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\usepackage{amsmath}
\usepackage{graphicx}
\graphicspath{{.}{../../figures/}}


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%%%%%%%% Outline %%%%%%%%
%
% - Timing Mechanisms
%
% - White Rabbit
%
% - Fourier and Phase information
%
%

\title{Timing Accuracy in Air Shower Detectors}
\date{February 03, 2022}
\author{E.T. de Boone}

\begin{document}
\frame{\titlepage}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Timing Mechanisms in Detectors}
\begin{frame}{Timing Mechanisms}
	\begin{block}{Timing Mechanisms}
		\begin{itemize}
			\item GNSS (online)
			\item Beacon (offline)
		\end{itemize}
	\end{block}
	\begin{block}{}
		\begin{itemize}
			\item More accurate reference timing needed to characterise/improve current mechanisms.
		\end{itemize}
	\end{block}
\end{frame}

\begin{frame}{Timing Mechanisms: GNSS}
\end{frame}

\begin{frame}{Timing Mechanisms: Beacon}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Experimental Setup: White Rabbit}
\begin{frame}{White Rabbit}
\end{frame}

\begin{frame}{Precision Time Protocol}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Fourier and Phase information}
\begin{frame}{Discrete Fourier and Phase}
	\begin{block}{}
		\begin{equation*}
			N_{required} = f_{sample\_rate} / f_{signal}
		\end{equation*}
	\end{block}
\end{frame}

\begin{frame}{Phase reconstruction??}
	\begin{figure}
		\makebox[\textwidth][c]{\includegraphics[width=1.4\textwidth]{fourier/02-fourier_phase-phi_f_vs_phi_t.pdf}}%
	\end{figure}
\end{frame}
\begin{frame}{Phase reconstruction??}
	\begin{block}{}
		\begin{equation*}
			A_1 / A_2
		\end{equation*}
	\end{block}
	\begin{figure}
		\makebox[\textwidth][c]{\includegraphics[width=1.4\textwidth]{fourier/02-fourier_phase-relative_amplitudes_vs_N_samples.pdf}}%
	\end{figure}
\end{frame}
\end{document}