From f276cc0a3292e51284f7a168ffe0ee000aee18c6 Mon Sep 17 00:00:00 2001 From: Eric Teunis de Boone Date: Tue, 14 Nov 2023 16:40:59 +0100 Subject: [PATCH] Thesis: fix reference errors --- documents/thesis/chapters/beacon_discipline.tex | 2 +- documents/thesis/chapters/single_sine_interferometry.tex | 8 +++----- 2 files changed, 4 insertions(+), 6 deletions(-) diff --git a/documents/thesis/chapters/beacon_discipline.tex b/documents/thesis/chapters/beacon_discipline.tex index 7aabfdb..770e041 100644 --- a/documents/thesis/chapters/beacon_discipline.tex +++ b/documents/thesis/chapters/beacon_discipline.tex @@ -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. diff --git a/documents/thesis/chapters/single_sine_interferometry.tex b/documents/thesis/chapters/single_sine_interferometry.tex index a925335..30cefc5 100644 --- a/documents/thesis/chapters/single_sine_interferometry.tex +++ b/documents/thesis/chapters/single_sine_interferometry.tex @@ -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.