Ulrich Bangert df6jb at ulrich-bangert.de
Thu Jan 22 09:06:31 EST 2009

```Magnus,

the paper http://tf.nist.gov/timefreq/general/tn1337/Tn121.pdf is
thought-provoking. Not that I would simply say that you are right, but
because I dont't understand some things.

>
>                              N-2m
>                               ___
>       2              1       \                        2
> sigma  (tau) = -----------   >   (x     - 2x    + x )
>       y                   2  /___   i+2m     i+m    i
>                 2(N-2m)tau   i = 1
>
> a non-interleaved variant would have to be written as
> (assuming that m
> divides N):
>
>                N
>                - - 2
>                m
>                 ___
>       m        \                              2
> ------------   >   (x       - 2x       + x  )
>            2   /___   (i+2)m     (i+1)m    im
> 2(N-2m)tau    i = 1

No discussion about that, simply correct.

However the note to figure 8 as well as the note to figure 9 cover the
non-overlapping case. Indeed formulas (8) and (10) are overlapping and
to me it is a bit kind of magic where they come from in regard to thise
two notes.

Do you agree to the fact that the ADEV for Tau = 2 s should be the same,
regardless if computed from 1 s spaced phase data or from 2 s spaced
phase data?

Best regards
Ulrich

> -----Ursprungliche Nachricht-----
> Von: time-nuts-bounces at febo.com
> [mailto:time-nuts-bounces at febo.com] Im Auftrag von Magnus Danielson
> Gesendet: Donnerstag, 22. Januar 2009 12:53
> An: Discussion of precise time and frequency measurement
>
>
> Ulrich,
>
> Ulrich Bangert skrev:
> > Magnus,
> >
> >> Actually, what you describe is the estimator formulas rather than
> >> definition. This is also targeting the fine point that I
> am trying to
> >> make. It's not about the basic definition, but accepted
> convention to
> >> denote the estimators.
> >
> > I still do not understand the fine point! A estimator might
> have this
> > property and that property and may perform this task good
> and another
> > task bad, but at the basics we have a formula and if the formula is
> > new or different from prior art then the thing needs an name of its
> > own.
>
> This part we agree on, however, you fail to see that what I
> try to point
> out is that you seems to have the wrong reference to start
> with. What I
> am trying to say is that it seems that ADEV is being used to
> identify a
> different estimator than I have in my old material, including the
> articles collected in NIST TN1337, for instance "Time and Frequency
> (Time-Domain) Characterization, Estimation, and Prediction of
> Precision
> Clocks and Oscillators" by David W. Allan.
> http://tf.nist.gov/timefreq/general/tn1337/Tn121.pdf
> See page 4 and formulas 8 and 9. These are overlapping.
>
> > In this sense the summation over square(y(i+1)-y(i)) is called the
> > base of the "Allan variance/deviation" just for historical
> reasons. So
> > the name is "Allen deviation" and it is defined by its formula.
>
> A further reference would be the IEEE standard found in
>
> http://tf.nist.gov/timefreq/general/tn1337/Tn139.pdf
>
> This is also overlapping (from page 2):
>
>                              N-2m
>                               ___
>       2              1       \                        2
> sigma  (tau) = -----------   >   (x     - 2x    + x )
>       y                   2  /___   i+2m     i+m    i
>                 2(N-2m)tau   i = 1
>
> a non-interleaved variant would have to be written as
> (assuming that m
> divides N):
>
>                N
>                - - 2
>                m
>                 ___
>       m        \                              2
> ------------   >   (x       - 2x       + x  )
>            2   /___   (i+2)m     (i+1)m    im
> 2(N-2m)tau    i = 1
>
> and these obviously isn't the same, the later form skips over samples
> not being a multiple of m.
>
> Also, it is still overlapping in the sense that samples is
> being re-used.
>
> >> Disagree. The estimator formulation that is classically
> used includes
> >> these "missed" tau0 steps that you claim that OAVAR/OADEV
> >> includes. This is my point. Somewhere along the line the
> established
> >> became the OADEV estimator and another estimator took the
> >> This is what I oppose without a more detailed look at things.
> >
> > The OAVAR/OADEV has this name of its own BECAUSE it includes the
> > summands that are missed by the original AVAR/ADEV so its needs an
> > name of its own.
>
> I deeply disagree, see my reference to early papers (I agree not
> original). Also, the standardised form is overlapping.
>
> This is the reason for me to react.
>
> >> Somewhere along the line the established ADEV estimator became the
> >
> > If you had said: "The currently established estimator for
> oscillator
> > stability is the OADEV estimator" I would have perfectly agreed.
>
> Well, that part was never what we disagreed on IMHO.
>
> > However, ADEV does already point to a different thing, so to say
> > "Today we call ADEV what was formerly called OADEV and what was
> > formerly called ADEV now is also called different" is not
> excused with
> > a certain sloppiness in language but simply wrong use of terms.
> > Exactly this is the point why I said that the discussion is
> dangerous.
> > This is not a change in paradigm this is a case of
> inaccurate use of
> > scientifical terms.
>
> Well, if we were doing a shift in interpretation I fully
> agree with you,
> but what I reacted on was due to a shift in interpretation as I
> experienced it and when looking at the old reference material
> (altought
> I have not had the time for an extensive search that I would feel
> confident with). The issue was that I detected the dangerous
> shift and I
> wanted to bring it up to bring it back on tracks, or at least learn
> something useful.
>
> I really kindly ask you or anyone else to bring forward articles
> describing the non-overlapping ADEV and help plotting out the issues.
> What has become standardised (and thus assumed accepted) as the ADEV
> estimator is overlappping unless you can point out that I have made a
> very deep misunderstanding of all those papers, in which case
> I would be
> happy to be corrected.
>
> Cheers,
> Magnus
>
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