[time-nuts] Hadamard variance

Tom Van Baak tvb at LeapSecond.com
Thu Apr 9 14:28:50 UTC 2009

> Steve
> Just dont get too carried away.
> Remember that the Hadamard deviation is only insensitive to linear
> frequency drift.
> If the drift is quadratic for example then it will affect the Hadamard
> deviation.
> Bruce

Correct. This is another reason why the practice of removing
systematic drift from raw data first and then computing ADEV
on the residuals is quite useful.

It allows you to separate the task of modeling systematic effects
from the calculation of stability (ADEV) of the residuals.

For example, you may suspect ahead of time, or you may find
through analysis, that your DUT is following a slow logarithmic
drift trend rather than just linear drift. Either way, you can remove
the systematic effect to get to a closer measure of the intrinsic
stability limits of the DUT.

This is common with OCXO which have aged, say more than
a few days, but less than a few months. It's pretty cool to see
very linear drift rates each day, but to also notice that the rate
itself slowly decreases week by week.

As another example, you may find a strong correlation between
temperature and frequency. You could plot ADEV of the raw
data, and then plot ADEV of the temperature compensated
residuals and observe the difference in the plots.


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