Accurate phase measurement

Hi all,

I need to measure the phase of an I/Q signal with good accuracy (better than
0.005deg assuming a good SNR) using a complex FFT. I am already using the
weighted average of the frequencies around a detected peak to improve the
frequency resolution of the FFT. Should I use a similar technique for the
phase measurement? Are there other techniques? Any suggestions would be
welcome.

Thanks

Stephan

8.5 microradians is going to be very difficult with real world signals.  You 
need to know the frequency with far more precision than your message indicates 
since the measured signal phase is dependent on where the signal lies in the 
FFT bin.  There are several techniques to estimate the signal frequency 
accurately.  See

http://home.earthlink.net/~ejacobsensprint/fe.htm

then use the measured FFT phase and the frequency to compute the phase.

In article <psfnb.13168$P42.4821@charlie.risq.qc.ca>, "Stephan Boucher" 
<spock@tr.cgocable.ca> wrote:
>Hi all,
>
>I need to measure the phase of an I/Q signal with good accuracy (better than
>0.005deg assuming a good SNR) using a complex FFT. I am already using the
>weighted average of the frequencies around a detected peak to improve the
>frequency resolution of the FFT. Should I use a similar technique for the
>phase measurement? Are there other techniques? Any suggestions would be
>welcome.
>
>Thanks
>
>Stephan
>
>
>

On Mon, 27 Oct 2003 23:29:55 GMT, nobody@nowhere.nothing wrote:

>8.5 microradians is going to be very difficult with real world signals.  You 
>need to know the frequency with far more precision than your message indicates 
>since the measured signal phase is dependent on where the signal lies in the 
>FFT bin.  There are several techniques to estimate the signal frequency 
>accurately.  See
>
>http://home.earthlink.net/~ejacobsensprint/fe.htm
>
>then use the measured FFT phase and the frequency to compute the phase.
>

Hi nobody,
  I think it's 87 microradians, but in any case, 
I agree with you that Stephan has a tough problem 
here if he's dealing with real-world signals.

I wonder, does he *really* need such fine 
phase resolution and accuracy.
Stephan didn't say what kind of signal he's 
dealing with, but FFT phase measurement is 
corrupted by both FFT leakage and any noise 
that's accompanying the signal.

I'll send Stephan a paper that might help.

[-Rick-]

 

"Stephan Boucher" <spock@tr.cgocable.ca> wrote in message news:<psfnb.13168$P42.4821@charlie.risq.qc.ca>...
> Hi all,
> 
> I need to measure the phase of an I/Q signal with good accuracy (better than
> 0.005deg assuming a good SNR) using a complex FFT. I am already using the
> weighted average of the frequencies around a detected peak to improve the
> frequency resolution of the FFT. Should I use a similar technique for the
> phase measurement? Are there other techniques? Any suggestions would be
> welcome.

The approximate 1-sigma precision to which you can measure a signal's
phase (assuming an un-windowed time series) is (in radians):

sigma_phi = 1/sqrt(2P_meas-1)

where P_meas is the normalized power in the signal.  By normalized, I
mean, take the raw power at the peak of the signal (you can find the
peak exactly using Fourier interpolation or some other technique) and
divide by the average noise power off of the signal.  For a sinusoid
of amplitude "a" in a N-point time series with variance s^2, the
normalized power is (a^2 N)/(4 s^2).

So if we define the SNR as a/s, we get approx (for high SNR):

sigma_phi ~ 2/(SNR * sqrt(N)) in radians.  So for your case (0.005deg
= 8.7e-5 rad), you need either a very high SNR, a long time series, or
both.

Hope this helps (and sorry I don't use more "standard" DSP notation. 
I'm a scientist not an engineer!)

Scott

Stephan Boucher wrote:

> Hi all,
> 
> I need to measure the phase of an I/Q signal with good accuracy
> (better than 0.005deg assuming a good SNR) using a complex FFT. I
> am already using the weighted average of the frequencies around a
> detected peak to improve the frequency resolution of the FFT.
> Should I use a similar technique for the phase measurement? Are
> there other techniques? Any suggestions would be welcome.
> 
> Thanks
> 
> Stephan

Hi Stephan, 
depending on the signal content, you might try an approach by timing 
the zero transitions of your signal.
Either checking the sign of the digitized signal - or with analog 
comparators depending on your hardware.

