[time-nuts] Allan variance by sine-wave fitting
djl at montana.com
Wed Nov 22 14:58:33 EST 2017
Forgot to add I think this can be proved mathematically. It's been a
On 2017-11-22 12:52, djl wrote:
> You have it right, Bob. fitting is essentially a narrow band filter
> process. Fitting thus has essentially the same errors.
> On 2017-11-22 09:19, Bob kb8tq wrote:
>> 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
>> *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
>> As the number of samples goes up, your fit gets better. At 80us you
>> to have a pretty good dataset. Working out just what the “filtering”
>> is at shorter tau is not a simple task.
>> Indeed this conversation has been going on for as long as anybody has
>> 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.
>>> On Nov 22, 2017, at 10:58 AM, Ralph Devoe <rgdevoe at gmail.com> wrote:
>>> Hi time nuts,
>>> I've been working on a simple, low-cost, direct-digital method
>>> measuring the Allan variance of frequency standards. It's based on a
>>> Digilent oscilloscope (Analog Discovery, <$300) and uses a short
>>> routine to get a resolution of 3 x 10(-13) in one second. This
>>> 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
>>> 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
>>> spectral density. I've enclosed a screen-shot of the Python output,
>>> recording the frequency difference of two FTS-1050a standards at 1
>>> 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
>>> Ralph DeVoe
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Dr. Don Latham
PO Box 404, Frenchtown, MT, 59834
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