Digital Signal Processing Reference
In-Depth Information
e
()
Quantization error
y
()
encoded by m bits
w
()
x
()
1
1
Decimator
Hz
()
Hz
()
1
1
1
z
1
z
Anti-aliasing LPF
M
1
z
FIGURE 12.32
DSP model for the second-order SDM ADC.
f
s
2
f
max
5
4
5
2
2
ðnmÞ
¼
p
(12.35)
In general, the
K
th-order SDM DSP model and ADC resolution formulas are given as
Y
z
¼
þ
1
z
1
K
|
{z
}
Highpass
noise shaping
filter
XðzÞ
|
{z
}
Original
digital signal
transform
EðzÞ
|
{z
}
Quantization
error
transform
(12.36)
f
s
2
f
max
p
2
K
2
K þ
1
n ¼ m þ
0
:
5
$ð
2
K þ
1
Þ
log
2
0
:
5
log
2
(12.37)
f
s
2
f
max
2
Kþ
1
2
K
2
K þ
1
2
2
ðnmÞ
p
¼
(12.38)
EXAMPLE 12.10
Given an oversampling rate DSP system with the following specifications, determine the effective ADC resolution:
Second-order SDM ¼ 1-bit ADC
Sampling rate ¼ 1 MHz
Maximum audio input frequency ¼ 4 kHz
Solution:
1;000
kHz
2 4 kHz
n ¼ 1 þ 2:5 log
2
2:14
z
16 bits
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