[time-nuts] Modified Allan Deviation and counter averaging

Magnus Danielson magnus at rubidium.dyndns.org
Sun Aug 2 01:52:02 EDT 2015

Hi Poul-Henning,

On 08/01/2015 10:32 PM, Poul-Henning Kamp 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 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.
> 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.

I put that formula there, and I think Dave trimmed the text a little.

For true white PM *random* noise you can move your phase samples around, 
but you gain nothing by bursting them. For any other form of random 
noise and for the systematic noise, you alter the total filtering 
behavior as compared to AVAR or MVAR, and it is through altering the 
frequency behavior rhat biases in values is born. MVAR itself has biases 
compared to AVAR for all noises due to its filtering behavior.

The bursting that you propose is similar to the uneven spreading of 
samples you have in the dead-time sampling, where the time between the 
start-samples of your frequency measures is T, but the time between the 
start and stop samples of your frequency measures is tau. This creates a 
different coloring of the spectrum than if the stop sample of the 
previous frequency measure also is the start sample of the next 
frequency measure. This coloring then creates a bias-ing depending on 
the frequency spectrum of the noise (systematic or random), so you need 
to correct it with the appropriate biasing function. See the Allan 
deviation wikipedia article section of biasing functions and do read the 
original Dave Allan Feb 1966 article.

For doing what you propose, you will have to define the time properities 
of the burst, so that woould need to have the time between the bursts 
(tau) and time between burst samples (alpha). You would also need to 
define the number of burst samples (O). You can define a bias function 
through analysis. However, you can sketch the behavior for various 
noises. For white random phase noise, there is no correlation between 
phase samples, which also makes the time between them un-interesting, so 
we can re-arrange our sampling for that noise as we seem fit. For other 
noises, you will create a coloring and I predict that the number of 
averaged samples O will be the filtering effect, but the time between 
samples should not be important. For systematic noise such as the 
quantization noise, you will again interact, and that with a filtering 

At some times the filtering effect is useful, see MVAR and PVAR, but for 
many it becomes an uninteresting effect.

> 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 :-)

You're doing it wrong. :)

PS. At music festival, so quality references is at home.


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