Changeset 5568 for trunk


Ignore:
Timestamp:
12/08/04 12:31:26 (20 years ago)
Author:
gaug
Message:
*** empty log message ***
Location:
trunk/MagicSoft/TDAS-Extractor
Files:
4 edited

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  • trunk/MagicSoft/TDAS-Extractor/Algorithms.tex

    r5534 r5568  
    1 \section{Signal Reconstruction Algorithms}
     1\section{Signal Reconstruction Algorithms \label{sec:algorithms}}
    22
    33\ldots {\it In this section, the extractors are described, especially w.r.t. which free parameters are left to play,
    … …  
    176176The correlation of the noise contributions at times $t_i$ and $t_j$ is expressed in the noise autocorrelation matrix $\boldsymbol{B}$:
    177177
    178 \begin{equation}
     178\begin{equation} 
    179179\boldsymbol{B_{ij}} = \langle b_i b_j \rangle - \langle b_i \rangle \langle b_j
    180180\rangle  \ .
     181\label{eq:autocorr}
    181182\end{equation}
    182183%\equiv \langle b_i b_j \rangle with $\langle b_i \rangle = 0$.
    … …  
    393394%%% TeX-master: "MAGIC_signal_reco"
    394395%%% TeX-master: "MAGIC_signal_reco"
     396%%% TeX-master: "MAGIC_signal_reco"
    395397%%% End:

  • trunk/MagicSoft/TDAS-Extractor/Changelog

    r5566 r5568  
    1919
    2020                                                 -*-*- END OF LINE -*-*-
    21 2004/11/10: Hendrik Bartko
     212004/12/07: Markus Gaug
     22  * bibfile.bib: Modified slightly citation of NUMREC
     23  * Pedestal.tex: Modified writing a bit, added references to dig.filter
     24                  formulas.
     25  * Algorithms.tex: Added some reference labels
     26
     272004/12/06: Hendrik Bartko
    2228  * Reconstruction.tex: Added some paragraphs how we reconstruct the
    2329    average pulse shape from the recorded signal samples. Added some

