[time-nuts] Re: Timestamping counter techniques : phase computation question

[Erik Kaashoek]

Thanks all for the good input.

@Magnus, I need some time to understand the math as it has been over 30
years since when I used to do this kind of math.
There is no intention to store the collected captures, only to present a
measurement at the measurement interval, so currently I'm calculating
the 5 running sums from the captures and at the end of the interval I do
the regression calculation using these running sums like described in
the Wikipedia article on linear regression.
This is what I am storing now (Sum means running sum from start of
measurement interval till capture number n):  Sum(X), Sum(Y), Sum(X*X),
Sum (Y*Y) and Sum (X*Y) and n.

@Tom, thanks for checking, the range for the regression may have been
21, and the regression was done from the capture  up to the next 20
captures so the presented regression outcome at the end of the table
relied on 20 more  captures not present in the shortened table.
Let me double check the calculations

@Atilla, the purpose is to have the best approach for the chosen
interval into a single number (and possibly some statistical information
like  an error estimator), it is fully understood that for long
intervals and drifting/noisy oscillators this single number may have
little meaning but how else would you get to a single "measurement"?
Yes, I understand ADEV and the likes to be used as post processing for
the measurements to have more insight in the performance of the oscillator.
Most frequency counter present one number for each measurement (and
possibly some info on the statistics of that number), for me the number
and the statistics is enough if the interval can be set to any interval
between 0.1 ms and 10 s (just to give some numbers)
I will reread the two NIST documents you refer to. I can not access
articles behind a paywall unfortunately.


@Bob, The intended application for for this technique is:
- Either using a single good quality clock to measure the
characteristics of the events. It is understood the quality of the clock
sets a lower limit to what can be observed about the events. - Or
another, more interesting  application is where there is one, not so
perfect, clock and two events streams, each with their own event count
and clock captures. This, I hope, will allow to do measurements of the
relations between the two event streams with an accuracy not (or not
much) limited by the performance of the clock as any drift in the clock
will be (almost) equal in each clock capture. Even with hugely different
event intervals the measurement interval will always be at least one
event interval and any statement on the relation between the two event
streams will only have meaning at a timescale of the measurement interval.
If one would use a two channel frequency counter with a not so good
internal reference to measure the ratio or phase of two very good
clocks, what would be possible? How will the uncertainty, noise and
drift of the internal reference play a role in the performance or is
there a way to "average out" the impact of the internal reference? For
drift maybe yes, for noise maybe no.