Gentlemen:

I hate
to admit that my very strongly supported design idea of using a steep cut
digital filter is doing nearly nothing to the overall performance of the
radiometer. Allow me to rephrase this, the digital filter, plus the averaging
renders a noise RMS almost equal to that of the average alone. In any case, our
design should render a better NEDT (Noise Equivalent Delta Temperature*)*
than the original radiometer, since that one had only a soft RC filtering with
no averaging whatsoever.

The advantage of filtering stems from the fact that the useful temperature information in the signal lies mostly on part of the spectrum below 200 Hz (this is for 34 scans and 4 frames per second), so you may safely dispose of the spectral components above that frequency, thus reducing the total noise RMS. Averaging filtered white noise at 200 Hz, showed 33% improvement over the averaged unfiltered noise.

The effect of averaging is strong on white noise, unfortunately, the noise spectrum in our signal is reported to be of type 1/f or pink noise and this can make quite a difference.

Plain
averaging of subsets of samples may also reduce the noise RMS. Say you divide
the 2176 samples in a frame into 34 subsets of 64 samples, one subset for each
vertical pixel. The variances of the averages, according to the central limit theorem,
should be up to 64 times smaller than that of the parent distribution. The
variance (noise power) reduction of 64 brings down the noise RMS in 8 or 87.5%. Of
course, for this kind of variance reduction, the theorem requires total sample
independence, in signal terms, this implies a white noise. For other
distributions, like any of the 1/f^{n} types, the values of the samples are
not independent, but somewhat conditioned by the previous ones.

For
brown noise (1/f^{2}), which can be simulated by a random walker
algorithm, this effect is so strong, that the variance (noise power) of the
averages is only 6% smaller than that of the parent or a 3% in noise RMS. For
pink noise the variance reduction must be somewhere between the 3% of the brown
noise and the 87.5% of the white noise. After some numerical experimentation, we
also found that:

- Averaging a filtered brown noise at 200 Hz, showed less than 3% improvement on noise RMS.
- Averaging an actual sample from our signal (already filtered), the averaging showed less than 3% improvement on noise RMS.

Though I can't get unfiltered samples of our signal for a direct prove, for all the above arguments, both the filtering and the averaging act upon the same upper part of the noise spectrum. So filtering + averaging is just an overkill..

Armando