Allan variance by sine-wave fitting
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.
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.
Ralph
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
follow the SI brochure from the BIPM, it's available for free download,
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
Hi
To paraphrase a post made a few months back:
With ADEV, the “signal” is the noise. A lot of the things you would normally
do to improve the SNR can get in the way with ADEV measurements. That’s
not to say they invalidate the measure, they can “color” the result and make
comparison between methods a bit difficult.
Again, this conversation has been going on since the days of the original papers
on ADEV being presented.
Bob
On Nov 22, 2017, at 8:00 PM, Magnus Danielson magnus@rubidium.dyndns.org wrote:
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 follow the SI brochure from the BIPM, it's available for free download, 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
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Hi,
just my two cents on sine wave fitting.
A undamped sine wave is the solution of the difference equation
sig(n+1)=2*cos(w)*sig(n)-sig(n-1)
This is a linear system of equations mapping the sum of the samples n+1 and
n-1 to the sample n. The factor 2*cos(w) is the unknown. The least-squares
solution of the overdetermined system is pure linear algebra, no nonlinear
fitting involved. The trick also works for a damped sine wave. Care must be
taken for high 'oversampling' rates, it works best for 4samples/sinewave,
ie near Nyquist/2.
Cheers
Detlef
DD4WV
Hi,
There is trivial ways to estimate phase and amplitude of a sine using
linear methods. I saw however none of these properly referenced or
described. It would have been good to see those approaches attempted in
parallel on the same data and compare their performance with the
proposed approach. It seemed "fuzzy" how it worked, and that is never a
good sign in a scientific article, especially as it is n the heart of
the method described in the paper. The actual method should be named,
referenced and then also referenced with "as implemented by..." and we
only got the last part.
Cheers,
Magnus
On 11/23/2017 01:34 PM, d.schuecker@avm.de wrote:
Hi,
just my two cents on sine wave fitting.
A undamped sine wave is the solution of the difference equation
sig(n+1)=2*cos(w)*sig(n)-sig(n-1)
This is a linear system of equations mapping the sum of the samples n+1 and
n-1 to the sample n. The factor 2*cos(w) is the unknown. The least-squares
solution of the overdetermined system is pure linear algebra, no nonlinear
fitting involved. The trick also works for a damped sine wave. Care must be
taken for high 'oversampling' rates, it works best for 4samples/sinewave,
ie near Nyquist/2.
Cheers
Detlef
DD4WV
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I wonder how much a fitting approach is affected by distortion (especially
harmonic content) in the waveform.
Of course we can always filter the waveform to make it more sinusoidal but
then we are adding L's and C's and their tempcos to the measurement for
sure destroying any femtosecond claims.
Tim N3QE
On Wed, Nov 22, 2017 at 5:57 PM, Ralph Devoe rgdevoe@gmail.com 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.
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.
Ralph
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and follow the instructions there.
The harmonics limit the perfomance if you want to find the frequency of a
given, sampled sinewave with linear methods. Thats at least my finding when
I built a device to measure grid frequency fast and with high accuracy. I
had to use high-Q digital filters for the fundamental. Their slow transient
response limited the speed of new frequency measurements.
Cheers
Detlef
DD4WV
"time-nuts" time-nuts-bounces@febo.com schrieb am 23.11.2017 16:34:39:
Von: Tim Shoppa tshoppa@gmail.com
An: Discussion of precise time and frequency measurement
Datum: 23.11.2017 16:35
Betreff: Re: [time-nuts] Allan variance by sine-wave fitting
Gesendet von: "time-nuts" time-nuts-bounces@febo.com
I wonder how much a fitting approach is affected by distortion
(especially
harmonic content) in the waveform.
Of course we can always filter the waveform to make it more sinusoidal
but
then we are adding L's and C's and their tempcos to the measurement for
sure destroying any femtosecond claims.
Tim N3QE
On Wed, Nov 22, 2017 at 5:57 PM, Ralph Devoe rgdevoe@gmail.com 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.
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.
Ralph
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mailman/listinfo/time-nuts
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