Thesis: near final version for radio_measurement and beacon_disciplining

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}