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

djl djl at montana.com
Wed Nov 22 14:52:08 EST 2017


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 <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
>> <Capture.JPG>_______________________________________________
>> time-nuts mailing list -- time-nuts at febo.com
>> To unsubscribe, go to 
>> https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
>> and follow the instructions there.
> 
> _______________________________________________
> time-nuts mailing list -- time-nuts at febo.com
> To unsubscribe, go to 
> https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
> and follow the instructions there.

-- 
Dr. Don Latham
PO Box 404, Frenchtown, MT, 59834
VOX: 406-626-4304



More information about the time-nuts mailing list