Calculate spectral content from a series of zero crossing time stamps?
Consider the following scenario. We have a signal source of about 10 kHz,
with unknown phase noise. Let's for simplicity's sake assume for now that
the phase noise is large enough that it will be detectable by the following
approach.
We measure every zero crossing with lets say 1 ns accuracy. So we have a
signal with a nominal period of 100 us, and we can measure every zero crossing
to within 1 ns. This gives you ~ 10,000 data points every second.
Now how does one efficiently calculate the spectral content based on these
10,0000 zero crossings? The end result would be the spectral density, centered
around that nominal 10 kHz frequency.
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki that
extirpolates the unevenly timed samples to an regular timed mesh, after which
a regular DFT is done.
This is a nice enough approach, but you pay a computational price for the fact
that this algorithm is able to handle more generic inputs than is needed in
this particular case. So possibly there is a more efficient method, only
which one?
Any suggestions for methods/papers/etc are appreciated. :-)
thanks!
Fred
Forgot to mention that in this example we are only counting the zero crossings
on the positive edge.
(before some clever soul points out that it should be 20,000 zero crossings. :P
)
----- Original Message ----
From: Tijd Dingen tijddingen@yahoo.com
To: time-nuts@febo.com
Sent: Tue, February 8, 2011 4:02:19 AM
Subject: [time-nuts] Calculate spectral content from a series of zero crossing
time stamps?
Consider the following scenario. We have a signal source of about 10 kHz,
with unknown phase noise. Let's for simplicity's sake assume for now that
the phase noise is large enough that it will be detectable by the following
approach.
We measure every zero crossing with lets say 1 ns accuracy. So we have a
signal with a nominal period of 100 us, and we can measure every zero crossing
to within 1 ns. This gives you ~ 10,000 data points every second.
Now how does one efficiently calculate the spectral content based on these
10,0000 zero crossings? The end result would be the spectral density, centered
around that nominal 10 kHz frequency.
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki that
extirpolates the unevenly timed samples to an regular timed mesh, after which
a regular DFT is done.
This is a nice enough approach, but you pay a computational price for the fact
that this algorithm is able to handle more generic inputs than is needed in
this particular case. So possibly there is a more efficient method, only
which one?
Any suggestions for methods/papers/etc are appreciated. :-)
thanks!
Fred
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and follow the instructions there.
DFT? Direct Fourier Transform?
Thanks,
Joe
-----Original Message-----
From: time-nuts-bounces@febo.com [mailto:time-nuts-bounces@febo.com] On
Behalf Of Tijd Dingen
Sent: Monday, February 07, 2011 9:02 PM
To: time-nuts@febo.com
Subject: [time-nuts] Calculate spectral content from a series of
zerocrossing time stamps?
Consider the following scenario. We have a signal source of about 10 kHz,
with unknown phase noise. Let's for simplicity's sake assume for now that
the phase noise is large enough that it will be detectable by the following
approach.
We measure every zero crossing with lets say 1 ns accuracy. So we have a
signal with a nominal period of 100 us, and we can measure every zero
crossing to within 1 ns. This gives you ~ 10,000 data points every second.
Now how does one efficiently calculate the spectral content based on these
10,0000 zero crossings? The end result would be the spectral density,
centered around that nominal 10 kHz frequency.
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki
that extirpolates the unevenly timed samples to an regular timed mesh, after
which a regular DFT is done.
This is a nice enough approach, but you pay a computational price for the
fact that this algorithm is able to handle more generic inputs than is
needed in this particular case. So possibly there is a more efficient
method, only which one?
Any suggestions for methods/papers/etc are appreciated. :-)
thanks!
Fred
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Discrete Fourier Transform. Bit disregard that, because I /should/ have written
"FFT", since the Press & Rybicki approach uses the Fast Fourier Transform.
As in the N log N one. ;)
regards,
Fred
----- Original Message ----
From: J. L. Trantham jltran@att.net
To: Discussion of precise time and frequency measurement time-nuts@febo.com
Sent: Tue, February 8, 2011 4:42:06 AM
Subject: Re: [time-nuts] Calculate spectral content from a series of
zerocrossing time stamps?
