Thesis: near final version for radio_measurement and beacon_disciplining

documents/thesis/chapters/beacon_discipline.tex

@@ -75,7 +75,7 @@ If the time of emitting the signal at the transmitter $\tTrueEmit$ is known, thi
 	,
 \end{equation}%>>>
 where $(\tTrueArriv)_i$ and $(\tMeasArriv)_i$ are respectively the true and measured arrival time of the signal at antenna $A_i$.
-The difference between these two terms gives the clock deviation term $(\tClock)_i$.\Todo{different symbols math}
+The difference between these two terms gives the clock deviation term $(\tClock)_i$.
 \\
 
 % relative timing; synchronising without t0 information
@@ -373,7 +373,6 @@ It shows that, as long as the pulse is (much) stronger than the noise ($\mathrm{
 	\caption{
 		Pulse timing accuracy obtained by matching $N=500$ waveforms, sampled at $2\ns$, to a templated pulse, sampled at $\Delta t = 0.5\ns$ (blue), $0.1\ns$ (orange) and $0.01\ns$ (green).
 		Dashed lines indicate the asymptotic best time accuracy ($\Delta t/\sqrt{12}$) per template sampling rate.
-		\protect\Todo{points in legend}
 		}
 	\label{fig:pulse:snr_time_resolution}
 \end{figure}

documents/thesis/chapters/introduction.tex

@@ -189,7 +189,7 @@ This is limited by the so-called Cherenkov angle.
 \bigskip
 At the very highest energy, the flux is in the order of one particle per square kilometer per century (see Figure~\ref{fig:cr_flux}).
 Observatories therefore have to span huge areas to gather decent statistics at these highest energies on a practical timescale.
-In recent and upcoming experiments, such as \gls{Auger}, \gls{GRAND} or \gls{LOFAR}, the approach is typically to instrument an area with a sparse grid of detectors to detect the generated air shower.
+In recent and upcoming experiments, such as \gls{Auger} (and its upgrade \gls{AugerPrime}), \gls{GRAND} or \gls{LOFAR}, the approach is typically to instrument an area with a (sparse) grid of detectors to detect the generated air shower.\Todo{cite experiments here}
 With distances up to $1.5\;\mathrm{km}$ (\gls{Auger}), the detectors therefore have to operate in a self-sufficient manner\Todo{word} with only wireless communication channels.
 \\
 

documents/thesis/chapters/radio_measurement.tex

@@ -16,7 +16,7 @@
 
 Radio antennas are sensitive to changes in their surrounding electric fields.
 The polarisation of the electric field that a single antenna can record is dependent on the geometry of this antenna.
-Therefore, in experiments such as \gls{Auger} or \gls{GRAND}, multiple antennas (called channels) are incorporated into a single unit to obtain complementary polarisation recordings.
+Therefore, in experiments such as \gls{Auger} or \gls{GRAND}, multiple antennas are incorporated into a single unit to obtain complementary polarisation recordings.
 Additionally, the shape and size of antennas affect how well the antenna responds to certain frequency ranges, resulting in different designs meeting different criteria.
 \\
 
@@ -36,13 +36,12 @@ To prevent such aliases, these frequencies must be removed by a filter before sa
 \\
 For air shower radio detection, very low frequencies are also not of interest.
 Therefore, this filter is generally a bandpass filter.
-For example, in \gls{AERA} and AugerPrime's RD\Todo{RD name} the filter attenuates all of the signal except for the frequency interval between $30 \text{--} 80\MHz$.\Todo{citation?}
+For example, in the \gls{AERA} and in AugerPrime's radio detector \cite{Huege:2023pfb}, the filter attenuates all of the signal except for the frequency interval between $30 \text{--} 80\MHz$.
 \\
 In addition to a bandpass filter, more complex filter setups are used to remove unwanted components or introduce attenuation at specific frequencies.
-For example, in \gls{GRAND}, the total frequency band ranges from $20\MHz$ to $200\MHz$
+For example, in \gls{GRAND} \cite{GRAND:2018iaj}, the total frequency band ranges from $20\MHz$ to $200\MHz$.
 such that the FM broadcasting band ($87.5\MHz \text{--} 108\MHz$) falls within this range.
 Therefore, notch filters have been introduced to suppress signals in this band.
-\Todo{citation?}
 \\
 
 % Filter and Antenna response
@@ -127,7 +126,6 @@ Implementing the above decomposition of $t[n]$, \eqref{eq:fourier:dtft} can be r
 The direct computation of this transform takes $2N$ complex multiplications and $2(N-1)$ complex additions for a single frequency $k$.
 When computing this transform for all integer $0 \leq k < N$, this amounts to $\mathcal{O}(N^2)$ complex computations.
 \acrlong{FFT}s (\acrshort{FFT}s) are efficient algorithms that derive all $X( 0 \leq k < N)$ in $\mathcal{O}( N \log N)$ calculations.
-\Todo{citation?}
 %For integer $0 \leq k < N $, efficient algorithms exist that derive all $X( 0 \leq k < N )$ in $\mathcal{O}( N \log N )$ calculations instead of $\mathcal{O}(kcalled \acrlong{FFT}s, sampling a subset of the frequencies.\Todo{citation?}
 
 \begin{figure}
@@ -290,6 +288,7 @@ This allows to approximate an analog time delay between two waveforms when one w
 
 % >>>
 \section{Hilbert Transform}% <<<<
+\Todo{remove section?}
 The analytic signal $s_a(t)$ of a waveform $x(t)$ can be obtained using the Hilbert Transform through
 \begin{equation}
 	\label{eq:analytic_signal}