rather aged thread, but the way to do it is to "back into" the characteristics of the sytem via a "lock-in" or "multi-channel averaging system. The noise you have is inseparably wedded to your signal source
and overall setup.
IF your SNR is >1 to begin with, then just measure the noise and signal + noise separately.
IF your signal is weak and buried in noise, SNR << 1, then you have to take multiple measurements, add them, and measure the SD of the fluctuations. If you can do this wothout signal (difficult for a star, etc.), then you can get a "noise signature," which is better but not essential.
THEN take a large number of measurements, add them together, and look for an emerging signal. Now, the noise increases as the Square Root of the noise value, but the signal increases linearly. So suppose the signal is 1 and the noise is 999 - signal buried in noise. Now do 10,000 measurements - the signal will be 10,000 and the noise will be the SQRT of 10,000,000 or 3100. This can be compared with the "noise only" measurement series as well.
SO then you can back-track and estimate a SNR corresponding to 1/1000.
This is the general approach used on the Hubble telescope, and its difficult to short-cut it. The good news is that you have to go down this road anyway if you have a very eak signal.
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