Changeset 5709 for trunk

Timestamp:

01/05/05 16:13:21 (20 years ago)

Author:

hbartko

Message:

Algorithms.tex

Location:

trunk/MagicSoft/TDAS-Extractor

Files:

• Algorithms.tex (modified) (9 diffs)
• MAGIC_signal_reco.bbl (modified) (1 diff)

trunk/MagicSoft/TDAS-Extractor/Algorithms.tex

@@ -120 +120 @@
 The following free adjustable parameters have to be set from outside: 
 \begin{description}
-\item[Window sizes:\xspace] Independenty for high-gain and low-gain (default: 6,6)
+\item[Window sizes:\xspace] Independently for high-gain and low-gain (default: 6,6)
 \end{description}
 
@@ -246 +246 @@
 \end{equation}
 
-where $\Delta T_{\mathrm{FADC}} = 3.33$ ns is the sampling intervall of the MAGIC FADCs.
+where $\Delta T_{\mathrm{FADC}} = 3.33$ ns is the sampling interval of the MAGIC FADCs.
 
 
@@ -253 +253 @@
 The electronics noise is largely white, uncorrelated in time. The noise from the night sky background photons is the superposition of the detector response to single photo electrons arriving randomly distributed in time. Figure \ref{fig:noise_autocorr_AB_36038_TDAS} shows the noise autocorrelation matrix for an open camera. The large noise autocorrelation in time of the current FADC system is due to the pulse shaping with a shaping constant of 6 ns. 
 
-In general the amplitude and timing weights, $\boldsymbol{w}_{\text{amp}}$ and $\boldsymbol{w}_{\text{time}}$, depend on the pulse shape, the derivative of the pulse shape and the noise autocorrelation. In the high gain samples the correlated night sky background noise dominates over the white electronics noise. Thus different noise levels just cause the noise autocorrelation matrix $\boldsymbol{B}$ to change by a factor, which cancells out in the weights calculation. Thus in the high gain the weights are to a very good approximation independent of the night sky background noise level.
+In general the amplitude and timing weights, $\boldsymbol{w}_{\text{amp}}$ and $\boldsymbol{w}_{\text{time}}$, depend on the pulse shape, the derivative of the pulse shape and the noise autocorrelation. In the high gain samples the correlated night sky background noise dominates over the white electronics noise. Thus different noise levels just cause the noise autocorrelation matrix $\boldsymbol{B}$ to change by a factor, which cancels out in the weights calculation. Thus in the high gain the weights are to a very good approximation independent of the night sky background noise level.
 
 Contrary to that in the low gain samples ... .
@@ -268 +268 @@
 
 
-Using the average reconstructed pulpo pulse shape, see figure \ref{fig:pulpo_shape_low}, and the reconstructed noise autocorrelation matrix from a pedestal run with random triggers, the digital filter weights are computed. Figures \ref{fig:w_time_MC_input_TDAS} and \ref{fig:w_amp_MC_input_TDAS} show the parameterization of the amplitude and timing weights for the MC pulse shape as a fuction of the ...
+Using the average reconstructed pulpo pulse shape, see figure \ref{fig:pulpo_shape_low}, and the reconstructed noise autocorrelation matrix from a pedestal run with random triggers, the digital filter weights are computed. Figures \ref{fig:w_time_MC_input_TDAS} and \ref{fig:w_amp_MC_input_TDAS} show the parameterization of the amplitude and timing weights for the MC pulse shape as a function of the ...
 
 
@@ -275 +275 @@
 \includegraphics[totalheight=7cm]{w_time_MC_input_TDAS.eps}
 \end{center}
-\caption[Time weights.]{Time weights $w_{\mathrm{time}}(t_0) \ldots w_{\mathrm{time}}(t_5)$ for a window size of 6 FADC slices. The first weight $w_{\mathrm{time}}(t_0)$ is plotted as a fuction of the relative time $t_{\text{rel}}$ the trigger and the FADC clock in the range $[-0.5;0.5[ \ T_{\text{ADC}}$, the second weight in the range $[0.5;1.5[ \ T_{\text{ADC}}$ and so on. A binning resolution of $0.1  T_{\text{ADC}}$ has been chosen.} \label{fig:w_time_MC_input_TDAS}
+\caption[Time weights.]{Time weights $w_{\mathrm{time}}(t_0) \ldots w_{\mathrm{time}}(t_5)$ for a window size of 6 FADC slices for the pulse shape used in the MC simulations. The first weight $w_{\mathrm{time}}(t_0)$ is plotted as a function of the relative time $t_{\text{rel}}$ the trigger and the FADC clock in the range $[-0.5;0.5[ \ T_{\text{ADC}}$, the second weight in the range $[0.5;1.5[ \ T_{\text{ADC}}$ and so on. A binning resolution of $0.1  T_{\text{ADC}}$ has been chosen.} \label{fig:w_time_MC_input_TDAS}
 \end{figure}
 
