In this Appendix we will discuss how to account for the distribution of the acquisition parameters between the different detectors in the computation of the overall compression rate. Since the formalism is simpler we will develop expressions for instead of .
We have pointed out in Sect. 5.2 that the compression
efficiency is a random variable, whose distribution
is a function
of all those parameters which are relevant to fix the statistical
distribution of the input signal. In our case: ,
are the relevant parameters, so that the conditioned
probability to have a compression efficiency in the range
Presently there are no data to know in advance the
values between the different
detectors. For this reason in this work we assumed simply flat
distributions, identical for each frequency for such parameters.
More over, the
contribution is negligible, so that the
variance introduced by this parameter is neglected. From
(9) we assumed that the compression efficiency is
approximately a linear function of
is the first
example, at 30 GHz for arith-n1 the
full signal compression rate is
with one interpolation error less
With these approximations Eq.
To understand the influence of the error in the determination over the distribution on the final predictions the computation is made for a truncated (i.e. zero outside the range of interest) normal distribution of . The rms for the distribution is chosen in the range [0.5, 1.5] V/K we obtain respectively , 0.34, 0.34; which corresponds to , 2.91, 2.92 respectively. Similar results are obtained with a quadratic distribution. In conclusion these predictions are robust against the shape of the distribution, at least for distributions which are symmetric around the nominal V/K value.
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