Hi Paul,
On 15/08/11 05:10, Paul Cianciolo wrote:
Folks,
I amtrying to understand some of the terms used here quite often.
I quoted this from Wikipedia
An Allan deviation of 1.3×10−9 at observation time 1 s (i.e. τ = 1 s) should be
interpreted as there being an instability in frequency between two observations
a second apart with a relative root mean square(RMS) value of 1.3×10−9.
OK, I take the blame for that one, as I wrote it.
Does this mean the observations made were at the very begining and the very end
of the 1 second time.
Yes, as the observation interval is one second in this case, but you can
make it arbitrary to fit your needs, your application, such as 314,159 s
or whatever.
If so what value about all the values in between? What happens if the
oscillator deviated far worse than this during the interrim.
Well, you should not interpret it as a particular interval, but rather a
typical interval. ADEV is there to handle noises. If you use a shorter
interval, the collection of noises will be different so your ADEV will
be different. If you only have one ADEV value, you need to get the right
interval. If your interval is inbetween known values, you can kind of
guess as for pure noises the slopes is smooth.
But, the important aspect is that you need to measure for the interval
of your interest, a single measure (such as RMS) will not satisfy your
needs. It can be better or worse than the single point you have.
However, if you measure with a basic interval (tau0) you can
algoritmically achieve integer multiple intervals. Modern algorithms
interlace in an overlapping fashion these measures, so parts of an
interval is used by several intervals being used as samples in the
estimate. Hence, no particular interval can be expected.
Or does the measurement consist of making measurements every cycle during that
1 second and then entering all those values into a formula that accounts for
them all??
Assuming that we are after ADEV(1s) then you can make say 100 measures 1
s inbetween. This takes 100 s. We process these for tau0=1 and
tau-multiplier 1... which is the classic simple ADEV formula.
Another approach is to take samples more often, say every 100 ms and
then take 100 such measures. This takes 10 s. We process these for
tau0=0,1 and tau-multiplier 10. The benefit is a significant shorter
measurement interval, which isn't too great effort... but using 100 ms
measurement interval you can get 10 times the samples for the same
measurement time, so you can gain in improved predictor precission.
Thus, I toss in the confusing factor of improving quality of measure by
increasing amount of samples.
However, I want to show you that you can achieve the measures by
different approaches, essentially showing that you will not have to make
unique measurement series for 1s, 2s, 4s, 10s etc. but that you can get
these out of the same measurement series and in fact I highly encourage
you to do so and regularly plot them.
Maybe a very basic tutorial on this topic would help but I cant find one
You only proove that there is more work to be done on the wikipedia
article. It also lacks some illustrative plots.
Cheers,
Magnus
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