DFT? Direct Fourier Transform?
Thanks,
Joe
-----Original Message-----
From: time-nuts-bounces@febo.com [mailto:time-nuts-bounces@febo.com] On
Behalf Of Tijd Dingen
Sent: Monday, February 07, 2011 9:02 PM
To: time-nuts@febo.com
Subject: [time-nuts] Calculate spectral content from a series of
zerocrossing time stamps?
Consider the following scenario. We have a signal source of about 10 kHz,
with unknown phase noise. Let's for simplicity's sake assume for now that
the phase noise is large enough that it will be detectable by the following
approach.
We measure every zero crossing with lets say 1 ns accuracy. So we have a
signal with a nominal period of 100 us, and we can measure every zero
crossing to within 1 ns. This gives you ~ 10,000 data points every second.
Now how does one efficiently calculate the spectral content based on these
10,0000 zero crossings? The end result would be the spectral density,
centered around that nominal 10 kHz frequency.
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki
that extirpolates the unevenly timed samples to an regular timed mesh, after
which a regular DFT is done.
This is a nice enough approach, but you pay a computational price for the
fact that this algorithm is able to handle more generic inputs than is
needed in this particular case. So possibly there is a more efficient
method, only which one?
Any suggestions for methods/papers/etc are appreciated. :-)
thanks!
Fred
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https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
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SpectrumLab uses the Goertzel-Algorithm to trim the time reference to
the millisecond range. Maybe that is comparable and as algoritm
transverable?
- Henry
J. L. Trantham schrieb:
DFT? Direct Fourier Transform?
Thanks,
Joe
-----Original Message-----
From: time-nuts-bounces@febo.com [mailto:time-nuts-bounces@febo.com] On
Behalf Of Tijd Dingen
Sent: Monday, February 07, 2011 9:02 PM
To: time-nuts@febo.com
Subject: [time-nuts] Calculate spectral content from a series of
zerocrossing time stamps?
Consider the following scenario. We have a signal source of about 10 kHz,
with unknown phase noise. Let's for simplicity's sake assume for now that
the phase noise is large enough that it will be detectable by the following
approach.
We measure every zero crossing with lets say 1 ns accuracy. So we have a
signal with a nominal period of 100 us, and we can measure every zero
crossing to within 1 ns. This gives you ~ 10,000 data points every second.
Now how does one efficiently calculate the spectral content based on these
10,0000 zero crossings? The end result would be the spectral density,
centered around that nominal 10 kHz frequency.
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki
that extirpolates the unevenly timed samples to an regular timed mesh, after
which a regular DFT is done.
This is a nice enough approach, but you pay a computational price for the
fact that this algorithm is able to handle more generic inputs than is
needed in this particular case. So possibly there is a more efficient
method, only which one?
Hello Henry,
Didn't know that one yet, so will check it out. Thank you for the suggestion! :)
regards,
Fred
----- Original Message ----
From: ehydra ehydra@arcor.de
To: Discussion of precise time and frequency measurement time-nuts@febo.com
Sent: Tue, February 8, 2011 5:24:39 AM
Subject: Re: [time-nuts] Calculate spectral content from a series of
zerocrossing time stamps?
SpectrumLab uses the Goertzel-Algorithm to trim the time reference to the
millisecond range. Maybe that is comparable and as algoritm transverable?
- Henry
J. L. Trantham schrieb:
DFT? Direct Fourier Transform?
Thanks,
Joe
-----Original Message-----
From: time-nuts-bounces@febo.com [mailto:time-nuts-bounces@febo.com] On
Behalf Of Tijd Dingen
Sent: Monday, February 07, 2011 9:02 PM
To: time-nuts@febo.com
Subject: [time-nuts] Calculate spectral content from a series of
zerocrossing time stamps?
Consider the following scenario. We have a signal source of about 10 kHz,
with unknown phase noise. Let's for simplicity's sake assume for now that
the phase noise is large enough that it will be detectable by the following
approach.
