Pulse (Energy) & Position Reconstruction in the CMS ECAL - INFN
Pulse (Energy) & Position Reconstruction in the CMS ECAL - INFN
Pulse (Energy) & Position Reconstruction in the CMS ECAL - INFN
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<strong>Pulse</strong> <strong>Reconstruction</strong> Method<br />
Calor 2004 (March 2004) Ivo van Vulpen 8<br />
Average pulse shape<br />
F(t)<br />
How to extract <strong>the</strong> optimal weights:<br />
χ<br />
2<br />
= ( S − A×<br />
F)<br />
T<br />
Cov<br />
−1<br />
( S − A×<br />
F )<br />
Sample heights<br />
Amplitude<br />
Covariance Matrix<br />
Expected sample heights: F(t)<br />
<strong>in</strong>imize χ 2 w.r.t A<br />
assum<strong>in</strong>g<br />
No pedestal<br />
No correlations<br />
w<br />
i<br />
=<br />
∑<br />
i<br />
f<br />
(<br />
i<br />
f<br />
2<br />
i<br />
)<br />
= Tim<strong>in</strong>g: Def<strong>in</strong>e a set of weights for each 1 ns b<strong>in</strong> of <strong>the</strong> TDC offset<br />
= Knowledge of expected shape required: shape itself, tim<strong>in</strong>g <strong>in</strong>fo and ga<strong>in</strong> rati
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