WarrenS wrote:
Bruce Posted
"Rectangular integration isn't particularly accurate or efficient, better
techniques exist."
True, but in this case it is the easiest and at these speeds, efficiency is not
a big concern, It is made up for with faster oversampling.
and it is obvious so far, better is not needed here, this is 'Good enough'.
(and that answers your other question, why don't I do it better.)
Why do that when its so easy to do much better?
You do bring up an interesting point. There is lots of things that could be
(and have been) done better than on that simple one IC BB circuit that was
tested, and yet it was good enough to match the TSC 5120A pretty much point for
point over the whole tau range and ADEV range. (limited only by it's Ref
Osc.) Think KISS, enought said.
You've entirely missed the point, such errors need to be quantified not
swept under the carpet.
Trapezoidal integration is almost as simple as rectangular integration
and comes at low cost.
However if you look at equation 44 in the paper I cited an even better
technique is described.
"Try to desist from the pathetic attempts at insults"
I don't know what that even means, but sorry about the oversampling comments.
It did seem you did not know what that was or at least its advantages when it
comes to simplifying things.
Ditto on the Phase and Freq differences comment, which I fear still may be the
case.
Sure if one has a sufficiently high oversampling factor crude
approximations may work reasonably well.
However one ought to strive to do better particularly when its easy to
do so and requires no additional hardware.
One doesn't always have the luxury of an extremely high oversampling ratio.
A better filter than a single pole RC filter may also be required to
take full advantage.
"You seem to be unaware of just how easy it is to create a dataset for which any
given algorithm will fail catastrophically."
True, I'm unaware of ANYTHING Normal that will make this fail.
send me something, It'll be fun to try it, If you can break it, I can fix it.
Lets start small, give me any two numbers, I'll give you the average
Now three, then four, how far do you want to go? I'm sure I can still give you
the average value.
Now for the big test, can I give you the average of several of the previous
averages, This is not going to be a problem either.
I can give you the average for any reasonable numbers that could be presented
to the ADC in normal operation thru the restricted PLL BW and the BW filter.
That IS about ALL there is to it. It needs to give the AVERAGE Frequency of
the oversampled average frequencies.
Then it needs to give the average of these averages. As long all samples are
taken at the same rate, it works good. (Average = Sum_nSamples / n )
The oversampled has to be done fast enough and with the appropriate B/W limit
so there is no dead time or aliasing or significant change happens during one
sample period.
The other H/W takes care of that. Oversampling>> TC filter.
To understand why that is all that is needed, one need to only look at what
basic Allan deviation is.
Allan deviation is the Average of the neighboring frequency differences that
have been averaged for a given length of time. That length of time is called
tau.
Actually you should be using fractional frequency differences.
That is needed then is to find (the Average_Freq over a tau period) - (the
Average_Freq over the next same length time period).
Do some squaring of the differences and some more averaging and scaling and
some sq root and out pops an ADEV answer.
The important point is that it ALL just starts with the Average Frequency over
a period of time called tau.
If you can get accurate average freq over tau0 time then any standard Allan
calculation S/W can turn it into ADEV and at any tau.
ws
*******************
Bruce
WarrenS wrote:
Bruce posted
The RC filter doesn't accurately integrate the frequency difference
over time interval Tau0.
For you to even state that means you still have NO idea what I'm
doing, It is getting sort of sad.
Correct the RC filter is not an integrator, it is used for the
combination Bandwidth and anti-aliasing filter.
It is the oversampling average that does the integration.
How? Rectangular integration isnt particularly accurate or efficient,
better techniques exist.
What would explain a lot is, if you do not know what oversampling even
is?
Try to desist from the pathetic attempts at insults as they merely
distract from the real questions about the signal processing techniques
adopted.
You need to get yourself a refresher course on the advantages of
oversampling to do integration, brick wall filtering, anti-aliasing and
why a single RC works just fine for integration when oversampling is
used and why you don't need anything but simple averaging of sum n
samples /n when oversampling is used.
Don't need all the unnecessary fir filter crap, just oversample.
Not so, as anyone with a comprehensive understanding of the subject will
attest.
Seat of the pants methods produce misleading predictions when noise isnt
statistically stationary.
If you have spare bandwidth like I have, then it sure saves a lot of
stuff. Ever hear of "KISS'.
Most are aware of the principle but over simplification leads to
erroneous results.
