Digital Signal Processing Reference
In-Depth Information
Table 2.1
Quantization Table for the 3-Bit Unipolar Quantizer (step size ¼ D ¼ðx
max
x
min
Þ=2
3
,
x
max
¼ maximum voltage, and
x
min
¼ 0)
Binary Code
Quantization Level
x
q
(V)
Input Signal Subrange (V)
000
0
x
<
:
D
0
0
5
001
D
:
D
x
<
:
D
0
5
1
5
010
D
:
D
x
<
:
D
2
1
5
2
5
011
D
:
D
x
<
:
D
3
2
5
3
5
100
D
:
D
x
<
:
D
4
3
5
4
5
101
D
:
D
x
<
:
D
5
4
5
5
5
110
D
:
D
x
<
:
D
6
5
5
6
5
111
D
:
D
x
<
:
D
7
6
5
7
5
Binary code
x
q
111
3Δ
110
2 Δ
101
Δ
x
100
0
−
4
Δ
−
3
Δ
−
2
Δ
−Δ
Δ
2 Δ
3Δ
4 Δ
011
−Δ
010
−
2
Δ
001
−
3
Δ
000
−
4
Δ
e
q
Δ
/
2
x
−Δ
/2
FIGURE 2.30
Characteristics for the bipolar quantizer.
EXAMPLE 2.9
Assuming that a 3-bit ADC channel accepts analog input ranging from 0 to 5 volts, determine
a.
the number of quantization levels;
b.
the step size of the quantizer or resolution;
c.
the quantization level when the analog voltage is 3.2 volts;
d.
the binary code produced by the ADC.
Solution:
Since the range is from 0 to 5 volts and a 3-bit ADC is used, we have
x
min
¼ 0 volt;
x
max
¼ 5 volts;
and
m ¼ 3 bits
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