[time-nuts] Allan variance by sine-wave fitting

Magnus Danielson magnus at rubidium.dyndns.org
Wed Nov 22 17:31:53 EST 2017


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 <rgdevoe at 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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