Changeset 6554
- Timestamp:
- 02/16/05 20:00:33 (20 years ago)
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trunk/MagicSoft/TDAS-Extractor/Algorithms.tex
r6541 r6554 1 1 \section{Signal Reconstruction Algorithms \label{sec:algorithms}} 2 3 {\it Missing coding:4 \begin{itemize}5 \item Real fit to the expected pulse shape \ldots Hendrik, Wolfgang ???6 \end{itemize}7 }8 2 9 3 \subsection{Implementation of Signal Extractors in MARS} … … 271 265 272 266 \begin{equation} 273 t = \frac{\sum_{i=i_0}^{i_0+ws} s_i \cdot i}{\sum_{i=i_0}^{i_0 t+ws} i}267 t = \frac{\sum_{i=i_0}^{i_0+ws} s_i \cdot i}{\sum_{i=i_0}^{i_0+ws} i} 274 268 \end{equation} 275 269 where $i$ denotes the FADC slice index, starting from $i_0$ … … 502 496 where $\Delta T_{\mathrm{FADC}} = 3.33$ ns is the sampling interval of the MAGIC FADCs. 503 497 The error in the reconstructed signal corresponds to about one photo electron. 504 For signals of the size of two photo electrons, the timing error is a bit higher than 1\,ns.498 For signals of the size of two photo electrons, the timing error is about 1.4\,ns. 505 499 \par 506 500 … … 520 514 depend on the pulse shape, the derivative of the pulse shape and the noise autocorrelation. 521 515 In the high gain samples, the correlated night sky background noise dominates over 522 the white electronics noise. Thus, different noise levels just cause the elements of the noise autocorrelation 523 matrix to change by a same factor, 524 which cancels out in the weights calculation. 525 Thus, the weights are to a very good approximation independent from the night 526 sky background noise level in the high gain. 527 528 Contrary to that in the low gain samples the correlated noise from the LONS is in the same order of magnitude as the white electronics and digitization noise. Moreover the noise autocorrelation for the low gain samples can not directly be determined from the data. The low gain is only switched on if the pulse exceeds a presets threshold. There are no pedestals in the low gain available. Thus the noise auto-correlation determined from MC simulations for an extragalactic background is also used to compute the weights for cosmics and calibration pulses. 529 530 531 532 516 the white electronics noise. Thus, different noise levels cause the elements of the noise autocorrelation 517 matrix to change by a same factor, which cancels out in the weights calculation. Figure~\ref{fig:noise_autocorr_allpixels} 518 shows the noise autocorrelation matrix for two different levels of night sky background (top) and the ratio between the 519 corresponding elements of both (bottom). The central regions of $\pm$3 FADC slices around the diagonal (which is used to 520 calculate the weights) deviate by less than 10\%. 521 Thus, the weights are to a very good approximation independent of the night sky background noise level in the high gain. 522 \par 523 Contrary to that in the low gain samples the correlated noise from the LONS is in the same order of magnitude as the white electronics and digitization noise. Moreover the noise autocorrelation for the low gain samples cannot be determined directly from the data. The low gain is only switched on if the pulse exceeds a preset threshold. There are no pedestals in the low gain available. Thus the noise auto-correlation determined from MC simulations for an extragalactic background is also used to compute the weights for cosmics and calibration pulses. 533 524 534 525 %\begin{figure}[h!] … … 558 549 \end{figure} 559 550 560 Using the average reconstructed pulpo pulse shapes, as shown in figure \ref{fig:pul po_shape_low}, and the reconstructed noise autocorrelation matrices from a pedestal runs with random triggers, the digital filter weights are computed. As the pulse shapes in the high and low gain and for cosmics, calibration and pulpo events are somewhat different, dedicated digital filter weights are computed for these event classes. Also filter weights optimized for MC simulations are calculated. High/low gain filter weights are computed for the following event classes:551 Using the average reconstructed pulpo pulse shapes, as shown in figure \ref{fig:pulse_shapes}, and the reconstructed noise autocorrelation matrices from a pedestal runs with random triggers, the digital filter weights are computed. As the pulse shapes in the high and low gain and for cosmics, calibration and pulpo events are somewhat different, dedicated digital filter weights are computed for these event classes. Also filter weights optimized for MC simulations are calculated. High/low gain filter weights are computed for the following event classes: 561 552 562 553 \begin{enumerate}
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