[time-nuts] Characterising frequency standards

[Steve Rooke]

If I take two sequential phase readings from an input source and place
this into one data set and aniother two readings from the same source
but spaced by one cycle and put this in a second data set. From the
first data set I can calculate ADEV for tau = 1s and can calculate
ADEV for tau = 2 sec from the second data set. If I now pre-process
the data in the second set to remove all the effects of drift (given
that I have already determined this), I now have two 1 sec samples
which show a statistical difference and can be fed to ADEV with a tau0
= 1 sec producing a result for tau = 1 sec. The results from this
second calculation should show equal accuracy as that using the first
data set (given the limited size of the data set).

I now collect a large data set but with a single cycle skipped between
each sample. I feed this into ADEV using tau0 = 2 sec to produce tau
results >= 2 sec. I then pre-process the data to remove any drift and
feed this to ADEV with a tau0 = 1 sec to produce just the tau = 1 sec
result. I now have a complete set of results for tau >= 1 sec. Agreed,
there is the issue of modulation at 1/2 input f but ignoring this for
the moment, this should give a valid result.

Now indulge me while I have a flight of fantasy.

As the effects of jitter and phase noise will produce a statistical
distribution of measurements, any results from these ADEV calculations
will be limited on accuracy by the size of the data set. Only if we
sample for a very long time will we see the very limits of the effects
of noise. The samples which deviate the most from the median will
occur very infrequently and it is statistically likely that they will
not occur adjacent to another highly deviated sample. We could
pre-process the data to remove all drift and then sort it into an
array of increasing size. This would give the greatest deviations at
each end of the array. For 1 sec stability the deviation would be the
greatest difference from the median of the first and last samples in
the array. For a 2 sec stability, this same calculation could be made
taking the first two and last two readings in the array and
calculating their difference from 2 x the median. This calculation
could be continued until all the data is used for the final
calculation. In fact the whole sorted data set could be fed to ADEV to
produce a result that would show better worse case measurement of the
input source which still has some statistical probability. In theory,
if we took an infinite number of samples, there would be a whole
string of absolutely maximum deviation measurements in a row which
would show the absolute worse case.

Is any of this valid or just bad physics, I don't know, but I'm sure
it will solicit interesting comment.

73,
Steve

2009/4/10 Tom Van Baak <tvb at leapsecond.com>:
>> I think the penny has dropped now, thanks. It's interesting that the
>> ADEV calculation still works even without continuous data as all the
>> reading I have done has led me to belive this was sacrosanct.
>
> We need to be careful about what you mean by "continuous".
> Let me probe a bit further to make sure you or others understand.
>
> The data that you first mentioned, some GPS and OCXO data at:
>    http://www.leapsecond.com/pages/gpsdo-sim
> was recorded once per second, for 400,000 samples without any
> interruption; that's over 4 days of continuous data.
>
> As you see it is very possible to extract every other, or every 10th,
> every 60th, or every Nth point from this large data set to create a
> smaller data set.
>
> Is it as if you had several counters all connected to the same DUT.
> Perhaps one makes a new phase measurement each second,
> another makes a measurement every 10 seconds; maybe a third
> counter just measures once a minute.
>
> The key here is not how often they make measurements, but that
> they all keep running at their particular rate.
>
> The data sets you get from these counters all represent 4 days
> of measurement; what changes is the measurement interval, the
> tau0, or whatever your ADEV tool calls it.
>
> Now the ADEV plots you get from these counters will all match
> perfectly with the only exception being that the every-60 second
> counter cannot give you any ADEV points for tau less than 60;
> the every-10 second counter cannot give you points for tau less
> than 10 seconds; and for that matter; the every 1-second counter
> cannot give you points for tau less than 1 second.
>
> So what makes all these "continuous" is that the runs were not
> interrupted and that the data points were taken at regular intervals.
>
> The x-axis of an ADEV plot spans a logarithmic range of tau. The
> farthest point on the *right* is limited by how long your run was. If
> you collect data for 4 or 5 days you can compute and plot points
> out to around 1 day or 10^5 seconds.
>
> On the other hand, the farthest point on the *left* is limited by how
> fast you collect data. If you collect one point every 10 seconds,
> then tau=10 is your left-most point. Yes, it's common to collect data
> every second; in this case you can plot down to tau=1s. Some of
> my instruments can collect phase data at 1000 points per second
> (huge files!) and this means my leftmost ADEV point is 1 millisecond.
>
> Here's an example of collecting data at 10 Hz:
> http://www.leapsecond.com/pages/gpsdo/
> You can see this allows me to plot from ADEV tau = 0.1 s.
>
> Does all this make sense now?
>
>> What I now believe is that it's possible to measure oscillator
>> performance with less than optimal test gear. This will enable me to
>> see the effects of any experiments I make in the future. If you can't
>> measure it, how can you know that what your doing is good or bad.
>
> Very true. So what one or several performance measurements
> are you after?
>
> /tvb
>
>
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-- 
Steve Rooke - ZL3TUV & G8KVD & JAKDTTNW
Omnium finis imminet