We measure every zero crossing with lets say 1 ns accuracy. So we have a
signal with a nominal period of 100 us, and we can measure every zero
crossing to within 1 ns. This gives you ~ 10,000 data points every second.
Now how does one efficiently calculate the spectral content based on these
10,0000 zero crossings? The end result would be the spectral density,
centered around that nominal 10 kHz frequency.
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki
that extirpolates the unevenly timed samples to an regular timed mesh, after
which a regular DFT is done.
This is a nice enough approach, but you pay a computational price for the
fact that this algorithm is able to handle more generic inputs than is
needed in this particular case. So possibly there is a more efficient
method, only which one?
time-nuts mailing list -- time-nuts@febo.com
To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
In message 224676.41616.qm@web120905.mail.ne1.yahoo.com, Tijd Dingen writes:
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki that
extirpolates the unevenly timed samples to an regular timed mesh, after which
a regular DFT is done.
Just knowing the time of the zero-crossings is very little information
to go by, but you have to make some kind of assumption about the
perfection of curve shape between those points, in order to say
anything meaningful.
The dirty but not necessarily quick way to analyze the data, is to
turn it into a +/- 1 squarewave at 1GHz (1/1ns), low-pass filter
it with a 15-18 kHz cut-off and do the usual FFT.
The other option is to normalize your zero-crossings, so you get
signed numbers telling how early/late they happen, and do a FFT
on that. Its too early in the morning for me to be able to see
how you transform the resulting phase-deviation spectrum to a
normal frequency offset plot, but a few tests with synthetic data
should tell you that.
--
Poul-Henning Kamp | UNIX since Zilog Zeus 3.20
phk@FreeBSD.ORG | TCP/IP since RFC 956
FreeBSD committer | BSD since 4.3-tahoe
Never attribute to malice what can adequately be explained by incompetence.
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki
that extirpolates the unevenly timed samples to an regular timed mesh,
after which a regular DFT is done.
Just knowing the time of the zero-crossings is very little information
to go by, but you have to make some kind of assumption about the
perfection of curve shape between those points, in order to say
anything meaningful.
Correct. And for now the working assumption is that the input signal is
sinusoidal, with just a smattering of noise.
The dirty but not necessarily quick way to analyze the data, is to
turn it into a +/- 1 squarewave at 1GHz (1/1ns), low-pass filter
it with a 15-18 kHz cut-off and do the usual FFT.
Yeah, I thought of that one. But it becomes prohibitive in terms of resources
real fast. ;)
The other option is to normalize your zero-crossings, so you get
signed numbers telling how early/late they happen, and do a FFT
on that. Its too early in the morning for me to be able to see
how you transform the resulting phase-deviation spectrum to a
normal frequency offset plot, but a few tests with synthetic data
should tell you that.
There's an idea. I will be doing a curve fit of the time stamps anyway, so I
get the time deviations from the fit for "free". Normalize the time deviations
into
phase deviations, and use that. Worth a try, thanks!
Fred
The Goertzel algorithm is only useful when you want a few frequences
(i.e., it evaluates specific frequencies on the unit circle). For
general all purpose slicing and dicing, the FFT is what you want. See
the ancient book by Rabiner for the details.
On Tue, Feb 8, 2011 at 3:14 AM, Tijd Dingen tijddingen@yahoo.com wrote:
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki
that extirpolates the unevenly timed samples to an regular timed mesh,
after which a regular DFT is done.
Just knowing the time of the zero-crossings is very little information
to go by, but you have to make some kind of assumption about the
perfection of curve shape between those points, in order to say
anything meaningful.
Correct. And for now the working assumption is that the input signal is
sinusoidal, with just a smattering of noise.
The dirty but not necessarily quick way to analyze the data, is to
turn it into a +/- 1 squarewave at 1GHz (1/1ns), low-pass filter
it with a 15-18 kHz cut-off and do the usual FFT.
