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Almost finished, need to work on introduction
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@ -9,34 +9,21 @@
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\addbibresource{../../../bibliotheca/bibliography.bib}
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%%%%%%
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% Disable Captions
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%%%%%
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\setbeamertemplate{caption}{\raggedright\small\insertcaption\par}
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\newcommand\blfootnote[1]{%
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\begingroup
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\renewcommand\thefootnote{}\footnote{#1}%
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\addtocounter{footnote}{-1}%
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\endgroup
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% Show Section overview at beginning of section
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\AtBeginSection[]
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{
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\begin{frame}<beamer>{Table of Contents}
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\tableofcontents[currentsection, currentsubsection, sectionstyle=show/shaded, subsectionstyle=hide]
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\end{frame}
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}
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%\addtobeamertemplate{navigation symbols}{}{%
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% \usebeamerfont{footline}%
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% \usebeamercolor[fg]{footline}%
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% \hspace{1em}%
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% \insertframenumber
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%}
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%%%%%%%% Outline %%%%%%%%
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%
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% - Timing Mechanisms
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%
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% - White Rabbit
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%
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% - Fourier and Phase information
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%
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%
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% no to navigation, yes to frame numbering
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\beamertemplatenavigationsymbolsempty
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\setbeamerfont{page number in head/foot}{size=\normalsize}
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\setbeamertemplate{footline}[frame number]
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\title[Timing Accuracy]{Timing Accuracy in Air Shower Detectors}
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\date{February 03, 2022}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Timing Mechanisms in Detectors}
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\begin{frame}{Timing Mechanisms}
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{Timing Mechanisms}
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\begin{block}{Timing Mechanisms}
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\begin{itemize}
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\item GNSS (online)
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\item Beacon (offline)
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\end{itemize}
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\end{block}
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\vspace{2em}
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\begin{itemize}
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\item More accurate reference timing needed to characterise/improve current mechanisms.
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@ -60,6 +48,7 @@
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\end{frame}
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%%%%%%%%%%%%%
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\subsection{GNSS}
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\begin{frame}{Timing Mechanisms: GNSS}
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\begin{block}{}
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\begin{itemize}
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@ -69,6 +58,7 @@
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\end{frame}
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%%%%%%%%%%%%%
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\subsection{Beacon}
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\begin{frame}{Timing Mechanisms: Beacon}
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\begin{itemize}
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\item Beating between frequency signals indicate timing
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@ -86,7 +76,7 @@
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\begin{column}{.5\textwidth}
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\begin{figure}
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\includegraphics[width=\textwidth]{beacon/auger/1512.02216.figure4.ads-b.png}
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\caption{Automatic Dependent Surveillance Broadcasts (ADS-B) intercepts. From \cite{PierreAuger:2015aqe}}
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\caption{ADS-B and signal intercepts. From \cite{PierreAuger:2015aqe}}
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\end{figure}
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\end{column}
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\end{columns}
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@ -94,6 +84,7 @@
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Experimental Setup: White Rabbit}
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\subsection[PTP]{Precision Time Protocol}
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\begin{frame}{Precision Time Protocol}
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\begin{itemize}
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\item Time synchronisation over (long) distance between (multiple) nodes
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@ -105,12 +96,13 @@
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\end{frame}
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%%%%%%%%%%%%%
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\subsection[WR]{White Rabbit}
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\begin{frame}{White Rabbit}
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\begin{columns}
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\begin{column}{.5\textwidth}
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White Rabbit:
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\begin{itemize}
