Test data

We test here the AVERAGE command behavior and the noise properties on a frequency switch dataset. Here we use the 3 frequency switch tracked spectra observed on 03-jun-2013, scans 100, 101, and 102, on the Vespa 4 backend part (30ME2VLI-V04).




Table 1: Status of the raw spectra w/t their theoretical and measured noise in all CLASS versions. $t$ is the integration time, $f_{\ensuremath {\mathrm {res}}}$ is the frequency resolution. The theoretical noise is computed from $T_{\ensuremath {\mathrm {sys}}}$, $t$, and $f_{\ensuremath {\mathrm {res}}}$ (in Hz): $\sigma = T_{\ensuremath {\mathrm {sys}}}/\sqrt {t \times f_{\ensuremath {\mathrm {res}}}}$. The measured noise is computed by the BASELINE command, excluding the windows with signal.
Scan Tsys t $f_{\ensuremath {\mathrm {res}}}$ Theoretical noise Measured noise Status
  (K) (s) (MHz) (K) (K)  
100 224.66 56.61 0.0195 0.214 0.219 OK
101 224.53 56.61 0.0195 0.214 0.220 OK
102 224.40 56.61 0.0195 0.213 0.217 OK




Table 2: Same as Table 1, for the averaged spectra produced by the command AVERAGE in CLASS version feb21. We combine the 3 spectra either in a single call (100+101+102), or in 2 calls with an intermediate average (100+101, then (100+101)+102). This CLASS version gives unexpected results (in red). 1) After a single average, the system temperature, and thus the theoretical noise, is underestimated by a factor $\sqrt {2}$, but the measured noise is correct as the weighted average used proper weights. 2) when averaging in several calls, the error on the system temperature propagates also to the weighted average; we can show that the measured noise is divided by $\sqrt {14/5}$ instead of $\sqrt {3}$ ($3.5\%$ overestimate) after the 2-average sequence.
Average Tsys t $f_{\ensuremath {\mathrm {res}}}$ Theoretical noise Measured noise Status
100+101+102 158.77 169.84 0.0195 0.087 0.127 Unexpected \bgroup\color{red}$^1$\egroup
100+101 158.81 113.23 0.0195 0.107 0.154 Unexpected \bgroup\color{red}$^1$\egroup
(100+101)+102 122.99 169.84 0.0195 0.068 0.131 Unexpected \bgroup\color{red}$^2$\egroup




Table 3: Same as Table 1, for the averaged spectra produced by the command AVERAGE in CLASS version mar21.
Average Tsys t $f_{res}$ Theoretical noise Measured noise Status
100+101+102 224.53 169.84 0.0195 0.123 0.127 OK
100+101 224.59 113.23 0.0195 0.151 0.154 OK
(100+101)+102 224.53 169.84 0.0195 0.123 0.127 OK