Digital Signal Processing Reference
In-Depth Information
FIGURE 7.4.
Adaptive predictor structure.
FIGURE 7.5.
Adaptive notch structure with two weights.
The LMS is well suited for a number of applications, including adaptive echo and
noise cancellation, equalization, and prediction.
Other variants of the LMS algorithm have been employed, such as the sign-error
LMS, the sign-data LMS, and the sign-sign LMS.
1.
For the sign-error LMS algorithm, (7.3) becomes
(
)
=
()
+
[
()
]
(
)
wn
+
1
wn
b
sgn
enxn k
-
(7.4)
k
k
where sgn is the signum function,
1
if
if
u
u
0
Ó
()
=
sgn
u
(7.5)
-
1
<
0
2.
For the sign-data LMS algorithm, (7.3) becomes
(
)
=
()
+
()
[
(
)
]
wn
+
1
wn
b
en
sgn
xn k
-
(7.6)
k
k
3.
For the sign-sign LMS algorithm, (7.3) becomes
(
)
=
()
+
[
()
]
[
(
)
]
wn
+
1
wn
b
sgn
en
sgn
xn k
-
(7.7)
k
k
which reduces to
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