Image Processing Reference
In-Depth Information
ADC
counts
ADC
counts
ADC
counts
ADC
counts
ADC samples : a new small
incoming pulse
ADC samples: x 0 = x 1 = 0
ADC samples: x 0 = 0
ADC samples: x 0 = max
100
100
100
100
Shape_A
Shape_B
Shape_C
Shape_D
80
80
80
80
60
60
60
60
40
40
40
40
20
20
20
20
0
0
0
0
0
50
100 150 200 250
time (ns)
0
50
100 150 200 250
0
50
100 150 200 250
time (ns)
0
50
100 150 200 250
time (ns)
time (ns)
ȟ k (%)
DCT - II
DCT - II
ȟ k (%)
DCT - II
ȟ k (%)
DCT - II
ȟ k (%)
100
105
90
100
80
70
80
60
60
60
35
30
40
40
index (k)
0
0
20
20
13579 1 3 5
index (k)
-35
-30
0
0
index (k)
13579 1 3 5
13579 1 3 5
13579 1
index (k)
-60
-70
-20
|X FFT k | /|X FFT 1 |
|X FFT k | /|X FFT 1 |
|X FFT k | /|X FFT 1 |
|X FFT k | /|X FFT 1 |
%
%
%
%
100
100
100
100
80
80
80
80
60
60
60
60
40
40
40
40
20
20
20
20
0
0
0
0
123456
123456
index (k)
123456
index (k)
123456
index (k)
index (k)
%
(X FFT .Re,Im) k /|X FFT 1 |
%
(X FFT .Re,Im) k /|X FFT 1 |
%
(X FFT .Re,Im) k /|X FFT 1 |
%
(X FFT .Re,Im) k /|X FFT 1 |
50
Re
Im
100
Re
Im
50
Re
Im
40
75
0
25
50
0
3456
25
index (k)
0
-50
2
45678
0
index (k)
Re
Im
-40
index (k)
-25
index (k)
-25
345678
-100
12345678
-50
-80
-50
Fig. 3. A propagation of the pulse (1st row) through the shift register, DCT-II coefficients (2nd
row), absolute values of the DFT (3rd row) and corresponding real (Re), imaginary parts (Im)
(4th row). The 1st column shows the pulse (shape A), when two time bins are on the pedestal
level, the 2nd one (shape B), when only the one time bin is still on the pedestal level, while
the 3rd one (shape C) shows the pulse fully fulfilled the range of investigating shift registers.
For a signal shape related to the exponential attenuation (shape C), the contribution of higher
DCT coefficients is small and suitable for a trigger. When a peak appears in the declining
signal (last column - shape D), the DCT coefficients immediately excesses assumed relatively
narrow acceptance range for triggers. The DFT coefficients (Re and Im in 4th row) have
similar structure as the DCT, however for the pure exponentially declining signal the higher
real DFT harmonics have relatively high values and they are not suitable for triggering.
Absolute values of DFT components (3rd row) are clearly insensitive on discussed
conditions.
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