Digital Signal Processing Reference
In-Depth Information
As well as having to select l, one needs to select an appropriate filter length.
A larger filter length M ? 1 is likely to give better estimation, but it also intro-
duces more delay into the output. Again, a compromise is desirable.
3.5.6 Hardware Implementation of Adaptive FIR Filters
The adaptive LMS algorithm can be implemented in either digital hardware or
software. A digital hardware implementation is depicted in Fig.
3.24
. Note that
adaptive filters really only became practical with the advent of digital signal
processing—the intelligence required to implement these algorithms is generally
problematical for analog hardware.
3.5.7 An Example of LMS Filtering
Example Consider a 2-tap FIR adaptive LMS filter. If y(4) = 0.25, y(5) =
0.5, d(4) = 1.03, d(5) =-0.27, and h
ð
4
Þ¼½
1
:
23
:
7
, use the LMS algorithm
with l = 0.02 to update the impulse response of the filter.
Solution
: Applying the LMS filter algorithm to the above data specifications gives:
h
ð
5
Þ¼
h
ð
5
Þþ
l
½
0
:
50
:
25
e
ð
5
Þ
e
ð
5
Þ¼
d
ð
5
Þ
x
ð
5
Þ¼
d
ð
5
Þ
h
ð
4
Þ
y
T
ð
5
Þ
¼
1
:
79
0
:
5
0
:
25
¼
0
:
27
½
1
:
23
:
7
h
ð
5
Þ¼
h
ð
4
Þþ
0
:
02
½
0
:
50
:
25
ð
1
:
79
Þ
¼½
1
:
23
:
7
½
0
:
0179 0
:
0089
¼½
1
:
18 3
:
69
:
Observed signal
z
−1
z
−1
z
−1
y
(
n
)
h
o
y
(
n
)
h
1
y
(
n
−1)
h
M
y
(
n
−M)
^
x
(
n
)
h
1
h
M
h
o
z
−1
z
−1
z
−1
d
(
n
)
e
(
n
)
μ
y
(
n
)
e
(
n
)
μ
y
(
n
−1)
e
(
n
)
μ
y
(
n
−
M
)
e
(
n
)
μ
μ
e
(
n
)
Fig. 3.24
Hardware implementation of the adaptive LMS filter
Search WWH ::
Custom Search