You have it right, Bob. fitting is essentially a narrow band filter
process. Fitting thus has essentially the same errors.
Don
On 2017-11-22 09:19, Bob kb8tq wrote:
Hi
The “risk” with any fitting process is that it can act as a filter.
Fitting a single
sine wave “edge” to find a zero is not going to be much of a filter. It
will not
impact 1 second ADEV much at all. Fitting every “edge” for the entire
second
*will* act as a lowpass filter with a fairly low cutoff frequency.
That *will* impact
the ADEV.
Obviously there is a compromise that gets made in a practical
measurement.
As the number of samples goes up, your fit gets better. At 80us you
appear
to have a pretty good dataset. Working out just what the “filtering”
impact
is at shorter tau is not a simple task.
Indeed this conversation has been going on for as long as anybody has
been
presenting ADEV papers. I first ran into it in the early 1970’s. It is
at the heart
of recent work recommending a specific filtering process be used.
Bob
On Nov 22, 2017, at 10:58 AM, Ralph Devoe <[email protected]> wrote:
Hi time nuts,
I've been working on a simple, low-cost, direct-digital method
for
measuring the Allan variance of frequency standards. It's based on a
Digilent oscilloscope (Analog Discovery, <$300) and uses a short
Python
routine to get a resolution of 3 x 10(-13) in one second. This
corresponds
to a noise level of 300 fs, one or two orders of magnitude better than
a
typical counter. The details are in a paper submitted to the Review of
Scientific Instruments and posted at arXiv:1711.07917 .
The method uses least-squares fitting of a sine wave to determine
the
relative phase of the signal and reference. There is no zero-crossing
detector. It only works for sine waves and doesn't compute the phase
noise
spectral density. I've enclosed a screen-shot of the Python output,
recording the frequency difference of two FTS-1050a standards at 1
second
intervals. The second column gives the difference in milliHertz and
one can
see that all the measurements are within about +/- 20 microHertz, or 2
x
10(-12) of each other, with a sigma much less than this.
It would interesting to compare this approach to other
direct-digital
devices.
Ralph DeVoe
KM6IYN
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Dr. Don Latham
PO Box 404, Frenchtown, MT, 59834
VOX: 406-626-4304
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