Almost finished, need to work on introduction

presentations/2022-02-03_group_meeting/2022-02-03_group_meeting.tex

@@ -9,34 +9,21 @@
 
 \addbibresource{../../../bibliotheca/bibliography.bib}
 
-%%%%%%
 % Disable Captions
-%%%%%
 \setbeamertemplate{caption}{\raggedright\small\insertcaption\par}
 
-\newcommand\blfootnote[1]{%
-  \begingroup
-  \renewcommand\thefootnote{}\footnote{#1}%
-  \addtocounter{footnote}{-1}%
-  \endgroup
+% Show Section overview at beginning of section
+\AtBeginSection[]
+{
+	\begin{frame}<beamer>{Table of Contents}
+		\tableofcontents[currentsection, currentsubsection, sectionstyle=show/shaded, subsectionstyle=hide]
+	\end{frame}
 }
 
-%\addtobeamertemplate{navigation symbols}{}{%
-%    \usebeamerfont{footline}%
-%    \usebeamercolor[fg]{footline}%
-%    \hspace{1em}%
-%    \insertframenumber
-%}
-
-%%%%%%%% Outline %%%%%%%%
-%
-% - Timing Mechanisms
-%
-% - White Rabbit
-%
-% - Fourier and Phase information
-%
-%
+% no to navigation, yes to frame numbering
+\beamertemplatenavigationsymbolsempty
+\setbeamerfont{page number in head/foot}{size=\normalsize}
+\setbeamertemplate{footline}[frame number]
 
 \title[Timing Accuracy]{Timing Accuracy in Air Shower Detectors}
 \date{February 03, 2022}
@@ -48,11 +35,12 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Timing Mechanisms in Detectors}
 \begin{frame}{Timing Mechanisms}
-	{Timing Mechanisms}
+	\begin{block}{Timing Mechanisms}
 	\begin{itemize}
 		\item GNSS (online)
 		\item Beacon (offline)
 	\end{itemize}
+	\end{block}
 	\vspace{2em}
 	\begin{itemize}
 		\item More accurate reference timing needed to characterise/improve current mechanisms.
@@ -60,6 +48,7 @@
 \end{frame}
 
 %%%%%%%%%%%%%
+\subsection{GNSS}
 \begin{frame}{Timing Mechanisms: GNSS}
 	\begin{block}{}
 		\begin{itemize}
@@ -69,6 +58,7 @@
 \end{frame}
 
 %%%%%%%%%%%%%
+\subsection{Beacon}
 \begin{frame}{Timing Mechanisms: Beacon}
 			\begin{itemize}
 				\item Beating between frequency signals indicate timing
@@ -86,7 +76,7 @@
 		\begin{column}{.5\textwidth}
 			\begin{figure}
 				\includegraphics[width=\textwidth]{beacon/auger/1512.02216.figure4.ads-b.png}
-				\caption{Automatic Dependent Surveillance Broadcasts (ADS-B) intercepts. From \cite{PierreAuger:2015aqe}}
+				\caption{ADS-B and signal intercepts. From \cite{PierreAuger:2015aqe}}
 			\end{figure}
 		\end{column}
 	\end{columns}
@@ -94,6 +84,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Experimental Setup: White Rabbit}
+\subsection[PTP]{Precision Time Protocol}
 \begin{frame}{Precision Time Protocol}
 	\begin{itemize}
 		\item Time synchronisation over (long) distance between (multiple) nodes
@@ -105,12 +96,13 @@
 \end{frame}
 
 %%%%%%%%%%%%%
+\subsection[WR]{White Rabbit}
 \begin{frame}{White Rabbit}
 	\begin{columns}
 		\begin{column}{.5\textwidth}
 			White Rabbit:
 			\begin{itemize}
-				\item SyncE ($f=125\textrm{MHz}$) (shared oscillator)
+				\item SyncE (common oscillator)
 				\item PTP (synchronisation)
 			\end{itemize}
 
