[DSP-10] Something I don't understand about Alt/A box in LTI mode.

[Courtney Duncan]

Yes, this helps a lot.  I had worked this out when I wrote the AMSAT 
paper a year ago and the post processing software that supported it, 
but had forgotten.

It started with my confusion (yesterday) about why Cntr Sig was 
different from what the upper left spectrum value said for that 
signal.  This is because they are measuring two different things.  Up 
by the S-meter, we are measuring S+N.  Cntr Sig is S only which has 
been inferred from (S+N)/N as you describe.

What you do to find N in EME2, and probably also LTI, is what I 
borrowed for post processing.  Take the mean of bins [-9, -2] and [2, 
9] from the central signal.  It is assumed that there is no signal in 
these bins which means that we assume this mean corresponds to the N 
to which our system temperature refers.  (Fortunately all these 
values are recorded in the Alt/F file.)

The final piece of the puzzle was when I realized that (S+N)/N can 
get arbitrarily close to unity meaning that the implied S can get 
arbitrarily small, smaller in fact than N, as was happening when I 
claimed something like -187 dBm on QRPpp EME.  Indeed, if the ratio 
goes under one, the Alt/A box doesn't display a result because the 
randomness has made the calculation non-sensical.  (You are probably 
avoiding a "log of a negative number" error too.)

The reason the quality of the estimate improves is because the sigma 
on the mean of N goes down with averaging.  As this happens, we are 
only limited in how weak we can go by the stability of the signal and 
our patience, but the improvement slows down pretty fast, with sqrt( 
samples ) so in practice it's something like 20 - 30 dB.

The next project is to measure more accurately the system noise 
figure, and the noise figure of a preamp that I'll add after that. 
This will improve the accuracy of both the S-meter and the (S+N)/N 
calculation a little.

Thanks again, I'll keep you posted.

Courtney n5bf/6

>Hi Courtney,
>
>Great to hear from you.  Let me take a crack at what the A-box in 
>LTI is supposed to be.  It is different from the S-meter number, 
>over by the frequency display.
>
>The noise power, if the effective temperature was 290K, would be 
>-174 dBm/Hz.  If it is 600 K, this adds about 3 dB, to give -171 
>dBm/Hz.  The noise bandwidth per bin  is displayed in the upper 
>right corner of the screen, and is for your case, 9.4 Hz.  This adds 
>9.7 dB to the noise power in a bin, bringing the noise to  about 
>-161.3 dBm.  This is the noise power, referenced to the antenna 
>terminals and a power of  7.41 x10^-17 milliwatts in our bandwidth.
>
>Next,  (S+N)/N is what we see on the top display when a signal is 
>present, where we really mean S and N as powers, as opposed to dB. 
>So if (S+N)/N was 6.4 dB, this would be a power ratio of  4.37. The 
>power ratio of signal to noise is one less or 3.37. Thus the signal 
>must be 3.37 x 7.41x10^-17 or 2.50 x 10^-16 milliwatts.  This same 
>signal level in dBm is -156.0, which is shown as the Cntr Sig. This 
>agrees with what you see in LTI
>
>For really weak signals, this is a good way to estimate the power, 
>better than the s-meter system that requires knowledge of the analog 
>gain.  However, the LTI method does require that we can separate the 
>signal spectrally to allow measuring noise without the presence of 
>any signal. In LTI this is done away from the center signal, and I 
>don't remember the details<g>!
>
>Note also that increasing the averaging (the 1000 points) improves 
>the quality of the (S+N)/N estimate, but does not change the mean 
>value.
>
>Does that help??
>
>73, Bob  W7PUA
>
>At 05:32 PM 11/24/2007 -0800, you wrote:
>>I'm looking at the N6NB beacon which is coming in pretty well 
>>tonight.  I have Te set to 600K, the noise floor in the main 
>>spectral display is about 10, and the beacon, on peaks, is about 20 
>>which it says is -140 dBm.  Sampling is 9.4 Hz. so this all more or 
>>less adds up given Boltzman's Constant, -198.6 dB-Hz / K.
>>
>>In the LTI Alt/A box, it says about 1000 points, 15.0 dB.  Same Te. 
>>Cntr Sig = -155.9 which is 6.4 dB (S+N)/N.  This agrees with the 
>>yellow line.
>>
>>How is the Cntr Sig value calculated and what does it mean?
>>
>>Courtney, n5bf/6
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