Digital Signal Processing Reference
In-Depth Information
d
()
Unknown system
1
0.
502
5
105
.
z
H
z
()
.
z
1
Output
Input
e
()
x
()
y
()
Adaptive
FIR filter
FIGURE 10.26
System modeling in Problem 10.10.
using the LMS algorithm for
i ¼
0
;
1
;
2
;
3
;
4; that is, write the equations for all adaptive
coefficients:
wð
0
Þ¼
wð
1
Þ¼
wð
2
Þ¼
wð
3
Þ¼
wð
4
Þ¼
10.11. Consider the adaptive filter used for the noise cancellation application in Problem 10.9, in
which
dð
0
Þ¼
3,
dð
1
Þ¼
2,
dð
2
Þ¼
1,
xð
0
Þ¼
3,
xð
1
Þ¼
1,
xð
2
Þ¼
2, and an adap-
tive filter with three taps
yðnÞ¼wð
0
ÞxðnÞþwð
1
Þxðn
1
Þþwð
2
Þxðn
2
Þ
with initial
values
wð
0
Þ¼
0,
wð
1
Þ¼
0,
wð
2
Þ¼
0 and
m ¼
0
:
2.
a. Determine the LMS algorithm equations
yðnÞ¼
eðnÞ¼
wð
0
Þ¼
wð
1
Þ¼
wð
2
Þ¼
b. Perform adaptive filtering for each of
n ¼
0
;
1
;
2.
10.12. Consider the DSP system with a sampling rate of 8,000 samples per second in Problem
10.10. Implement an adaptive filter with five taps for system modeling, assuming the
unknown system transfer function is
H
z
¼
0
:
2
þ
0
:
3
z
1
þ
0
:
2
z
2
Determine the DSP equations
yðnÞ¼
eðnÞ¼
wðiÞ¼
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