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

Pete Rawson peterawson at earthlink.net
Mon Feb 1 04:40:11 UTC 2010

```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?)

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.

Pete Rawson

On Jan 31, 2010, at 8:50 PM, Tom Van Baak wrote:

> Magnus,
>
> Correct, all the terms cancel between the end points. Note
> that this is exactly equivalent to the way a traditional gated
> frequency counter works -- you open the gate, wait some
> sample period (maybe 1, 10, or 100 seconds) and then
> close the gate. In this scenario it's clear that all the phase
> information during the interval is ignored; the only points
> that matter are the start and the stop.
>
> Modern high-resolution frequency counters don't do this;
> and instead they use a form of "continuous counting" and
> take a massive number of short phase samples and create
> a more precise average frequency out of that.
>
> There are some excellent papers on the subject; start with
> the one by Rubiola:
>
> < http://www.femto-st.fr/~rubiola/pdf-articles/journal/2005rsi-hi-res-freq-counters.pdf >
>
> There are additional papers (perhaps Bruce can locate them).
>
> I wonder if fully overlapped frequency calculations would be
> one solution to your query; similar to the advantage that the
> overlapping ADEV sometimes has over back-to-back ADEV.
>
> Related to that, I recently looked into the side-effects of using
> running averages on phase or frequency data, specifically
> what it does to a frequency stability plot (ADEV). See:
>
> http://www.leapsecond.com/pages/adev-avg/
>
> Not surprising, you get artificially low ADEV numbers when
> you average in this way; the reason is that running averages,
> by design, tend to smooth out (low pass filter) the raw data.
>
> One thing you can play with is computing average frequency
> using the technique that MDEV uses.
>
> /tvb
>
> ----- Original Message ----- From: "Magnus Danielson" <magnus at rubidium.dyndns.org>
> To: "Discussion of precise time and frequency measurement" <time-nuts at febo.com>
> Sent: Sunday, January 31, 2010 6:53 PM
> Subject: [time-nuts] Zero dead time and average frequency estimation
>
>
>> Fellow time-nuts,
>> I keep poking around various processing algorithms trying to figure out what they do and perform. One aspect which may be interesting to know about is the use of zero dead time phase or frequency data and the frequency estimation from that data. One may be compelled to differentiate the time data into frequency data by using nearby data samples, according to y(i) = (x(i+1)-x(i))/tau0 and then just form the average of those. The interesting thing about that calculations is that the x(i+1) and x(i) terms cancels except for x(1) and x(N) so effectively only two samples of phase data is being used. This is a simple illustration of how algorithms may provide less degrees of freedom than one may initially assume it to have (N-1 in this case).
>> Similar type of cancellation occurs in linear drift estimation.
>> Maybe this could spark some interest in the way one estimates the various parameters and what different estimators may do to cancel noise of individual samples.
>> Cheers,
>> Magnus
>
>
>
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