Almost finished, need to work on introduction

This commit is contained in:
Eric Teunis de Boone 2022-02-02 12:55:01 +01:00
parent 51b2dca7e9
commit 45bfc8e9a7
5 changed files with 41 additions and 53 deletions

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@ -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}