Hi,
Sure, fitting is a filtering process. The least square estimation is
really a filtering with a ramp-like response in phase and parabolic in
frequency.
The critical aspect here is over which length the filtering occurs and
thus the resulting bandwidth. If you only filters down white phase
noise, this is good and the bandwidth of the filter should classically
be mentioned.
Few people know the resulting noise bandwidth of their estimator filter.
The estimator should never overlap another sample, then it becomes, Hrm,
problematic.
I've not had time to even download Ralphs paper, so I will have to come
back to it after reviewing it.
Cheers,
Magnus
On 11/22/2017 05:19 PM, 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 <rgde...@gmail.com> 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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