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diff --git a/figures/gnss/phase-delocked-gps-white-rabbit-setup-colored.svg b/figures/gnss/src/phase-delocked-gps-white-rabbit-setup-colored.svg
similarity index 80%
rename from figures/gnss/phase-delocked-gps-white-rabbit-setup-colored.svg
rename to figures/gnss/src/phase-delocked-gps-white-rabbit-setup-colored.svg
index e09f4df..fdeb241 100644
--- a/figures/gnss/phase-delocked-gps-white-rabbit-setup-colored.svg
+++ b/figures/gnss/src/phase-delocked-gps-white-rabbit-setup-colored.svg
@@ -2,20 +2,20 @@
diff --git a/figures/gnss/phase-locked-gps-white-rabbit-setup-colored.svg b/figures/gnss/src/phase-locked-gps-white-rabbit-setup-colored.svg
similarity index 52%
rename from figures/gnss/phase-locked-gps-white-rabbit-setup-colored.svg
rename to figures/gnss/src/phase-locked-gps-white-rabbit-setup-colored.svg
index 5adc890..40ec287 100644
--- a/figures/gnss/phase-locked-gps-white-rabbit-setup-colored.svg
+++ b/figures/gnss/src/phase-locked-gps-white-rabbit-setup-colored.svg
@@ -2,20 +2,20 @@
diff --git a/figures/gnss/phase-locked-gps-white-rabbit-setup.svg b/figures/gnss/src/phase-locked-gps-white-rabbit-setup.svg
similarity index 100%
rename from figures/gnss/phase-locked-gps-white-rabbit-setup.svg
rename to figures/gnss/src/phase-locked-gps-white-rabbit-setup.svg
diff --git a/figures/white-rabbit/README.md b/figures/white-rabbit/README.md
new file mode 100644
index 0000000..a4c42f9
--- /dev/null
+++ b/figures/white-rabbit/README.md
@@ -0,0 +1,6 @@
+# White Rabbit figures
+
+Probably most of the figures in this directory are directly from the
+White Rabbit repository at https://ohwr.org/project/white-rabbit/.
+
+I intend to keep the original filenames.
diff --git a/figures/white-rabbit/protocol/delaymodel.pdf b/figures/white-rabbit/protocol/delaymodel.pdf
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index 0000000..e36333b
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diff --git 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
index 43c6210..7d9beaf 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
@@ -1,22 +1,221 @@
\documentclass[showdate=false]{beamer}
+\usepackage[british]{babel}
+\usepackage{amsmath}
+\usepackage{hyperref}
+\usepackage[backend=bibtex,style=trad-plain]{biblatex}
+\usepackage{graphicx}
+\graphicspath{{.}{../../figures/}}
-\addtobeamertemplate{navigation symbols}{}{%
- \usebeamerfont{footline}%
- \usebeamercolor[fg]{footline}%
- \hspace{1em}%
- \insertframenumber
+\addbibresource{../../../bibliotheca/bibliography.bib}
+
+% Disable Captions
+\setbeamertemplate{caption}{\raggedright\small\insertcaption\par}
+
+% Show Section overview at beginning of section
+\AtBeginSection[]
+{
+ \begin{frame}{Table of Contents}
+ \tableofcontents[currentsection, currentsubsection, sectionstyle=show/shaded, subsectionstyle=hide]
+ \end{frame}
}
+% no to navigation, yes to frame numbering
+\beamertemplatenavigationsymbolsempty
+\setbeamerfont{page number in head/foot}{size=\normalsize}
+\setbeamertemplate{footline}[frame number]
-\title{}
-\date{February 03, 2022}
+\title[Timing Accuracy]{Timing Accuracy in Air Shower Detectors}
+\date{February 10, 2022}
\author{E.T. de Boone}
\begin{document}
\frame{\titlepage}
-\begin{frame}
+
+\section{Timing Mechanisms in Detectors}
+\begin{frame}{Timing Mechanisms}
+ \begin{block}{Why improve timing accuracy?}
+ \begin{itemize}
+ \item Better statistics (narrow down direction of air showers)
+ \item Interferometry
+ \end{itemize}
+ \end{block}
+ \begin{block}{Strategy}
+ \begin{itemize}
+ \item Simulations for synchronisation techniques
+ \item Characterising current methods
+ \end{itemize}
+ \end{block}
+\end{frame}
+\begin{frame}{Characterising current methods}
+ \begin{block}{Current Timing Methods}
+ \begin{itemize}
+ \item GNSS (online)
+ \item Beacon (offline)
+ \end{itemize}
+ \end{block}
+ \vspace{2em}
+ \begin{itemize}
+ \item GPS Accuracy $\leq 30 \mathrm{ns}$ for $95$\% time (often better)
+ \item Total time accuracy in the order of 5 -- 10~ns
+ \item More accurate reference timing needed to characterise/improve current mechanisms.