Yeah, I thought of that one. But it becomes prohibitive in terms of resources
real fast. ;)
The other option is to normalize your zero-crossings, so you get
signed numbers telling how early/late they happen, and do a FFT
on that. Its too early in the morning for me to be able to see
how you transform the resulting phase-deviation spectrum to a
normal frequency offset plot, but a few tests with synthetic data
should tell you that.
There's an idea. I will be doing a curve fit of the time stamps anyway, so I
get the time deviations from the fit for "free". Normalize the time deviations
into
phase deviations, and use that. Worth a try, thanks!
Fred
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On 2/8/11 6:32 AM, Mark Kahrs wrote:
The Goertzel algorithm is only useful when you want a few frequences
(i.e., it evaluates specific frequencies on the unit circle). For
general all purpose slicing and dicing, the FFT is what you want. See
the ancient book by Rabiner for the details.
The Chirp-z transform (Bluestein) is also useful when you want a small
range of frequencies at higher resolution, but since it relies on a fast
convolution of the whole data set, it's more computationally intensive
than a straight FFT.
I ran across a nice explanation of how it works and why it's useful the
other day
http://www.katjaas.nl/chirpZ/chirpZ.html
(if you want some ancient FORTRAN IV code for this, I've probably got a
listing in a box out in the garage from the 70s)
08.02.2011 08:17, Poul-Henning Kamp:
In message 224676.41616.qm@web120905.mail.ne1.yahoo.com, Tijd Dingen writes:
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki that
extirpolates the unevenly timed samples to an regular timed mesh, after which
a regular DFT is done.
Just knowing the time of the zero-crossings is very little information
to go by, but you have to make some kind of assumption about the
perfection of curve shape between those points, in order to say
anything meaningful.
As far as I know a bandpass signal is described uniquely by its zero
crossings to within a constant. That is due to the Weierstrass
factorization theorem. A more practical foundation is outlined in
"B.F.Logan: 'Information in the zero crossings of bandpass signals', The
Bell System Technical Journal vol. 56 Number 4, April 1977" and some
other publications by the same author in the same journal.
Recently these techniques have been exploited in 'zepoc' algorithms for
low power hifi class D amplifiers and the 'click modulation' scheme.
But there were also publications which were in doubt that a real valued
signal can be reconstructed by its zero crossings.
Sadly, my mathematical background is not sufficient to follow the
arguments. But nonetheless zero crossing algorithms and nonuniform
sampling are very promising fields.
Cheers
Detlef
Hi,
Wavecrest uses algorithms for this and their software gives a spectrum. They also give some info on their site.
Henk
Op 8 feb 2011, om 20:51 heeft Detlef.Amberg@gmx.de het volgende geschreven:
08.02.2011 08:17, Poul-Henning Kamp:
In message 224676.41616.qm@web120905.mail.ne1.yahoo.com, Tijd Dingen writes:
From what I could find so far, one method to go about this is use a
Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki that
extirpolates the unevenly timed samples to an regular timed mesh, after which
a regular DFT is done.
Just knowing the time of the zero-crossings is very little information
to go by, but you have to make some kind of assumption about the
perfection of curve shape between those points, in order to say
anything meaningful.
As far as I know a bandpass signal is described uniquely by its zero
crossings to within a constant. That is due to the Weierstrass
factorization theorem. A more practical foundation is outlined in
"B.F.Logan: 'Information in the zero crossings of bandpass signals', The
Bell System Technical Journal vol. 56 Number 4, April 1977" and some
other publications by the same author in the same journal.
Recently these techniques have been exploited in 'zepoc' algorithms for
low power hifi class D amplifiers and the 'click modulation' scheme.
But there were also publications which were in doubt that a real valued
signal can be reconstructed by its zero crossings.
Sadly, my mathematical background is not sufficient to follow the
arguments. But nonetheless zero crossing algorithms and nonuniform
sampling are very promising fields.
Cheers
Detlef
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and follow the instructions there.
----- Original Message ----
From: jimlux jimlux@earthlink.net
To: time-nuts@febo.com
Sent: Tue, February 8, 2011 4:00:43 PM
Subject: Re: [time-nuts] Calculate spectral content from a series of zero
crossing time stamps?
