Changeset 6401 for trunk/MagicSoft

Timestamp:

02/12/05 15:27:22 (20 years ago)

Author:

gaug

Message:

*** empty log message ***

File:

• trunk/MagicSoft/TDAS-Extractor/Pedestal.tex (modified) (3 diffs)

trunk/MagicSoft/TDAS-Extractor/Pedestal.tex

@@ -296 +296 @@
 \par
 Table~\ref{tab:bias} shows bias, resolution and mean-square error for all extractors using
-a sliding window. Every extractor had the freedom to move 5 slices, i.e. the global window size
-was fixed to five slices plus the extractor window. One can see that 
+a sliding window. In this sample, every extractor had the freedom to move 5 slices, 
+i.e. the global window size was fixed to five plus the extractor window size. This first line 
+shows the resolution of the smallest, robust fixed window algorithm in order to give a reference.
+One can see that the bias $B$ typically decreases 
+with increasing window size (except for the digital filter), while the error $R$ increases with 
+increasing window size. There is also a small difference between the obtained error on a fixed window 
+extraction and the one obtained from a sliding window extraction in the case of the spline and digital 
+filter algorithms.
+The mean-squared error has an optimum somewhere between: In the case of the 
+sliding window and the spline at the lowest window size, in the case of the digital filter
+at 4 slices. The global winners are extractors \#25 (spline with integration of 1 slice) and \#29 
+(digital filter with integration of 4 slices). All sliding window extractors -- except \#21 -- 
+have a smaller mean-square error than the resolution of the fixed window reference extractor.
 
 \begin{table}[htp]
@@ -313 +324 @@
 Nr. & Name         &  $R$  & $R$ & $B$ & $\sqrt{MSE}$ &  $R$ &$R$  & $B$ & $\sqrt{MSE}$& $R$ &  $R$& $B$ & $\sqrt{MSE}$ \\
     &              &  (FW) & (SW)& (SW)& (SW) & (FW) &(SW) & (SW)& (SW) & (FW)&(SW) & (SW)&(SW) \\
+\hline                                                     
+\hline                                                     
+4   & Fixed Win. 8  & 1.2  & --  & 0.0 & 1.2  & 2.5  & --  & 0.0 &  2.5 & 3.0 &  -- & 0.0 & 3.0 \\   
 \hline                                                     
 17  & Slid. Win. 2  & 0.5  & 0.5 & 0.4 & 0.6  & 1.4  & 1.4 & 1.2 &  1.8 & 1.6 & 1.6 & 1.5 & 2.2 \\
@@ -331 +345 @@
 \end{tabular}
 }
-\caption{The statistical parameters bias, resolution and mean error. All units in equiv. 
+\caption{The statistical parameters bias, resolution and mean error for the sliding window 
+algorithm. The first line displays the resolution of the smallest, robust fixed window extractor 
+for reference. All units in equiv. 
 photo-electrons, uncertainty: 0.1 phes. All extractors were allowed to move 5 FADC slices plus 
 their window size. The ``winners'' for each row are marked in red. Global winners (within the given