+ \end{itemize}
+
\end{frame}
+%%%%%%%%%%%%%
+\subsection{Beacon}
+\begin{frame}{Timing Mechanisms: Beacon}
+ \begin{itemize}
+ \item Beating between frequency signals indicate timing
+ \item PA: located in physics band $\mapsto$ offline analysis, \\
+ corrects for GPS drift.
+ \item different frequency responses for antenna models and directions
+ \end{itemize}
+ \begin{columns}
+ \begin{column}{.5\textwidth}
+ \begin{figure}
+ \includegraphics[width=\textwidth]{beacon/auger/1512.02216.figure2.beacon_beat.png}
+ \caption{
+ \cite{PierreAuger:2015aqe}
+ Four beacon frequencies beating at PA.
+ }
+ \end{figure}
+ \end{column}
+ \begin{column}{.5\textwidth}
+ \begin{figure}
+ \includegraphics[width=\textwidth]{beacon/auger/1512.02216.figure4.ads-b.png}
+ %\caption{
+ % \cite{PierreAuger:2015aqe}
+ % ADS-B and signal intercepts.
+ %}
+ \end{figure}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\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
+ \end{itemize}
+ \begin{figure}
+ \includegraphics[width=0.4\textwidth]{white-rabbit/protocol/ptpMSGs-color.pdf}
+ \caption{
+ \cite{WRPTP}
+ Precision Time Protocol messages.
+ }
+ \end{figure}
+\end{frame}
+
+%%%%%%%%%%%%%
+\subsection[WR]{White Rabbit}
+\begin{frame}{White Rabbit}
+ \begin{columns}
+ \begin{column}{.5\textwidth}
+ White Rabbit:
+ \begin{itemize}
+ \item SyncE (common oscillator)
+ \item PTP (synchronisation)
+ \end{itemize}
+
+ \vspace{2em}
+
+ Factors:
+ \begin{itemize}
+ \item device ($\Delta_{txm}$, $\Delta_{rxs}$, ...)
+ \item link ($\delta_{ms}$, ...)
+ \end{itemize}
+ \begin{figure}
+ \makebox[\textwidth][c]{\includegraphics[width=1.1\textwidth]{white-rabbit/protocol/delaymodel.pdf}}
+ %\caption{\small From \cite{WRPTP}}.
+ \end{figure}
+ \end{column}
+ \begin{column}{.5\textwidth}
+ \begin{figure}
+ \makebox[\textwidth][c]{\includegraphics[width=1.1\textwidth]{white-rabbit/protocol/wrptpMSGs_1.pdf}}
+ %\caption{From \cite{WRPTP}}.
