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Ardo Illaste edited res_fitting.md
about 10 years ago
Commit id: f5da563f1595cd2dee633d411b9e1fcf2753adbb
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index 3e5bdf2..77d9e1f 100644
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\[
F_i(t) = b(\mathbf{q}_i, t) + \sum_{k=0}^{m} f(\mathbf{p}_{i,k},t) + W + R
\]
, where \(b\) is a n-th order polynomial with \(\mathbf{q}_i\) being the polynomial coefficients for the *i*-th pixel, summation is performed over all *m* events in the pixel, \(W\) consists of the noise and \(R\) is remaining residual not captured in the baseline nor events. Ideally, \(R=0\), but
in achieving this
we are is limited by the accuracy of the event region detection (we cannot fit what we do not detect) and whether or not our fitting function is general enough to be able to approximate various types of events.
Because it is not know which part of the signal is the event and which is the baseline the first fit also has to estimate the baseline properties.
Signal in the candidate region is fitted with an extended fit function (Figure \ref{fig:fig2}) that also depends on relaxation baseline \(B\) and baseline offset \(C\). The \(C\) parameter allows for the possibility of an elevated background before the release event.