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

Bob kb8tq kb8tq at n1k.org
Wed Nov 22 11:19:01 EST 2017

```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

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.

```