The Chirp-z transform (Bluestein) is also useful when you want a small range of
frequencies at
higher resolution, but since it relies on a fast convolution of the whole data
set, it's more
computationally intensive than a straight FFT.
I ran across a nice explanation of how it works and why it's useful the other
day
http://www.katjaas.nl/chirpZ/chirpZ.html
For another look at zero padding in one domain to interpolate in the other
domain, this one
might be of interest:
http://www.dspguru.com/dsp/howtos/how-to-interpolate-in-time-domain-by-zero-padding-in-frequency-domain
(if you want some ancient FORTRAN IV code for this, I've probably got a listing
in a box out in the garage from the 70s)
Does this box also happen to contain verilog code for it?
regards,
Fred
----- Original Message ----
From: Henk henk@deriesp.demon.nl
To: Discussion of precise time and frequency measurement time-nuts@febo.com
Sent: Tue, February 8, 2011 10:19:38 PM
Subject: Re: [time-nuts] Calculate spectral content from a series of zero
crossing time stamps?
Wavecrest uses algorithms for this and their software gives a spectrum. They
also give some info on their site.
Looks like Wavecrest is now Gigamax. Did you mean their tailfit method, or
something else?
thanks,
Fred
On 2/9/11 3:17 AM, Tijd Dingen wrote:
(if you want some ancient FORTRAN IV code for this, I've probably got a listing
in a box out in the garage from the 70s)
Does this box also happen to contain verilog code for it?
I don't think Verilog was even a gleam in the inventors' eyes back in
the 70s. And even then, I think it was a simulation language first
Back in the 80s, I was more into solder-ware and wire-wrap-ware for
hardware implementation. (Got a couple Z80 boards with SRAM and EPROM
out there, probably..)
Hi Fred,
"A METHOD OF SERIAL DATA JITTER ANALYSIS USING ONE-SHOT TIME INTERVAL MEASUREMENTS" is in the white paper section of GigaMax 'tecnical resources'.
They split GigaMax from Wavecrest, probably after some bad financial times. The Wavecrest white papers are now at GigaMax.
Henk
Op 9 feb 2011, om 12:31 heeft Tijd Dingen het volgende geschreven:
----- Original Message ----
From: Henk henk@deriesp.demon.nl
To: Discussion of precise time and frequency measurement time-nuts@febo.com
Sent: Tue, February 8, 2011 10:19:38 PM
Subject: Re: [time-nuts] Calculate spectral content from a series of zero
crossing time stamps?
Wavecrest uses algorithms for this and their software gives a spectrum. They
also give some info on their site.
Looks like Wavecrest is now Gigamax. Did you mean their tailfit method, or
something else?
thanks,
Fred
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and follow the instructions there.
Hi Henk,
On 08/02/11 22:19, Henk wrote:
Hi,
Wavecrest uses algorithms for this and their software gives a spectrum. They also give some info on their site.
In "Jitter, Noise and Signal Integrity at High-Speed" by Mike Peng Li,
Prentice Hall, ISBN 0-13-242961-6 it is covered in pages 200-207.
It converts the phase jitter Phi(t) into the autocorrelation function
R_Phi(tau) (equation 7.40) and then the phase jitter PSD can be
estimated using the fourier transform (equation 7.41). The phase-noise
can then be calculated using the standard L(f) = 10*log10(PSD(f)/2).
It's pretty straight-forward.
The autocorrelation processing is O(N^2) while the DFT can be done in
O(N log N) when using FFT. As usual these can be implemented in reversed
order such that first the FFT is done to the phase jitter and
auto-correlation can be found using O(N) post-processing.
The phase-noise measuring ability of the SIA-3000 I have is not
competing with real phase-noise measuring sets. It doesn't say it can't
be useful.
Cheers,
Magnus
On 09/02/11 19:11, Henk wrote:
Hi Fred,
"A METHOD OF SERIAL DATA JITTER ANALYSIS USING ONE-SHOT TIME INTERVAL MEASUREMENTS" is in the white paper section of GigaMax 'tecnical resources'.
