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\title{Comparison of Signal Reconstruction Algorithms for the MAGIC Telescope}
\author{H. Bartko, M. Gaug, F. Goebel, A. Moralejo,\\
Th. Schweizer, M. Shayduk, N. Sidro, W. Wittek}
\date{February 21$^{\mathrm{st}}$, 2005\\}
\TDAScode{MAGIC-TDAS 05-xx\\ 050221}
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\begin{abstract}
Presently, the MAGIC telescope uses a 300~MHz FADC system to sample the transmitted and shaped signals from 
the captured Cherenkov light of air showers.
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, 
extractors are recommended for the most conservative and the most advanced and demanding analyses.
It is shown that the digital filter 
can be used to extract and fit single photo-electron pulses from the night sky background.
The achievable time resolution has been derived as a function of the incident number of 
photo-electrons.
%\begin{equation}
%\Delta T_{\mathrm{cosmics}} \approx \sqrt{\frac{(2\,\mathrm{ns})^2}{<Q>/{\mathrm{phe}}} 
%+ \frac{(4.5\,\mathrm{ns})^2}{<Q>^2/{\mathrm{phe^2}}} + (0.2\,\mathrm{ns})^2} . \nonumber
%\label{eq:time:fitprediction}
%\end{equation}
For galactic backgrounds an image cleaning threshold as low as 5~photo-electrons can be achieved 
without using the timing information and for rejecting 99.7\% of noise.
\end{abstract}

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\include{Introduction}
\include{Reconstruction}
\include{Algorithms}
\include{Criteria}
\include{Pedestal}
\include{Calibration}
\include{Pulpo}
\include{MonteCarlo}
\include{Speed}
\include{Results}
\include{Conclusions}
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