM which
> would get messed up by this and that general low-pass filtering
> would be much more suspect.
> But what bothers me is that as far as I can tell from real-life
> measurements, as long as the dominant noise process is white PM,
> even 99% Tau averaging gives me the right result.

Indeed a number of people noticed this with low pass filtering …. back 
a number (~1975) of years ago….

The key point being that white PM is the dominant noise process. If you have a discrete spur in there, 
it will indeed make a difference. You can fairly easily construct a sample averaging process that drops a zero on a spur 
(average over a exactly a full period …). How that works with discontinuous sampling is 
not quite as clean as how it works with a continuous sample (you now average over N out of M periods… ). 

> I have tried to find a way to plug this into the MVAR definition
> based on phase samples (Wikipedia's first formula under "Definition")
> and as far as I can tell, it comes out the same in the end, provided
> I assume only white PM noise.

Which is why *very* sharp people debated filtering on ADEV for years before anything really 
got even partial settled.

> But I have not found any references to this "optimization" anywhere
> and either I'm doing something wrong, or I'm doing something else
> wrong.
> I'd like to know which it is :-)

Well umm …. errr …. *some* people have been known to simply document
what they do. They then demonstrate that for normal noise processes it’s not an issue. 
Do an “adequate” number of real world comparisons and then move on with it. 
There are some pretty big names in the business that have gone that route. Some
of them are often referred to with three and four letter initials …. In this case probably note
the issue (or advantage !!) with discrete spurs and move on. 

If you are looking for real fun, I would dig out Stein’s paper on pre-filtering and ADEV. That would 
give you you a starting point and a framework to extend to MADEV. 

Truth in lending: The whole discrete spur thing described above is entirely from work on a very similar 
problem. I have *not* proven it with your sampling approach. 


> -- 
> Poul-Henning Kamp       | UNIX since Zilog Zeus 3.20
> phk at FreeBSD.ORG         | TCP/IP since RFC 956
> FreeBSD committer       | BSD since 4.3-tahoe    
> Never attribute to malice what can adequately be explained by incompetence.

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