Thesis: fix reference errors

This commit is contained in:
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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@ -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}, 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}), 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}). 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 $1/\sqrt{2\pi}$.
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% longer traces % longer traces
However, for sine waves, an additional method to increase the \gls{SNR} is available. However, for sine waves, an additional method to increase the \gls{SNR} is available.

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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 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.
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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). 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:time_accuracy} for a treatise on the timing accuracy of a sine beacon). 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).
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\begin{figure}% <<< \begin{figure}% <<<
@ -172,12 +172,10 @@ Of course, a gaussian white noise component is introduced to the waveform as a s
\begin{figure}% <<< \begin{figure}% <<<
\begin{subfigure}[t]{0.49\textwidth} \begin{subfigure}[t]{0.49\textwidth}
\includegraphics[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.zoomed.pdf} \includegraphics[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.zoomed.pdf}
\label{fig:single:annotated_full_waveform}
\end{subfigure} \end{subfigure}
\hfill \hfill
\begin{subfigure}[t]{0.49\textwidth} \begin{subfigure}[t]{0.49\textwidth}
\includegraphics[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.fourier.pdf} \includegraphics[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.fourier.pdf}
\label{fig:single:fourier}
\end{subfigure} \end{subfigure}
\caption{ \caption{
\textit{Left:} \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 % separate air shower from beacon
To correctly recover the beacon from the waveform, it must be separated from the air shower. 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. 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. 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 % 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. The remaining waveform is fed into a \gls{DTFT} \eqref{eq:fourier:dtft} to measure the beacon's phase $\pMeas$ and amplitude.