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Thesis: introduce vim markers into beacon chapter
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1 changed files with 27 additions and 28 deletions
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@ -1,5 +1,7 @@
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% vim: fdm=marker fmr=<<<,>>>
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\documentclass[../thesis.tex]{subfiles}
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% Local preamble <<<
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\graphicspath{
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{.}
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{../../figures/}
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@ -32,9 +34,10 @@
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\newcommand{\pProp}{\pTrue_d}
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\newcommand{\pClock}{\pTrue_c}
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% >>> Local Preamble
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\begin{document}
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\chapter{Disciplining by Beacon}
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\chapter{Disciplining by Beacon} %<<<
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\label{sec:disciplining}
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Time synchronisation for autonomous stations is typically performed with a \gls{GNSS} clock in each station.
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The time accuracy supplied by the \gls{GNSS} clock ($\sim 10 \ns$) is not enough to do effective interferometry.
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@ -58,8 +61,7 @@ This influences the tradeoff between methods.
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In the following, the synchronisation scheme for both the continuous and intermittent beacon are elaborated upon.
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\Todo{further outline}
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\section{Physical Setup}
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\section{Physical Setup} %<<<
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\begin{figure}
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\centering
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@ -178,11 +180,10 @@ The nature of the beacon allows for different methods to determine $(\tMeasArriv
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In the following, two approaches for measuring $(\tMeasArriv)_i$ are examined.
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\Todo{reword towards next sections?}
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%%%%
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%%%% >>>
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%%%% Pulse
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%%%%
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\section{Intermittent Pulse Beacon}
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\section{Intermittent Pulse Beacon}% <<<
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\label{sec:beacon:pulse}
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If the stability of the clock allows for it, the synchronisation can be performed during a discrete period.
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The tradeoff between the gained accuracy and the timescale between synchronisation periods allows for a dead time of the detectors during synchronisation.
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@ -293,13 +294,10 @@ Since the filtered signal is sampled discretely, this means the start of the
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% dead time
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%%%%
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%%%% >>>
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%%%% Sine
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%%%%
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\section{Continuous Sine Beacon}
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\section{Continuous Sine Beacon}% <<<
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\label{sec:beacon:sine}
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% continuous -> can be discrete
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In the case that the stations need continuous synchronisation, a different route must be taken.
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@ -374,7 +372,7 @@ Later, a mechanism to lift the period degeneracy using an airshower as discrete
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%%
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%% Phase measurement
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\subsection{Phase measurement}
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\subsection{Phase measurement}% <<<
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A continuous beacon can syntonise an array of antennas by correcting for the measured difference in beacon phases $(\Delta \pMeasArriv)_{ij}$.
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They are derived by applying a \gls{FT} to the traces of each antenna.
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@ -417,9 +415,9 @@ These aspects are examined in the following section.
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}
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\label{fig:beacon:ttl_sine_beacon}
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\end{figure}
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% >>>
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% DTFT
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\subsubsection{Discrete Time Fourier Transform}
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\subsubsection{Discrete Time Fourier Transform}% <<<
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% FFT common knowledge ..
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The typical \gls{FT} to obtain spectral information from periodic data is the \gls{FFT} (a fast implementation of the \gls{DFT} \eqref{eq:fourier:dft}).
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Such an algorithm efficiently finds the magnitudes and phases within a trace $x$ at specific frequencies $f = f_s \tfrac{k}{N}$ determined solely by the number of samples $N$ ($0 \leq k < N$) and the sampling frequency $f_s$.
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@ -485,9 +483,9 @@ With a constant beacon frequency, the coefficients for evaluating the \gls{DTFT}
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% Removing the beacon from the signal trace
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% >>>
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% Signal to noise
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\subsubsection{Signal to Noise}
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\subsubsection{Signal to Noise}% <<<
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% Gaussian noise
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The traces will contain noise from various sources, both internal (e.g. LNA) and external (e.g. radio communications) to the detector.
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@ -587,20 +585,22 @@ Phase distribution: gaussian
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\label{fig:time_res_vs_snr}
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\end{figure}
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% Signal to Noise >>>
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\subsection{Period degeneracy}
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\subsection{Period degeneracy}% <<<
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% period multiplicity/degeneracy
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% airshower gives t0
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% Period Degeneracy >>>
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% Continuous Sine Beacon >>>
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% >>>
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\bigskip
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\section{Old work on Sine Beacon}
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\chapter{Old work on Sine Beacon}% <<<
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\Todo{fully rewrite}
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The idea of a sine beacon is semi-analogous to an oscillator in electronic circuits.
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A periodic signal is sent out from a transmitter (the oscillator), and captured by an antenna (the chip the oscillator drives).
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@ -681,17 +681,14 @@ This slower timescale allows to count the ticks of the quicker signal.\todo{Exte
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\end{figure}
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\subsection{Beacons in Airshower timing}
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\subsection{Beacons in Airshower timing}% <<<
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To setup a time synchronising system for airshower measurements, actually only the high frequency part of the beacon must be employed.
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The low frequency part, from which the number of oscillations of the high frequency part are counted, is supplied by the very airshower that is measured.
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% >>>
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\section{Beacon synchronisation}
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\section{Beacon synchronisation}% <<<
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As outlined in Section~\ref{sec:time:beacon}, a beacon can also be employed to synchronise the stations.
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@ -768,7 +765,7 @@ However, while in a static setup the value of $k$ can be estimated from the dist
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\\
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\subsection{Lifting period degeneracy}
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\subsection{Lifting period degeneracy}% <<<
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\begin{figure}
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\begin{subfigure}[t]{0.5\textwidth}
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\includegraphics[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.no_offset.scale4d.pdf}
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@ -795,7 +792,9 @@ However, while in a static setup the value of $k$ can be estimated from the dist
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\label{fig:grid_power_time_fixes}
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\end{figure}
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% >>>
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%>>>
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\end{document}
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