  • trunk/MagicSoft/TDAS-Extractor/Pedestal.tex

    r5556 r5568  
    1919\vspace{1cm}
    2020
    21 The Pedestal RMS can be completely described by the matrix
    22 
    23 \begin{equation}
    24    < (P_i - <P_i>) * (P_j - <P_j>) >
    25 \end{equation}
    26 
    27 where $i$ and $j$ denote the $i^{th}$ and $j^{th}$ FADC slice and
    28 $P_i$ is the pedestal
    29 value in slice $i$ for an event and the average $<>$ is over many events (usually 1000).
    30 \par
    31 
    32 By definition, the pedestal RMS is independent from the signal extractor.
    33 Therefore, no signal extractor is needed to calculate the pedestals.
     21The background $BG$ (Pedestal)
     22can be completely described by the noise-autocorrelation matrix $\boldsymbol{B}$
     23(eq.~\ref{eq:autocorr}),
     24where the diagonal elements give what is usually denoted as the ``Pedestal RMS''. Note that
     25in the MAGIC readout, the diagonal elements do not scale exactly with the square root of
     26the number of slices as would be expected from pure stochasitic noise.
     27
     28\par
     29
     30By definition, the noise autocorrelation matrix $B$ and thus the ``pedestal RMS''
     31is independent from the signal extractor.
    3432
    3533\subsection{Bias and Error}
    … …  
    108106for large signals (e.g. calibration signals).
    109107\par
    110 In the case of the optimum filter, $R$ can be obtained from the
     108In the case of the optimum filter, $R$ is in theory independent from the
     109signal amplitude $ST$ and depends only on the background $BG$, see eq.~\ref{of_noise}.
     110It can be obtained from the
    111111fitted error of the extracted signal ($\Delta(SE)_{fitted}$),
    112 which one can calculate for every event.
    113 
    114 \vspace{1cm}
    115 \ldots {\it Whether this statemebt is true should be checked by MC.}
    116 \vspace{1cm}
    117 
    118 For large signals, one would expect the bias of the extracted signal
    119 to be small and negligible (i.e. $<ST> \approx <SE>$).
     112which one can calculate for every event or by applying the extractor to a fixed window
     113of pure background events (``pedestal events'').
     114
    120115\par
    121116
    122117In order to get the missing information, we did the following investigations:
    123118\begin{enumerate}
     119\item Determine $R$ by applying the signal extractor to a fixed window
     120    of pedestal events. The background fluctuations can be simulated with different
     121    levels of night sky background and the continuous light, but no signal size
     122    dependency can be retrieved with the method.
    124123\item Determine bias $B$ and resolution $R$ from MC events with and without added noise.
    125124    Assuming that $R$ and $B$ are negligible for the events without noise, one can
    126125    get a dependency of both values from the size of the signal.
    127126\item Determine $R$ from the fitted error of $SE$, which is possible for the
    128     fit and the digital filter. In prinicple, all dependencies can be retrieved with this
    129     method.
    130 \item Determine $R$ for low signals by applying the signal extractor to a fixed window
    131     of pedestal events. The background fluctuations can be simulated with different
    132     levels of night sky background and the continuous light, but no signal size
    133     dependency can be retrieved with the method. Its results are only valid for small
    134     signals.
     127    fit and the digital filter (eq.~\ref{of_noise}).
     128    In prinicple, all dependencies can be retrieved with this method.
    135129\end{enumerate}
    136 
    137 \par
    138130
    139131\subsubsection{Determine error $R$ by applying the signal extractor to a fixed window
    140132of pedestal events}
    141133
    142 By applying the signal extractor to pedestal events we want to
    143 determine these parameters. There are the following possibilities:
    144 
    145 \begin{enumerate}
    146 \item Applying the signal extractor allowing for a possible sliding window
    147     to get information about the bias $B$ (valid for low signals).
    148 \item Applying the signal extractor to a fixed window, to get something like
    149     $R$. In the case of the digital filter and the spline, this has to be done
    150     by randomizing the time slice indices.
    151 \end{enumerate}
    152 
    153 \vspace{1cm}
    154 \ldots {\it This assumptions still have to proven, best mathematically!!! Wolfgang, Thomas???}
    155 \vspace{1cm}
     134By applying the signal extractor to a fixed window of pedestal events, we
     135determined the parameter $R$ for the case of no signal ($ST = 0$). In the case of
     136all extractors using a fixed window from the beginning (extractors nr. \#1 to \#22
     137in section~\ref{sec:algorithms}), the results were exactly the same as calculating
     138the mean and the RMS of a same (fixed) number of FADC slices (the conventional ``Pedestal
     139Calculation'').
     140
     141\par
     142In the case of the amplitude extracting spline (extractor nr. \#27), we took the
     143spline value at a random place within the digitizing binning resolution (0.02 FADC slices) of
     144one central FADC slice.
     145In the case of the digital filter (extractor nr. \#28), the time shift was 
     146randomized for each event within one central FADC slice.
     147
    156148\par
    157149
    … …  
    331323%%% TeX-master: "MAGIC_signal_reco."
    332324%%% TeX-master: "MAGIC_signal_reco"
     325%%% TeX-master: "Pedestal"
    333326%%% End:

  • trunk/MagicSoft/TDAS-Extractor/bibfile.bib

    r5266 r5568  
    1616}
    1717
    18 @Book{NumRec,
    19   author =   "W.H.Press and  S.A.Teukolsky and  W.T.Vetterling and  B.P.Flannery",
    20   title =    "Numerical Recipes in C++, 2nd edition",
     18@Book{NUMREC,
     19  author =   "W.H.Press and S.A.Teukolsky and W.T.Vetterling and B.P.Flannery",
     20  title =    "Numerical Recipes in C++",
     21  edition =  "Second",
    2122  publisher = "Cambridge University Press",
    2223  year =     "2002"
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