On 05/13/2011 05:28 PM, Tijd Dingen wrote:
In trying to put together a way to calculate Allan variance based on a series
of timestamps of every Nth cycle, I ran into the following...
Suppose you have an input signal, but it's a bit on the high side. So you use a
prescaler to divide it down to a manageable frequency range. And now you want
to use that signal to be able to say something useful about the original high
frequency signal.
Now taking a look at the part about "Non-overlapped variable tau estimators" in
the wikipedia article here:
http://en.wikipedia.org/wiki/Allan_variance#Non-overlapped_variable_.CF.84_estimators
Nice to see people actually read and use what I wrote.
It seems to me that "divide by 4 and then measure all cycles back-to-back" is essentially the same
as "measure all cycles of the undivided high frequency signal back-to-back" and decimate. Or
"skipping past n − 1 samples" as the wiki article puts it. And that is disregarding /extra/ jitter
due to the divider, purely for the sake of simplicity.
If you use a prescaler of say 1/64 then it takes 64 cycles of the
original signal to cause a cycle to the counter core. These are then
time-stamped, i.e. a time-measure and an event counter measure is taken.
To transform the event-counter value into the properly scaled event
value, you then multiply the event counter by 64, since it took 64 times
more events than counted by the counter. The time-stamps does not have
to be modified.
Notice that the pre-scaler is only used for higher frequencies.
Plus, I strongly suspect that all these commercial counters that can
handle 6 Ghz and such are not timestamping every single cycle
back-to-back either. Especially the models that have a few versions
in the series. One cheaper one that can handle 300 MHz for example,
and a more expensive one that can handle 6 GHz. That reads like:
"All models share the same basic data processing core and the same
time interpolators. For the more expensive model we just slapped on
an high bandwidth input + a prescaler."
You never time-stamp individual cycles anyway, so a pre-scaler doesn't
do much difference. It does limit the granularity of the tau values you
use, but usually not in a significant way since Allan variance is rarely
used for taus shorter than 100 ms and well... pre-scaling usually is
below 100 ns so it isn't a big difference.
Anyways, any drawbacks to calculating Allan Variance of a divided signal that I
am overlooking here?
No significant, it adds to the noise floor, but in practice the
time-stamping and processing doesn't have big problems due to it.
Cheers,
Magnus
_______________________________________________
time-nuts mailing list -- [email protected]
To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
