[time-nuts] Zero dead time and average frequency estimation

Magnus Danielson magnus at rubidium.dyndns.org
Mon Feb 1 09:54:23 UTC 2010

Pete Rawson wrote:
> Gentlemen,
> You've hit a topic I've become more confused about after 
> researching some of the original papers on this subject.
> Here are a few questions which I would like to become 
> educated about.
> 1) Will the calculated results of ADEV, ODEV, MDEV & TOTDEV
>      suggest which result applies best to the data being analyzed?
> 2) What attributes of the data to be analyzed suggest which
>      computation is most appropriate?
> 3) Will some computed results indicate that the analysis is NOT
>      appropriate? (Are false results obvious?)

There are two things to keep in mind, the bias and the error bars.

Some of these estimators produces biased values as a result of the 
dominant noise source. You need to identify the dominant noise source 
(use the lag 1 autocorrelation noise identification, almost trivial to 
perform). Then with the dominant noise source identified the bias can be 

Error bars will high-light in which area of the graph where a particular 
estimator has problems. Comparing the spread of the error-bars between 
various estimators allow for identifying which is best for the task. 
Look at TOTAL and Theo variants.

Error bars is essentially a reformulation of the Equivalent Degrees of 
Freedom (EDF) and EDF change quite drastically with m. Comparison 
between different measurements can be done on EDF for m, and highest EDF 
wins. It's a measurement on how well the data in the sequence is used by 
the estimator.

> I'm sure there are more aspects worth learning than these, but
> they might serve to get a conversation underway.
> Any enlightenment would be greatly appreciated.

This has been the point of the exercise... spreading the knowledge.

I am digging too... but the little stuff I have picked up could probably 
be good knowledge to others, so I stirred the pot a little.


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