They split GigaMax from Wavecrest, probably after some bad financial times. The Wavecrest white papers are now at GigaMax.
Wavecrest just fell of the Internet for some time and then eventually
re-appeared as GigaMax. All material quite obvious just changed company
name and logo. A few things was cleaned out. Haven't checked since.
I would think they had financial problems and was reconstructed one way
or another. The DTS series got support from a new separate company,
forgot the name but it was a Wavecrest variant if I recall it correctly.
Cheers,
Magnus
Henk wrote:
Wavecrest uses algorithms for this and their software gives a spectrum.
They also give some info on their site.
Henk, the paper you mentioned put me on the right track. Thanks. :)
Magnus wrote:
In "Jitter, Noise and Signal Integrity at High-Speed" by Mike Peng Li,
Prentice Hall, ISBN 0-13-242961-6 it is covered in pages 200-207.
It converts the phase jitter Phi(t) into the autocorrelation function
R_Phi(tau) (equation 7.40) and then the phase jitter PSD can be estimated
using the fourier transform (equation 7.41). The phase-noise can then be
calculated using the standard L(f) = 10*log10(PSD(f)/2). It's pretty
straight-forward.
While I don't have that book lying around here, going from the Wavecrest paper
Henk mentioned, I did find out that indeed the method is to calculate the
autocorrelation of the timeseries and then FFT this autocorrelation. The method
even has this easy to google name: Blackman-Tukey.
LeCroy has a paper with a short explanation that I found useful:
http://www.lecroy.com/files/WhitePapers/WP_TechBrief_Var_of_Time.pdf
The autocorrelation processing is O(N^2) while the DFT can be done in
O(N log N) when using FFT. As usual these can be implemented in reversed
order such that first the FFT is done to the phase jitter and auto-correlation
can be found using O(N) post-processing.
If it can be done in N log N that would be nice. :)
The phase-noise measuring ability of the SIA-3000 I have is not competing with
real phase-noise measuring sets. It doesn't say it can't be useful.
And what I am trying to do will probably not even compete with that SIA-3000.
It is more along the lines of... Hey I have these times stamps anyway. Now what
can I do with those besides calculate a frequency estimate of the frequency
under test?
Fred
Sucker-punch spam with award-winning protection.
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On 09/02/11 23:08, Tijd Dingen wrote:
Henk wrote:
Wavecrest uses algorithms for this and their software gives a spectrum.
They also give some info on their site.
Henk, the paper you mentioned put me on the right track. Thanks. :)
Magnus wrote:
In "Jitter, Noise and Signal Integrity at High-Speed" by Mike Peng Li,
Prentice Hall, ISBN 0-13-242961-6 it is covered in pages 200-207.
It converts the phase jitter Phi(t) into the autocorrelation function
R_Phi(tau) (equation 7.40) and then the phase jitter PSD can be estimated
using the fourier transform (equation 7.41). The phase-noise can then be
calculated using the standard L(f) = 10*log10(PSD(f)/2). It's pretty
straight-forward.
While I don't have that book lying around here, going from the Wavecrest paper
Henk mentioned, I did find out that indeed the method is to calculate the
autocorrelation of the timeseries and then FFT this autocorrelation. The method
even has this easy to google name: Blackman-Tukey.
LeCroy has a paper with a short explanation that I found useful:
http://www.lecroy.com/files/WhitePapers/WP_TechBrief_Var_of_Time.pdf
The autocorrelation processing is O(N^2) while the DFT can be done in
O(N log N) when using FFT. As usual these can be implemented in reversed
order such that first the FFT is done to the phase jitter and auto-correlation
can be found using O(N) post-processing.
If it can be done in N log N that would be nice. :)
It's a reason why FFT has become so popular...
The phase-noise measuring ability of the SIA-3000 I have is not competing with
real phase-noise measuring sets. It doesn't say it can't be useful.
And what I am trying to do will probably not even compete with that SIA-3000.
It is more along the lines of... Hey I have these times stamps anyway. Now what
can I do with those besides calculate a frequency estimate of the frequency
under test?
Knock yourself out.. :)
Cheers,
Magnus