@@ -137,13 +129,17 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Fourier and Phase information}
-\begin{frame}{Discrete Fourier and Phase}
-	\begin{block}{}
+\begin{frame}{(Discrete) Fourier and Phase}
 	\begin{equation*}
-			u(t) = \exp(2i\pi ft + \phi_t)
+		\hspace{-2em}
+		u(t) = \exp(i2\pi ft + \phi_t)	\xrightarrow{\mathrm{Fourier\; Transform}} f', \phi_f
+	\end{equation*}
+	\begin{block}{Discrete}
+		\begin{equation*}
+			N_\mathrm{required} := f_\mathrm{sample\_rate} / f_\mathrm{signal}
 		\end{equation*}
 		\begin{equation*}
-			N_{required} := f_{sample\_rate} / f_{signal}
+			f_\mathrm{Nyquist} = \frac{1}{2} f_\mathrm{sample\_rate}
 		\end{equation*}
 	\end{block}
 	\includegraphics[width=\textwidth]{fourier/02-fourier_phase-f_max_showcase.pdf}
@@ -151,7 +147,8 @@
 
 
 %%%%%%%%%%%%%
-\begin{frame}{Phase reconstruction??}
+\subsection{Phase reconstruction}
+\begin{frame}{Phase reconstruction?}
 	\begin{block}{}
 		\begin{equation*}
 			u(t) = \exp(2i\pi ft + \phi_t)
@@ -166,38 +163,29 @@
 \end{frame}
 
 %%%%%%%%%%%%%
-\begin{frame}{Phase reconstruction??}
-	\begin{block}{}
-		What if sample rate ``incorrect''?
-	\end{block}
-	\begin{figure}
-		\makebox[\textwidth][c]{\includegraphics[width=1.4\textwidth]{fourier/02-fourier_phase-phi_f_vs_f_max_increasing_N_samples.pdf}}%
-	\end{figure}
-\end{frame}
-
-%%%%%%%%%%%%%
-\begin{frame}{Phase reconstruction??}
+\begin{frame}{Phase reconstruction?}
 	\begin{block}{}
 		What if sample rate ``incorrect''? \\
-
-		Linear interpolation ({\small $f_\mathrm{max}$, $f_\mathrm{submax}$, $\phi_\mathrm{max}$ and $\phi_\mathrm{submax}$}) 
 	\end{block}
+	\begin{block}<2->{}
+		$\rightarrow$ Linear interpolation ({\small $f_\mathrm{signal}$, $f_\mathrm{max}$, $f_\mathrm{submax}$, $\phi_\mathrm{max}$ and $\phi_\mathrm{submax}$})
+	\end{block}
+	\vspace{2em}
 	\begin{figure}
 		\makebox[\textwidth][c]{
-			\includegraphics[width=\textwidth]{fourier/02-fourier_phase-phase_reconstruction-unfolded.pdf}
-		}
+			\includegraphics<1-2>[width=1.4\textwidth]{fourier/02-fourier_phase-phi_f_vs_f_max_increasing_N_samples.pdf}
+			\includegraphics<3>[width=1.3\textwidth]{fourier/02-fourier_phase-phase_reconstruction-unfolded.pdf}
+			\includegraphics<4>[width=1.3\textwidth]{fourier/02-fourier_phase-phase_reconstruction-unfolded-zoomed.pdf}
+		}%
 	\end{figure}
 \end{frame}
 
 %%%%%%%%%%%%%
-\begin{frame}{}
-	\begin{block}{}
-		\begin{equation*}
-			A_1 / A_2
-		\end{equation*}
-	\end{block}
+\subsection{Without interpolation?}
+\begin{frame}{Without interpolation? (Coming)}
 	\begin{figure}
-		\makebox[\textwidth][c]{\includegraphics[width=1.4\textwidth]{fourier/02-fourier_phase-relative_amplitudes_vs_N_samples.pdf}}%
+		\makebox[\textwidth][c]{\includegraphics[width=1.3\textwidth]{fourier/02-fourier_phase-relative_amplitudes_vs_N_samples_absolute.pdf}}\\%
+		\makebox[\textwidth][c]{\includegraphics[width=1.3\textwidth]{fourier/02-fourier_phase-relative_amplitudes_vs_N_samples_power.pdf}}\\%
 	\end{figure}
 \end{frame}
 \end{document}