+ \end{figure}
+ \end{column}
+ \end{columns}
+\end{frame}
+
+\begin{frame}{White Rabbit}
+ \begin{figure}
+ \centering
+ \includegraphics<1>[width=0.8\textwidth]{gnss/phase-delocked-gps-white-rabbit-setup-colored.pdf}
+ \includegraphics<2>[width=0.8\textwidth]{gnss/phase-locked-gps-white-rabbit-setup-colored.pdf}
+ \end{figure}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Fourier and Phase information}
+\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 Fourier Transform}
+ \begin{equation*}
+ N_\mathrm{required} := f_\mathrm{sample\_rate} / f_\mathrm{signal}
+ \end{equation*}
+ \begin{equation*}
+ 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}
+\end{frame}
+
+
+%%%%%%%%%%%%%
+\subsection{Phase reconstruction}
+\begin{frame}{Phase reconstruction?}
+ \begin{block}{}
+ \begin{equation*}
+ u(t) = \exp(2i\pi ft + \phi_t)
+ \end{equation*}
+ \end{block}
+ \begin{figure}
+ \makebox[\textwidth][c]{\includegraphics[width=1.4\textwidth]{fourier/02-fourier_phase-phi_f_vs_phi_t.pdf}}%
+ \end{figure}
+ \begin{block}{}
+ Phase reconstruction is easy if sample rate ``correct''
+ \end{block}
+\end{frame}
+
+%%%%%%%%%%%%%
+\begin{frame}{Phase reconstruction?}
+ \begin{block}{}
+ What if sample rate ``incorrect''? \\
+ \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<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}
+
+%%%%%%%%%%%%%
+\subsection{Without interpolation?}
+\begin{frame}{Without interpolation? (Coming)}
+ \begin{figure}
+ \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}
+
+%%%%%%%%%%%%%
+\section*{References}
+\begin{frame}{References}
+ \printbibliography
+\end{frame}
\end{document}
diff --git a/presentations/2022-02-03_group_meeting/Makefile b/presentations/2022-02-03_group_meeting/Makefile
index 2a1985e..449c34a 100644
--- a/presentations/2022-02-03_group_meeting/Makefile
+++ b/presentations/2022-02-03_group_meeting/Makefile
@@ -1,24 +1,24 @@
# vim:ft=make
-include config.mk
-.PHONY: all clean
-
+.PHONY: all clean dist-clean
### Variables
-
MAIN_SRC ?= main.tex
-TEXENGINE ?= pdflatex
+TEXENGINE ?= latexmk --pdf
+
+MAIN_TARGET = $(patsubst %.tex,%.pdf,$(MAIN_SRC))
### Targets
-
-MAIN_TARGET=$(patsubst %.tex,%.pdf,$(MAIN_SRC))
-
all: $(MAIN_TARGET)
+dist: all clean
+
$(MAIN_TARGET): $(MAIN_SRC)
$(TEXENGINE) $^
- $(TEXENGINE) $^
+
+dist-clean: clean
+ @rm -vf *.pdf *.eps *.dvi *.ps
clean:
- @rm -f *.dat *.log *.out *.aux *.dvi *.ps *.nav *.snm *.toc *.vrb *~
- @rm -f *.pdf *.eps
+ @rm -vf *.dat *.log *.out *.aux *.nav *.snm *.toc *.vrb *~ *.fls *.fdb_latexmk *-blx.bib *.bbl *.blg *.run.xml
diff --git a/presentations/2022-02-03_group_meeting/README.md b/presentations/2022-02-03_group_meeting/README.md
index 7934a78..63ed19d 100644
--- a/presentations/2022-02-03_group_meeting/README.md
+++ b/presentations/2022-02-03_group_meeting/README.md
@@ -1,4 +1,16 @@
# Short Presentation on current status
Mostly to show what I've been doing uptil now.
-Maybe short description of experimental setup?
+Add short description of experimental setup?
+
+
+### Outline
+ * Timing Mechanisms (GNSS, Beacon)
+
+ * White Rabbit as reference timing mechanism
+ * White Rabbit
+ * PTP
+
+ * Fourier and Phase information
+ * precise measurement $N_{sample} = N_{required}$
+ * imprecise measurement $N_{sample} != N_{required}$
diff --git a/presentations/2022-02-03_group_meeting/config.mk b/presentations/2022-02-03_group_meeting/config.mk
index cb810d7..13b1456 100644
--- a/presentations/2022-02-03_group_meeting/config.mk
+++ b/presentations/2022-02-03_group_meeting/config.mk
@@ -1,2 +1 @@
MAIN_SRC=2022-02-03_group_meeting.tex
-TEXENGINE=pdflatex