Changeset 6438

Timestamp:

02/13/05 21:15:20 (20 years ago)

Author:

gaug

Message:

*** empty log message ***

File:

• trunk/MagicSoft/TDAS-Extractor/Pedestal.tex (modified) (5 diffs)

trunk/MagicSoft/TDAS-Extractor/Pedestal.tex

@@ -114 +114 @@
 \item Determine $MSE$ from the fitted error of $\widehat{S}$, which is possible for the 
     fit and the digital filter (eq.~\ref{eq:of_noise}). 
-    In prinicple, all dependencies can be retrieved with this method.
+    In principle, all dependencies can be retrieved with this method.
 \end{enumerate}
 
@@ -363 +363 @@
 Figures~\ref{fig:sw:distped} through~\ref{fig:df:distped} show the 
 extracted pedestal distributions for some selected extractors (\#18, \#23, \#25 and \#28)
- for one examplary channel (pixel 100) and two background situations: Closed camera with only electronic
+ for one exemplary channel (pixel 100) and two background situations: Closed camera with only electronic
 noise and open camera pointing to an extra-galactic source.
 One can see the (asymmetric) Poisson behaviour of the 
@@ -413 +413 @@
 (pixel 100). The result obtained from a simple addition of 2 FADC 
 slice contents (``fundamental'') is displayed as red histogram, the one obtained from the application 
-of time-randomized weigths on a fixed window of 2 FADC slices as blue histogram and the one obtained from the
+of time-randomized weights on a fixed window of 2 FADC slices as blue histogram and the one obtained from the
 full algorithm allowed to slide within a global window of 12 slices. The obtained histogram means and 
 RMSs have been converted to equiv. photo-electrons.}
@@ -428 +428 @@
 (pixel 100). The result obtained from a simple addition of 6 FADC 
 slice contents (``fundamental'') is displayed as red histogram, the one obtained from the application 
-of time-randomized weigths on a fixed window of 6 slices as blue histogram and the one obtained from the
+of time-randomized weights on a fixed window of 6 slices as blue histogram and the one obtained from the
 full algorithm allowed to slide within a global window of 12 slices. The obtained histogram means and 
 RMSs have been converted to equiv. photo-electrons.}
@@ -514 +514 @@
 \end{equation}
 
-We tested this relation assuming that the fitted area underneath the pedestal peak $Area_0$ is 
+We tested this relation assuming that the fitted area underneath the pedestal peak Area$_0$ is 
 proportional to $P(0)$ and the sum of the fitted areas underneath the single photo-electron peak 
-$Area_1$ and the double photo-electron peak $Area_2$ proportional to $P(>0)$. Thus, one expects:
-
-\begin{equation}
-Area_0 / (Area_1 + Area+2 ) = \frac{e^{-R\cdot WS}}{1-e^{-R\cdot WS}}
+Area$_1$ and the double photo-electron peak Area$_2$ proportional to $P(>0)$. Thus, one expects:
+
+\begin{equation}
+\mathrm{Area}_0 / (\mathrm{Area}_1 + \mathrm{Area}_2 ) = \frac{e^{-R\cdot WS}}{1-e^{-R\cdot WS}}
 \end{equation}