dc

Figure 3.11 Illustration of the quantization process
Let the quantizati on error bedenoted by the random
variable Q of sample value q
q m
Q M V
,
Assuming a uniform quantizer of the midrise type
2m
max
the step -size is
(3.25)
L
m max m m max,
L : total number of levels
1
,
( )
(3.26)
0, otherwise 2 q
fQ
q
2
2
Q
E[
Q
2
]
(3.23)
( E[
M ] 0)
(3.24)
2
2
q
2
f
Q
1
( q)
dq
2
2
2
(3.28)
12
q
2
dq
When the quatized
where R is the number of bits per sample
2m
max
R
2
(3.31)
2 1 2 2R
Q
mmax2
3
(3.32)
Let P denote the average power of m(
t)
(SNR)
o
L 2
R log
( SNR)
sample is
o
R
2
Q
3P
(
2
m
max
)2
increases exponentially with
2
L
P
expressed in binary form,
2R
(3.29)
(3.30)
(3.33)
increasing
R (bandwidth).