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Thesis: spell-check

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Eric-Teunis de Boone 2023-11-17 15:07:19 +01:00
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documents/thesis/chapters/radio_measurement.tex
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@ -31,10 +31,10 @@ The $n$-th sample in this waveform is then associated with a time $t[n] = t[0] +
% Filtering before ADC
The sampling is limited by the \gls{ADC}'s Nyquist frequency at half its sampling rate.
In addition, various frequency-dependent backgrounds can be reduced by applying a bandpass filter before digitisation.
In addition, various frequency-dependent backgrounds can be reduced by applying a band-pass filter before digitisation.
For example, in \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.
In addition to a band-pass filter, more complex filter setups are used to remove unwanted components or introduce attenuation at specific frequencies.
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.
@ -49,7 +49,7 @@ Thus to reconstruct properties of the electric field signal from the waveform, b
Different methods are available for the analysis of the waveform, and the antenna and filter responses.
A key aspect is determining the frequency-dependent amplitudes (and phases) in the measurements to characterise the responses and, more importantly, select signals from background.
With \glspl{FT}, these frequency spectra can be produced.
This technique is especially important for the sinewave beacon of Section~\ref{sec:beacon:sine}, as it forms the basis of the phase measurement.
This technique is especially important for the sine wave beacon of Section~\ref{sec:beacon:sine}, as it forms the basis of the phase measurement.
\\
The detection and identification of more complex time-domain signals can be achieved using the cross correlation,
which is the basis for the pulsed beacon method of Section~\ref{sec:beacon:pulse}.
@ -156,7 +156,7 @@ Since a complex plane wave can be linearly decomposed as
,
\end{aligned}
\end{equation*}
the above transforms can be decomposed into explicit real and imaginary parts aswell,
the above transforms can be decomposed into explicit real and imaginary parts as well,
i.e.,~\eqref{eq:fourier:dtft} becomes
\begin{equation}
\phantom{.}
@ -207,7 +207,7 @@ By missing the correct frequency bin for the sine wave, it estimates both a too
% % Static sin/cos terms if f_s, f and N static ..
When calculating the \gls{DTFT} for multiple inputs which share both an equal number of samples $N$ and equal sampling frequencies $f_s$, the $\sin$ and $\cos$ terms in \eqref{eq:fourier:dtft_decomposed} are the same for a single frequency $f$ upto an overall phase which is dependent on $t[0]$.
When calculating the \gls{DTFT} for multiple inputs which share both an equal number of samples $N$ and equal sampling frequencies $f_s$, the $\sin$ and $\cos$ terms in \eqref{eq:fourier:dtft_decomposed} are the same for a single frequency $f$ up to an overall phase which is dependent on $t[0]$.
Therefore, at the cost of an increased memory allocation, these terms can be precomputed, reducing the number of real multiplications to $2N+1$.
% .. relevance to hardware if static frequency