From 45bfc8e9a75c18eb3fc34dc3feefe0ffd904db14 Mon Sep 17 00:00:00 2001 From: Eric Teunis de Boone Date: Wed, 2 Feb 2022 12:55:01 +0100 Subject: [PATCH] Almost finished, need to work on introduction --- ...e-phase_reconstruction-unfolded-zoomed.pdf | Bin 0 -> 197843 bytes ...se-phi_f_vs_f_max_increasing_N_samples.pdf | Bin 0 -> 33892 bytes ...ative_amplitudes_vs_N_samples_absolute.pdf | Bin 0 -> 23077 bytes ...relative_amplitudes_vs_N_samples_power.pdf | Bin 0 -> 24709 bytes .../2022-02-03_group_meeting.tex | 94 ++++++++---------- 5 files changed, 41 insertions(+), 53 deletions(-) create mode 100644 figures/fourier/02-fourier_phase-phase_reconstruction-unfolded-zoomed.pdf create mode 100644 figures/fourier/02-fourier_phase-phi_f_vs_f_max_increasing_N_samples.pdf create mode 100644 figures/fourier/02-fourier_phase-relative_amplitudes_vs_N_samples_absolute.pdf create mode 100644 figures/fourier/02-fourier_phase-relative_amplitudes_vs_N_samples_power.pdf diff --git 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b/presentations/2022-02-03_group_meeting/2022-02-03_group_meeting.tex index 3f36250..e3bd1dd 100644 --- a/presentations/2022-02-03_group_meeting/2022-02-03_group_meeting.tex +++ b/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}{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*} + \hspace{-2em} + u(t) = \exp(i2\pi ft + \phi_t) \xrightarrow{\mathrm{Fourier\; Transform}} f', \phi_f + \end{equation*} + \begin{block}{Discrete} \begin{equation*} - u(t) = \exp(2i\pi ft + \phi_t) + 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}