Index: trunk/MagicSoft/TDAS-Extractor/Algorithms.tex
===================================================================
--- trunk/MagicSoft/TDAS-Extractor/Algorithms.tex	(revision 6552)
+++ trunk/MagicSoft/TDAS-Extractor/Algorithms.tex	(revision 6554)
@@ -1,9 +1,3 @@
 \section{Signal Reconstruction Algorithms \label{sec:algorithms}}
-
-{\it Missing coding: 
-\begin{itemize}
-\item Real fit to the expected pulse shape \ldots Hendrik, Wolfgang ???
-\end{itemize}
-}
 
 \subsection{Implementation of Signal Extractors in MARS}
@@ -271,5 +265,5 @@
 
 \begin{equation}
-  t = \frac{\sum_{i=i_0}^{i_0+ws} s_i \cdot i}{\sum_{i=i_0}^{i_0t+ws} i} 
+  t = \frac{\sum_{i=i_0}^{i_0+ws} s_i \cdot i}{\sum_{i=i_0}^{i_0+ws} i} 
 \end{equation}
 where $i$ denotes the FADC slice index, starting from $i_0$
@@ -502,5 +496,5 @@
 where $\Delta T_{\mathrm{FADC}} = 3.33$ ns is the sampling interval of the MAGIC FADCs. 
 The error in the reconstructed signal corresponds to about one photo electron. 
-For signals of the size of two photo electrons, the timing error is a bit higher than 1\,ns.
+For signals of the size of two photo electrons, the timing error is about 1.4\,ns.
 \par
 
@@ -520,15 +514,12 @@
 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 elements of the noise autocorrelation 
-matrix to change by a same factor, 
-which cancels out in the weights calculation. 
-Thus, the weights are to a very good approximation independent from the night 
-sky background noise level in the high gain.
-
-Contrary to that in the low gain samples the correlated noise from the LONS is in the same order of magnitude as the white electronics and digitization noise. Moreover the noise autocorrelation for the low gain samples can not directly be determined from the data. The low gain is only switched on if the pulse exceeds a presets threshold. There are no pedestals in the low gain available. Thus the noise auto-correlation determined from MC simulations for an extragalactic background is also used to compute the weights for cosmics and calibration pulses.
-
-
-
-
+the white electronics noise. Thus, different noise levels cause the elements of the noise autocorrelation 
+matrix to change by a same factor, which cancels out in the weights calculation. Figure~\ref{fig:noise_autocorr_allpixels} 
+shows the noise autocorrelation matrix for two different levels of night sky background (top) and the ratio between the 
+corresponding elements of both (bottom). The central regions of $\pm$3 FADC slices around the diagonal (which is used to 
+calculate the weights) deviate by less than 10\%. 
+Thus, the weights are to a very good approximation independent of the night sky background noise level in the high gain.
+\par
+Contrary to that in the low gain samples the correlated noise from the LONS is in the same order of magnitude as the white electronics and digitization noise. Moreover the noise autocorrelation for the low gain samples cannot be determined directly from the data. The low gain is only switched on if the pulse exceeds a preset threshold. There are no pedestals in the low gain available. Thus the noise auto-correlation determined from MC simulations for an extragalactic background is also used to compute the weights for cosmics and calibration pulses.
 
 %\begin{figure}[h!]
@@ -558,5 +549,5 @@
 \end{figure}
 
-Using the average reconstructed pulpo pulse shapes, as shown in figure \ref{fig:pulpo_shape_low}, and the reconstructed noise autocorrelation matrices from a pedestal runs with random triggers, the digital filter weights are computed. As the pulse shapes in the high and low gain and for cosmics, calibration and pulpo events are somewhat different, dedicated digital filter weights are computed for these event classes. Also filter weights optimized for MC simulations are calculated. High/low gain filter weights are computed for the following event classes:
+Using the average reconstructed pulpo pulse shapes, as shown in figure \ref{fig:pulse_shapes}, and the reconstructed noise autocorrelation matrices from a pedestal runs with random triggers, the digital filter weights are computed. As the pulse shapes in the high and low gain and for cosmics, calibration and pulpo events are somewhat different, dedicated digital filter weights are computed for these event classes. Also filter weights optimized for MC simulations are calculated. High/low gain filter weights are computed for the following event classes:
 
 \begin{enumerate}