@@ -282 +282 @@
 \includegraphics[totalheight=7cm]{w_amp_MC_input_TDAS.eps}
 \end{center}
-\caption[Amplitude weights.]{Amplitude weights $w_{\mathrm{amp}}(t_0) \ldots w_{\mathrm{amp}}(t_5)$ for a window size of 6 FADC slices. The first weight $w_{\mathrm{amp}}(t_0)$ is plotted as a fuction of the relative time $t_{\text{rel}}$ the trigger and the FADC clock in the range $[-0.5;0.5[ \ T_{\text{ADC}}$, the second weight in the range $[0.5;1.5[ \ T_{\text{ADC}}$ and so on. A binning resolution of $0.1  T_{\text{ADC}}$ has been chosen.} \label{fig:w_amp_MC_input_TDAS}
+\caption[Amplitude weights.]{Amplitude weights $w_{\mathrm{amp}}(t_0) \ldots w_{\mathrm{amp}}(t_5)$ for a window size of 6 FADC slices for the pulse shape used in the MC simulations. The first weight $w_{\mathrm{amp}}(t_0)$ is plotted as a function of the relative time $t_{\text{rel}}$ the trigger and the FADC clock in the range $[-0.5;0.5[ \ T_{\text{ADC}}$, the second weight in the range $[0.5;1.5[ \ T_{\text{ADC}}$ and so on. A binning resolution of $0.1  T_{\text{ADC}}$ has been chosen.} \label{fig:w_amp_MC_input_TDAS}
 \end{figure}
 
@@ -293 +293 @@
 \end{equation}
 
-for all possible signal start slicess $i_0$. Let $i_0^*$ be the signal start slice with the largest $e_{i_0}$. Then in a seconst step the timing offset $\tau$ is calculated:
+for all possible signal start slices $i_0$. Let $i_0^*$ be the signal start slice with the largest $e_{i_0}$. Then in a second step the timing offset $\tau$ is calculated:
 
 \begin{equation}
@@ -299 +299 @@
 \end{equation}
 
-and the weigths iterated:
+and the weights iterated:
 
 \begin{equation}
@@ -339 +339 @@
 \includegraphics[totalheight=7cm]{time_sliding.eps}
 \end{center}
-\caption[Digital filter weights applied.]{Digital filter weights applied.} \label{fig:amp_sliding}
+\caption[Digital filter weights applied.]{Digital filter weights applied to the recorded FADC time slices of one calibration pulse. The left plot shows the result of the applied amplitude weights $e(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{amp}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ and the right plot shows the result of the applied timing weights $e\tau(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{time}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ .} \label{fig:amp_sliding}
 \end{figure}
 

trunk/MagicSoft/TDAS-Extractor/MAGIC_signal_reco.bbl

@@ -1 +1 @@
 \begin{thebibliography}{1}
+
+\bibitem{Magic-PMT}
+A.~Ostankov et~al.,
+\newblock {\em A study of the new hemispherical 6-dynodes PMT from electron
+  tubes},
+\newblock Nucl. Instrum. Meth. {\bf A442} (2000) 117.
+
+\bibitem{MAGIC-analog-link-2}
+E.~Lorenz et~al.,
+\newblock {\em A fast, large dynamic range analog signal transfer system based
+  on optical fibers},
+\newblock Nucl. Instrum. Meth. {\bf A461} (2001) 517.
+
+\bibitem{MAGIC-calibration}
+T.~Schweizer et~al.,
+\newblock {\em The optical calibration of the MAGIC telescope camera},
+\newblock IEEE Trans. Nucl. Sci. {\bf 49} (2002) 2497.
 
 \bibitem{NUMREC}