Image Processing Reference
In-Depth Information
FADC traces from "Christian"
FADC traces from "Ramon"
240
240
PMT1
PMT2
PMT3
PMT1
PMT2
PMT3
PMT3
1.93 VEM
1.75 VEM
PMT3
1.75 VEM
1.64 VEM
160
160
80
80
0
0
time bin
time bin
240
244
248
252
256
260
240
244
248
252
256
260
FADC traces from "Juancho"
240
PMT1
PMT2
PMT3
PMT3
1.75 VEM
1.68 VEM
160
80
0
240
244
248
252
256
260
time bin
= 83.3
◦
)
registered in three detectors: Ramon, Christian and Juancho, respectively, and shown for the
range of (240 - 265) time bins. Only the signal in the Ramon detector (1.93
I
VEM
) is above the
standard threshold of 1.75
I
VEM
. Signals in Cristian (1.64
I
VEM
) and Juancho (1.68
I
VEM
)
detectors are below the standard thresholds and they are detected by chance (compare a
registration efficiency for a similar event shown in Fig. 1). For all very inclined showers the
rising edge corresponds to one or two time bins.
Fig. 2. FADC traces (in ADC-counts) of a horizontal shower (no. 01145055:
θ
1
√
N
and
2
√
N
for
k
where
1.
The DCT-III form is sometimes simply referred to as "the inverse DCT" (IDCT). A variant
of the DCT-IV, where data from different transforms are overlapped, is called the Modified
Discrete Cosine Transform (MDCT). The DCT is a Fourier-related transform similar to the
DFT, but using only real numbers. DCT are equivalent to DFT of roughly twice the length,
operating on real data with even symmetry (since the Fourier transform of a real and even
function is real and even), where in some variants the input and/or output data are shifted by
half a sample. The DCT-II and DCT-IV are considered as the alternative approach to the FFT.
In fact, the FFT routine can be supplied in an interleaving mode, even samples treated as real
data, odd samples as imaginary data. A trigger based on Discrete Fourier Transform (DFT)
(Radix-2 FFT) (Szadkowski, 2006) has already been implemented in the 3rd generation of the
Front FEB based on Cyclone™ Altera
®
chip (Szadkowski, 2005b). However, for real signal
x
n
α
0
=
α
k
=
≥
n
e
j
2
N
kn
∗
N
1
n
=
0
x
n
e
−
j
2
N
(
−
N
1
n
=
0
x
n
(
−
1
)
−
N
2
)
X
2
+
k
=
+
k
n
X
∗
2
−
k
=
=
(2)
