Image Processing Reference
In-Depth Information
2. Triggers
Two different triggers are currently implemented at the 1st level. The first is a single-bin
trigger generated as 3-fold coincidence of the 3 PMTs at a threshold equivalent to 1.75 vertical
emitted muons. The estimated current for a Vertical Equivalent Muon ( I VEM ) is the reference
unit for the calibration of FADC traces signals and corresponds to ca. 50 ADC-counts.
This trigger has a rate of about 100 Hz. It is used mainly to detect fast signals, which
correspond also to the muonic component generated by horizontal showers. The single bin
trigger is generated when the input signal is above the fixed thresholds calculated in the
micro-controller during the calibration process. It is the simplest trigger useful for high-level
signals. The second trigger is the Time over Threshold (ToT) trigger that requires at least 13
time bins above a threshold of 0.2 I VEM . A pre-trigger ("fired" time bin) is generated if in
a sliding time window of 120
25 ns length a coincidence of any two channels appears.
This trigger has a relatively low rate of about 1.6 Hz, which is the expected rate for two
muons crossing the Auger surface detector. It is designed mainly for selecting small but
spread-in-time signals, typical for high energy distant EAS or for low energy showers, while
ignoring the single muon background (Abraham J. et al., 2010).
Cherenkov light generated by very inclined showers crossing the Auger surface detector can
reach the PMT directly without reflections on Tyvec liners. Especially for "old" showers the
muonic front is very flat. This together corresponds to very short direct light pulse falling on
the PMT and in consequence very short rise time of the PMT response. For vertical or weakly
inclined showers, where the geometry does not allow reaching the Cherenkov light directly
on the PMT, the light pulse is collected from many reflections on the tank walls. Additionally,
the shower developed for not so high slant depth are relatively thick. These give a signal from
a PMT as spread in time and relatively slow increasing.
Hadron induced showers with dominant muon component give an early peak with a typical
rise time mostly from 1 to 2 time bins (by 40 MHz sampling) and decay time of the order
of 80 ns (Aglietta et al., 2005). The estimation of the rise time for the front on the base of
one or two time bins is rather rough. The rise time calculated as for two time bins may be
overestimated due to a low sampling rate and an error in a quantization in time. Higher
time resolution would be favorable. The expected shape of FADC traces suggests to use a
spectral trigger, instead of a pure threshold analysis in order to recognize the shape of the
FADC traces characteristic for the traces of very inclined showers. The monitoring of the shape
would include both the analysis of the rising edge and the exponentially attenuated tail. A
very short rise time together with a relatively fast attenuated tail could be a signature of very
inclined showers. We observe numerous very inclined showers crossing the full array but
which "fire" only few surface detectors (Fig. 1). For that showers much more detectors should
have been hit. Muonic front probably produces PMT signals not high enough to generate
3-fold coincidences, some of signals are below of thresholds (see Fig. 2). This may be a reason
of "gaps" in the array of activated surface detectors.
×
3. Discrete Fourier Transform vs. Discrete Cosine Transform
There are several variants of the DCT with slightly modified definitions. The DCT-I is exactly
equivalent (up to an overall scale factor of 2), to a DFT of 2N-2realnumbers with even
symmetry. The most commonly used form of the Discrete Cosine Transform is DCT-II.
n = 0 x n cos N ( n +
k
N
1
1
2 )
X k = α k
(1)
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