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

Magnus Danielson magnus at rubidium.dyndns.org
Wed Nov 22 20:00:01 EST 2017

```Hi,

On 11/22/2017 11:57 PM, Ralph Devoe wrote:
> Hi,
>         The fitting routine only takes up 40 uS of the 1 sec interval
> between measurements, as shown in Fig. 1 of the paper. This is less than
> 10(-4) of the measurement interval. It just determines the phase difference
> at the start of every second. I don't think the filtering effect is very
> large in this case.

Ok, this is where you have to learn one of the basic lessons on ADEV.
For white and flicker phase noise, you must always indicate the
bandwidth of the channel. The filtering is there and you need to care.
It's not necessarily wrong to filter, quite the opposite, but the
bandwidth needs to be shown.

The reason is that you need the bandwidth to relate it to the noise
level of that noise, which is the point of ADEV to begin with.

>          The interesting thing is that good results are achievable with such
> a short fitting interval. One way to think of it is to treat the fitting
> routine as a statistically optimized averaging process. Fitting 40 uS, that
> is 4096 points at 10 ns/point,  should reduce the noise by a factor of 64
> (roughly). The single shot timing resolution of the ADC is about 10 pS (see
> Fig. 4), so dividing this by 64 brings you down into the 100's of fs range,
> which is what you see.

Clean up your units. You neither mean to say 40 microsiemens nor 40
microsamples, which is the two ways to properly interpent "40 uS"
assuming u is shorthand for micro. Papers need to follow SI units, so
so there is no excuse. Attilas comments on units is relevant tough love.

Secondly, be extremely careful about such assumptions on what a
"statistcally optimized averaging process" does. We have noises in this
field which cause most assumptions of traditional textbooks completely
useless. As you reach noise being not white phase noise, convergence
rules no longer apply, we even talk about non-convergent noises. This is
why RMS estimator had to be replaced with Allan deviation in the first
place. I made sure to provide plenty of references and explanations in
the Allan Deviation Wikipedia article.

Cheers,
Magnus
```