At 06:10 PM 1/18/2006, John Ackermann N8UR wrote:
Jim Lux said the following on 01/18/2006 07:36 PM:
> At 04:24 PM 1/18/2006, John Ackermann N8UR wrote:
> As I recall, you can measure the phase of a tone with an uncertainty of
> 1/sqrt(T * CNR), where T is the integration time, and CNR is the carrier
> to noise spectral density ratio (C/Nzero). If you've got a SNR of say,
> 10 dB in a 2kHz bandwidth, that's a CNR of 20000, or a phase uncertainty
> for a 50 second measurement of 1/1000 radian (0.057 degree?)
>
> I can't recall off the top of my head how to convert a phase uncertainty
> into a frequency uncertainty (frequency just being the derivative of
> phase), but it should be straight forward.
I haven't worked through that bit of math, I'm just going on the results
we've gotten. The method I use is to inject a known signal very close
(within, say, 100Hz) of the unknown signal, and measure the delta
between the two using a sound card. By using a high decimation rate and
reasonably deep FFT, you can get resolution down well below a
milliHertz. The problem is getting enough samples to fill the FFT; you
end up dealing with an effective sample rate after decimation of maybe a
few hundred samples/second, which means that you need a long time to get
a useful output from the FFT.
But, if you have a decent SNR, you can get frequency resolution
substantially finer than 1/integration time. Example, if you measured the
time between two zero crossings on a 1kHz sine wave (i.e. 500 microseconds)
to an accuracy of a nanosecond, you'd know the frequency to 1 part in
500,000 ( 0.002 Hz).
The key is in not using something like an FFT, but in a tool specifically
designed to estimate the frequency of the sine wave. The Prony method is
one with historical significance (1700's, I think).
The software I use, Baudline (http://www.baudline.com) is a Linux based
spectrum analyzer package that has some neat features, including the
ability to automatically measure the delta between two signal peaks. It
makes the whole process pretty easy.
I've seen that program. It IS quite slick.
> It would be interesting to figure out a more meaningful competition,
> where ionospheric effects are compensatable, if you're clever. Perhaps
> measuring the relative phases/frequencies/amplitudes of multiple tones
> that are reasonably close together?
>
> Something that could be normalized to your propagation path. Otherwise,
> the guy sitting in the parking lot at W1AW has a huge advantage. Maybe,
> your results are scaled by the SNR or something?
We've thought a little about what kind of format would be really
challenging for the test, and measuring the delta between two tones is
one interesting idea. None of the folks I've talked to very much like
the format of the last two years, where you have to reduce to an audio
tone that's meaningless because the transmission in in SSB mode.
Exactly.. or how about some sort of (not quite) suppressed carrier DSB AM
(which, I suppose, is the same as measuring the delta between two tones).
Jim