You need to ask someone to explain that to you some day, along with
"close enough"
Hint, the simple Tester BB only takes ONE IC and it is just a single
op Amp.
That performance metric is irrelevant if it doesnt measure the desired
quantity for all cases of interest.
NB the case spectrum will vary from one user to another so the
limitations of the technique need to be well known.
These limitations will include limits on the phase noise spectra of the
devices being compared.
And Although John's Software makes it all much more user friendly and
makes user mistakes less likely to occur, It is not needed. Works just
fine with no special S/W code or filter S/W.
AND it still does integration just fine. (Send me that data file if
you want to see how it works).
You seem to be unaware of just how easy it is to create a dataset for
which any given algorithm will fail catastrophically.
ws
**************
Bruce last posted:
John Miles wrote:
The integration secret (which is no secret to anyone but
Bruce) is to analog filter, Oversample, then average the
Frequency data at a rate much faster than the tau0 data rate.
Which again is misleading as you specify neither the averaging method
nor the analog filter.
I can't speak for the analog side as I never saw a schematic of the
PLL, but
it may be worthwhile to point out that the averaging code in question
is in
SOURCE_DI154_proc() in ti.cpp, which is installed with
http://www.ke5fx.com/gpib/setup.exe . This is my code, not
Warren's. It
does a simple boxcar average on phase-difference data, the same as my
TSC
5120 acquisition routine does. Previous tests indicated that simple
averaging yields a good match to most ADEV graphs on TSC's LCD
display, so I
used it for the PLL DAQ code as well.
I also tried a Kaiser-synthesized FIR kernel for decimating the
incoming TSC
data, but found that its conformance against the TSC's display was worse
than what I saw with the simple average. More work needs to be done
here.
When will you understand that phase differences and differences of
average frequency (unit weight to frequency measures over the sampling
interval zero weight outside) are equivalent.
One subtlety is the question of whether to average (or otherwise
filter) the
DAQ voltage readings immediately after they're acquired and linearly
scaled
to frequency-difference values, versus after conversion of the
frequency-difference values to phase differences. I found that the best
agreement with the TSC plots was obtained by doing the latter:
val = (read and scale the DAQ voltage)
// val is now a frequency difference
// averaging val here yields somewhat higher
// sigma(tau) values in the first few bins
// after tau0
val = last_phase + (val / DI154_RATE_HZ);
last_phase = val;
This appears to use a rectangular approximation to the required integral.
A trapezoidal or even Simpson's rule integration technique should be
more accurate for a given sample rate.
One could even try a higher order polynomial fit to the sample points,
however this isnt the optimum technique to use.
If one uses WKS interpolation to reconstruct the continuous frequency vs
time function and integrates the result for a finite time interval
(Tau0) then one ends up with a digital filter with infinite number of
terms.
Since an infinite number of samples is required to do this using a
suitable window function is probably advisable.
The paper (below) illustrates how AVAR etc can be calculated from the
sampled frequency difference data using DFT techniques:
http://hal.archives-ouvertes.fr/docs/00/37/63/05/PDF/alaa_p1_v4a.pdf
// val is now a phase difference
// averaging val here matches the TSC better
The difference is not huge but it's readily noticeable.
This is subtly disturbing because the RC filter before the DAQ *does*
integrate the frequency-difference data directly. If it's correct to
band-limit the frequency-to-voltage data in the last analog stage of the
pipeline, it should be correct to do it in the first digital stage, I'd
think.
The RC filter doesnt accurately integrate the frequency difference over
time interval Tau0.
Further complicating matters is the question of whether the TSC 5120A's
filtering process is really all that 'correct,' itself. When they
downsample their own data by a large fraction, e.g. when you select
tau0=100
msec / NEQ BW = 5 Hz, there is often a slight droop near tau0 that
does not
correspond to anything visible at higher rates. To some extent we
may be
attempting to match someone else's bug.
This is the result of the choice of the low pass filter bandwidth made
by the designers.
The filter bandwidth increases as Tau0 decreases.
The traditional analyses of the dependence of AVAR on bandwidth of this
filter assume a brickwall filter.
At any rate I've run out of time/inclination to pursue it, at least
for now.
The SOURCE_DI154_proc() routine in TI.CPP is open for inspection and
modification by any interested parties, lines 6753-7045 in the current
build. :) Warren has his hardware back now, and would presumably be
able to
try any modifications.
-- john, KE5FX
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