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The commands AVERAGE, ACCUMULATE, and STITCH combine
the spectra available in the current index according to their relative
weights, and produce a single output spectrum with a proper
description in terms of observing time, resolution, and system
temperature.
Assuming the simplest case of a set of
spectra with identical
observing time, resolution, and system temperature, the output
spectrum has a resolution identical to the input one, and an observing
time which is the sum of all the inputs one. The output system
temperature is then derived by reverting the theoritical time weight
formula
 |
(3) |
 |
(4) |
When averaging folded fsw with TIME weighting, this gives:
 |
(5) |
If we reverse the generic
formula, this gives an
unexpected change of system temperature:
 |
(6) |
In other words, when the factor 2 was introduced in 2019, it was not
added symetrically in the
reverse operation done by AVERAGE. The result was that when all the averaged spectra were
folded fsw, the output Tsys was underestimated by a factor
. As of 24-feb-2021 and release mar21, this is fixed now:
 |
(7) |
This reverse function is used when mixing folded fsw spectra
only. When mixing psw or wsw spectra only, the generic
function is used. Finally, when mixing folded fsw with psw or wsw, the
output Tsys is more complicated to evaluate, as there is no unique
weight formula to revert. The chosen solution is to use also the
generic
function, leading to an approximate evaluation of
the output system temperature. In this latter case, we also introduce
a mix switching mode (reflecting the combination of spectra
observed in different modes), and the associated section in the
spectrum header is emptied except for this code.
For example, when mixing a one psw or wsw spectrum with one fsw
spectrum of same system temperature, integration time, and frequency
resolution, this gives:
with
(sum of input integration
times). Since
,
this yields:
 |
(11) |
We see that the resulting system temperature is underestimated because
the reverse weight formula is not ideal in the mixed case.
Next: Consequences
Up: class-weighting
Previous: Fixing folded frequency switching
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Gildas manager
2023-06-01