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\title{Comparison of Signal Reconstruction Algorithms for the MAGIC Telescope}
\author{H. Bartko, O. Blanch, M. Gaug, F. Goebel, A. Moralejo, A. Robert, \\
T. Schweizer, M. Shayduk,  N. Sidro, W. Wittek}
\date{Month dd, 2004\\}
\TDAScode{MAGIC-TDAS 04-xx\\ 04mmdd}
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\begin{abstract}
Presently MAGIC uses a 300~MHz FADC system to sample the Cherenkov signals. 
In this note different algorithms to reconstruct the signal from the read out samples 
are described and compared. Criteria for comparison are defined and used to judge the 
different extractors applied to calibration signals, cosmics and pedestals. At the end, 
a best extractor is proposed. The question 
of pedestal calculation for the different extractors is adressed.
\end{abstract}

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\section{Introduction}

\begin{itemize}
\item{Short description of the MAGIC read-out system}
\end{itemize}

\section{Pulse Shape Reconstruction}

\begin{itemize}
\item{Algorithm: overlay many events}
\item{Differences cosmics / calibration}
\item{Implementation / parameterization in the MC. 
\newline
\newline
\ldots {\it MAYBE, we should create MC calibration pulses for the subsequent studies }
\newline
\newline}
\end{itemize}

\section{Signal Reconstruction Algorithms}

\ldots {\it In this section, the extractors are described, especially w.r.t. which free parameters are left to play, 
how they subtract the pedestal, how they compare between calibration and cosmics pulses and how an 
extraction in case of a pure pedestal event takes place. }
\newline
\newline
{\it Missing coding: 
\begin{itemize}
\item Implementing the AB-flag for all extractors \ldots Markus
\item Implementing a low-gain extraction based on the high-gain information \ldots Arnau
\item Joining the Sliding Window and Highest Integral extractor into one \ldots Markus
\item Real fit to the expected pulse shape \ldots Hendrik, Wolfgang ???
\end{itemize}
}


\subsection{Pure signal extractors}
\subsubsection{Fixed Window}
\subsubsection{Fixed Window Peak Search}
\subsubsection{Fixed Window with integrated spline}

\subsection{Pure time extractors}
\subsubsection{Highest Integral}

\subsection{Combined extractors}
\subsubsection{Sliding Window with Highest Integral}
\subsubsection{Digital Filter}
\subsubsection{(Fast) Spline with Amplitude extraction}
\subsubsection{Real fit to the expected pulse shape \newline
\newline
}

%References: \cite{OF77} \cite{OF94}.

\section{Criteria for an optimal pedestal extraction}

\ldots {\it In this section, the distinction is made between: 
\begin{itemize}
\item Defining the pedestal RMS as contribution
to the extracted signal fluctuations (later used in the calibration) 
\item Defining the Pedestal Mean and RMS as the result of distributions obtained by 
applying the extractor to pedestal runs (yielding biases and modified widths).
\item Deriving the correct probability for background fluctuations based on the extracted signal height. 
  ( including biases and modified widths).
\end{itemize}
\ldots Florian + ??? 
\newline
\newline
}
\section{Criteria for the Optimal Signal Extraction}

\subsection{Resolution (amplitude and time)}
\ldots {\it In this section, the jitter to exactly identical input pulses is measured, for times, amplitudes, 
high-gain and low-gain pulses
\begin{itemize}
\item Jitter to pulpo pulses  \ldots Hendrik
\item Jitter to pedestals (of different intensity) \ldots Hendrik
\item Comparing MC signal with and w/o noise of different intensity \ldots Nuria
\item Comparing the low-gain to high-gain ratio for different intensities \ldots Markus
\item Derive the time jitter to calibration pulses \ldots Maxim ???
\end{itemize}
}

\subsection{Bias}
\ldots {\it In this section, the bias of the extractor for low and high intensities is defined and measured
\begin{itemize}
\item Bias to pedestals (of different intensity) \ldots Hendrik
\item Comparing MC signal with and w/o noise of different intensity \ldots Nuria
\end{itemize}
}

\subsection{Signal to Noise}
\ldots {\it In this section, the signal to noise of an extractor is determined, for times and amplitudes
\newline \ldots Maxim ???, Thomas ???
}

\subsection{Stability}
\ldots {\it In this section, the stability of an extractor to slightly varying pulse shapes is examined.
\begin{itemize}
\item Stability w.r.t. different weights files \ldots Hendrik
\item Outliers in time and amplitude extractions \ldots ???
\item Stability of conversion factors from the calibration \ldots Markus
\item Stability w.r.t. the calibration secondary pulses \ldots Hendrik ???
\end{itemize}
}

\subsection{Linearity}
\ldots {\it In this section, the Nuria plots are examined \newline \ldots Nuria

\subsection{Treatment of calibration pulses}
\ldots {\it In this section, the question of the different pulse shapes between calibration pulses, its 
secondary pulses, possible secondary pulses from hadronic showers and the typical Cherenkov 
pulses are extracted by the different extractors and typical dependencies examined, like the 
Razmik plot, the number of photo-electrons with number of slices, comparisons between different colours, etc.
\newline \ldots Hendrik??? , Markus???  + ????}

\subsection{Low gain extraction}
\ldots {\it In this section, the stability of the low-gain extraction w.r.t. the high-gain extraction is 
examined. Useful plots are still to be defined.
\newline \ldots Arnau ????}

\subsection{Applicability for different sampling speeds / no pulse shaping.}
\ldots {\it In this section, some comments of Hendrik will be made}

\subsection{CPU requirements}
\ldots {\it In this section, the needed CPU time is measured for each extractor independently
\newline \ldots ALL (after all)}

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\section{Performance}
\ldots {\it This section will be written after the previous one}

\subsection{Calibration}
\subsection{Pulpo Pulses}
\subsection{MC Data}
\subsection{Cosmics Data?}
\subsection{Pedestals}

\section{Discussion}
\ldots {\it This section will discuss the best signal extractor \newline \ldots Thomas ???, Florian }

\section{Conclusions}
\ldots {\it This section will propose the best signal extractor.}

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