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Thesis: fix reference errors

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Eric Teunis de Boone 2023-11-14 16:40:59 +01:00
parent 624c6a31b6
commit f276cc0a32
2 changed files with 4 additions and 6 deletions
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2
documents/thesis/chapters/beacon_discipline.tex
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@ -432,7 +432,7 @@ Of course, like the pulse method, the ability to measure the beacon's sine waves
To quantify this comparison in terms of \gls{SNR},
we define the signal level to be the amplitude of the frequency spectrum at the beacon's frequency determined by \gls{DTFT} (the orange line in Figure~\ref{fig:sine:snr_definition}),
and the noise level as the scaled \gls{RMS} of all amplitudes in the noise band determined by \gls{FFT} (blue line in Figure~\ref{fig:sine:snr_definition}).
Since gaussian noise has Rayleigh distributed amplitudes (see Figure~\ref{fig:noise:pdf:amplitude} in Appendix~\ref{sec:phasor_distributions}), this \gls{RMS} is scaled by $1/\sqrt{2\pi}$.
Since gaussian noise has Rayleigh distributed amplitudes (see Figure~\ref{fig:phasor_sum:pdf:amplitude} in Appendix~\ref{sec:phasor_distributions}), this \gls{RMS} is scaled by $1/\sqrt{2\pi}$.
\\
% longer traces
However, for sine waves, an additional method to increase the \gls{SNR} is available.

8
documents/thesis/chapters/single_sine_interferometry.tex
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@ -155,8 +155,8 @@ The distance between the antenna and the transmitter results in a phase offset w
} %>>>
The beacon signal was recorded over a longer time ($10240\,\mathrm{samples}$), to be able to distinguish the beacon and air shower later in the analysis.
\\
The final waveform of an antenna (see Figure~\ref{fig:single:annotated_full_waveform}) was then constructed by adding its beacon and air shower waveforms and band-passing with relevant frequencies (here $30$ and $80\MHz$ are taken by default).
Of course, a gaussian white noise component is introduced to the waveform as a simple noise model (see Figure~\ref{fig:sine:time_accuracy} for a treatise on the timing accuracy of a sine beacon).
The final waveform of an antenna (see Figure~\ref{fig:single:proton}) was then constructed by adding its beacon and air shower waveforms and band-passing with relevant frequencies (here $30$ and $80\MHz$ are taken by default).
Of course, a gaussian white noise component is introduced to the waveform as a simple noise model (see Figure~\ref{fig:sine:snr_time_resolution} for a treatise on the timing accuracy of a sine beacon).
\\
\begin{figure}% <<<
@ -172,12 +172,10 @@ Of course, a gaussian white noise component is introduced to the waveform as a s
\begin{figure}% <<<
\begin{subfigure}[t]{0.49\textwidth}
\includegraphics[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.zoomed.pdf}
\label{fig:single:annotated_full_waveform}
\end{subfigure}
\hfill
\begin{subfigure}[t]{0.49\textwidth}
\includegraphics[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.fourier.pdf}
\label{fig:single:fourier}
\end{subfigure}
\caption{
\textit{Left:}
@ -204,7 +202,7 @@ Moreover, it falls in the order of magnitude of clock defects that were found in
% separate air shower from beacon
To correctly recover the beacon from the waveform, it must be separated from the air shower.
Typically, a trigger sets the location of the airshower signal in the waveform.
In our case, the airshower signal is located at $t=500\ns$ (see Figure~\ref{fig:single:annotated_full_waveform}).
In our case, the airshower signal is located at $t=500\ns$ (see Figure~\ref{fig:single:proton}).
Since the beacon can be recorded for much longer than the air shower signal, we mask a window of $500$ samples around the maximum of the trace as the air shower's signal.
% measure beacon phase, remove distance phase
The remaining waveform is fed into a \gls{DTFT} \eqref{eq:fourier:dtft} to measure the beacon's phase $\pMeas$ and amplitude.