Image Processing Reference
In-Depth Information
of a signal requires a single clock cycle only. All routines are fast enough to work with 100
MHz sampling without an additional pipeline stages and they do not introduce an additional
latency.
8. Accuracy
10-bit resolution of FADC in the high-gain channels (responsible for a trigger generation)
implies the ranges of X k coefficients given in the 2nd column of Table 1. Multiplications of
integer values N by real scaling factors sf give floating-point results. In order to keep possible
high speed of calculation and not to utilize resources spendthrift the fixed-point algorithm
of processing has been chosen. N
sf were approximated on each pipeline stage again to
the integer value. For almost all scaling factors: sf
×
1, N
×
sf has a representation of the
same or less amount of bits. For sf
sf extends the representation on 1 or 2 bits. This
approximation introduces errors. However, the width of the data in the internal pipeline
stages is extended from the N at the shift register x 15 ,..., x 0 , to N+1, N+2, N+3, N+4, N+5, N+7,
N+8 in routines A, B, C, D, E, F, G, respectively (Fig. 8). This reduces approximation errors
mostly to the LSB, apart the X 15 . This coefficient will not be used for a trigger.
k range of LSB
1, N
×
2 nd
3 rd and k range of LSB
2 nd
3 rd and
X k
X k
bit more
bit
more
0 0...4092
0.0% 0.00% 0.00% 8
±
2041
0.0% 0.00% 0.00%
±
±
1
2521 13.1% 0.00% 0.00% 9
12224 23.8% 1.55% 0.00%
±
±
2
2581
8.7% 0.00% 0.00% 10
4557 12.8% 0.00% 0.00%
3
±
2914 13.1% 0.00% 0.00% 11
±
7519 17.7% 0.00% 0.00%
±
±
4
2348
4.8% 0.00% 0.00% 12
5671 11.5% 0.00% 0.00%
5
±
4019 15.1% 0.00% 0.00% 13
±
9605 24.3% 2.00% 0.00%
6
±
3045
8.6% 0.00% 0.00% 14
±
12978 26.9% 2.86% 0.00%
±
±
7
10032 23.1% 1.10% 0.00% 15
25597 30.9% 25.08% 6.83%
Table 1. Ranges of X k coefficients and relative errors for least significant bits of X k . For k
14
the errors appear practically only in the LSB.
According to above estimations, the configuration with 3 "engines" does not support all
ξ k
sub-triggers due to limited amount of DSP blocks. However, for the next generation of
the water Cherenkov detectors array, where probably only a single PMT will be used, 3
"engines" will be implemented to investigate and to detect 3 different shapes of FADC traces
corresponding to i.e. different rise times of the rising edge.
9. Preliminary tests
Analysis of Auger ADC traces of very inclined showers shows that the maximum of the signal
is mostly reach in a single time bin. The attenuation factor for a tail is in the range of
=
(0.2 - 0.5). Fig. 12 shows shapes of signals with various attenuation factors with two first
time bins on a pedestal level. For simplicity it has been set on zero. It does not reduce the
generality of analysis, because the pedestal is irrelevant for DCT (k
β
1). The corresponding
DCT coefficients are shown in upper Fig. 3 (Shape_A). After a single clock cycle, when data
is shifted in the registers chain, shifted signal with only one time bin on the pedestal level
determines a new set of the DCT coefficients shown in lower Fig. 3 (Shape_B). Pattern, which
is going to be recognized, can be selected by a setting of DCT coefficient in the DCT engines.
 
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