I know it won't help to overcome physical laws.
However, you'll work with a very sharp and easy to detect decision 
mark, and you'll get an initial guess very quickly. 

Bernhard 

As already noted, you are in a regime where "real world" effects could
make things quite complicated.  If the signal is strictly periodic and
well-approximated by a reasonable number of harmonics, and if the noise
is accurately described as white, then there are straightforward ways
of estimating frequency, phase, noise level, etc. (I personally would
use Bretthorst's approach; http://bayes.wustl.edu/glb/book.pdf).  But
any wobble in your signal or complexity in the noise could easily lead
you to make an estimate that you think is accurate (has small formal
uncertainties) but that is less accurate than formal estimates.

Good luck with it!
-Tom

--

To respond by email, replace "somewhere" with "astro" in the
return address.

On Tue, 28 Oct 2003 17:27:43 -0500, Tom Loredo
<loredo@somewhere.cornell.edu> wrote:

>
>As already noted, you are in a regime where "real world" effects could
>make things quite complicated.  If the signal is strictly periodic and
>well-approximated by a reasonable number of harmonics, and if the noise
>is accurately described as white, then there are straightforward ways
>of estimating frequency, phase, noise level, etc. (I personally would
>use Bretthorst's approach; http://bayes.wustl.edu/glb/book.pdf).  But
>any wobble in your signal or complexity in the noise could easily lead
>you to make an estimate that you think is accurate (has small formal
>uncertainties) but that is less accurate than formal estimates.
>
>Good luck with it!
>-Tom

Hi Tom,

   I tried to go to the 

       http://bayes.wustl.edu/glb/book.pdf

and nothing happened.  I'm usin' Netscape 
as my web browser.  Was the above URL correct?

Thanks,
[-Rick-]

On Tue, 28 Oct 2003 17:27:43 -0500, Tom Loredo
<loredo@somewhere.cornell.edu> wrote:

>
>As already noted, you are in a regime where "real world" effects could
>make things quite complicated.  If the signal is strictly periodic and
>well-approximated by a reasonable number of harmonics, and if the noise
>is accurately described as white, then there are straightforward ways
>of estimating frequency, phase, noise level, etc. (I personally would
>use Bretthorst's approach; http://bayes.wustl.edu/glb/book.pdf).  But
>any wobble in your signal or complexity in the noise could easily lead
>you to make an estimate that you think is accurate (has small formal
>uncertainties) but that is less accurate than formal estimates.
>
>Good luck with it!
>-Tom

Hi Tom,
   your URL address was correct.  I just didn't wait 
long enough.  My vacuum-tube computer and 'two tin 
cans and a string' modem' are very slow.

[-Rick-]

Rick Lyons wrote:
> 
>    your URL address was correct.  I just didn't wait
> long enough.  My vacuum-tube computer and 'two tin
> cans and a string' modem' are very slow.

Rick, if you happen to be interested in a quick summary of Bretthorst's
approach in an audio setting, check out a paper I gave at the 2001 AES:

http://www.museweb.com/bha.pdf

-Tom

-- 

To respond by email, replace "somewhere" with "astro" in the
return address.

On Wed, 29 Oct 2003 16:18:14 -0500, Tom Loredo
<loredo@somewhere.cornell.edu> wrote:

>Rick Lyons wrote:
>> 
>>    your URL address was correct.  I just didn't wait
>> long enough.  My vacuum-tube computer and 'two tin
>> cans and a string' modem' are very slow.
>
>Rick, if you happen to be interested in a quick summary of Bretthorst's
>approach in an audio setting, check out a paper I gave at the 2001 AES:
>
>http://www.museweb.com/bha.pdf
>
>-Tom

Hi Tom,
   Thanks, I'll check it.

Regards,
[-Rick-]