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\item SyncE ($f=125\textrm{MHz}$) (shared oscillator)
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\item SyncE (common oscillator)
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\item PTP (synchronisation)
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\end{itemize}
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@ -137,13 +129,17 @@
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Fourier and Phase information}
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\begin{frame}{Discrete Fourier and Phase}
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\begin{block}{}
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\begin{frame}{(Discrete) Fourier and Phase}
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\begin{equation*}
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\hspace{-2em}
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u(t) = \exp(i2\pi ft + \phi_t) \xrightarrow{\mathrm{Fourier\; Transform}} f', \phi_f
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\end{equation*}
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\begin{block}{Discrete}
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\begin{equation*}
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u(t) = \exp(2i\pi ft + \phi_t)
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N_\mathrm{required} := f_\mathrm{sample\_rate} / f_\mathrm{signal}
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\end{equation*}
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\begin{equation*}
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N_{required} := f_{sample\_rate} / f_{signal}
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f_\mathrm{Nyquist} = \frac{1}{2} f_\mathrm{sample\_rate}
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\end{equation*}
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\end{block}
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\includegraphics[width=\textwidth]{fourier/02-fourier_phase-f_max_showcase.pdf}
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@ -151,7 +147,8 @@
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%%%%%%%%%%%%%
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\begin{frame}{Phase reconstruction??}
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\subsection{Phase reconstruction}
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\begin{frame}{Phase reconstruction?}
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\begin{block}{}
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\begin{equation*}
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u(t) = \exp(2i\pi ft + \phi_t)
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@ -166,38 +163,29 @@
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\end{frame}
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%%%%%%%%%%%%%
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\begin{frame}{Phase reconstruction??}
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\begin{block}{}
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What if sample rate ``incorrect''?
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\end{block}
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\begin{figure}
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\makebox[\textwidth][c]{\includegraphics[width=1.4\textwidth]{fourier/02-fourier_phase-phi_f_vs_f_max_increasing_N_samples.pdf}}%
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\end{figure}
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\end{frame}
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%%%%%%%%%%%%%
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\begin{frame}{Phase reconstruction??}
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\begin{frame}{Phase reconstruction?}
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\begin{block}{}
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What if sample rate ``incorrect''? \\
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Linear interpolation ({\small $f_\mathrm{max}$, $f_\mathrm{submax}$, $\phi_\mathrm{max}$ and $\phi_\mathrm{submax}$})
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\end{block}
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\begin{block}<2->{}
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$\rightarrow$ Linear interpolation ({\small $f_\mathrm{signal}$, $f_\mathrm{max}$, $f_\mathrm{submax}$, $\phi_\mathrm{max}$ and $\phi_\mathrm{submax}$})
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\end{block}
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\vspace{2em}
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\begin{figure}
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\makebox[\textwidth][c]{
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\includegraphics[width=\textwidth]{fourier/02-fourier_phase-phase_reconstruction-unfolded.pdf}
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}
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\includegraphics<1-2>[width=1.4\textwidth]{fourier/02-fourier_phase-phi_f_vs_f_max_increasing_N_samples.pdf}
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\includegraphics<3>[width=1.3\textwidth]{fourier/02-fourier_phase-phase_reconstruction-unfolded.pdf}
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\includegraphics<4>[width=1.3\textwidth]{fourier/02-fourier_phase-phase_reconstruction-unfolded-zoomed.pdf}
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}%
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\end{figure}
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\end{frame}
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%%%%%%%%%%%%%
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\begin{frame}{}
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\begin{block}{}
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\begin{equation*}
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A_1 / A_2
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\end{equation*}
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\end{block}
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\subsection{Without interpolation?}
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\begin{frame}{Without interpolation? (Coming)}
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\begin{figure}
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\makebox[\textwidth][c]{\includegraphics[width=1.4\textwidth]{fourier/02-fourier_phase-relative_amplitudes_vs_N_samples.pdf}}%
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\makebox[\textwidth][c]{\includegraphics[width=1.3\textwidth]{fourier/02-fourier_phase-relative_amplitudes_vs_N_samples_absolute.pdf}}\\%
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\makebox[\textwidth][c]{\includegraphics[width=1.3\textwidth]{fourier/02-fourier_phase-relative_amplitudes_vs_N_samples_power.pdf}}\\%
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\end{figure}
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\end{frame}
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\end{document}
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