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xn
is signal of phase shifting
D
90 , and
In Fig.3,
xn
is in-phase signal of
1
()
x
(
n
)
,
2
()
a
in the experiment. Because
ref-
erence signal is a single frequency signal, the number of filter weights can be simplified
to two. At this time, the iterative equation of equation (6) weights can be rewritten as
follows:
a
is
α
in the equation (6). We suppose that
=
0
.
w
(
n
+
1
=
w
(
n
)
+
a
⋅
x
(
n
)
⋅
e
(
n
)
1
1
1
. (7)
w
(
n
+
1
=
w
(
n
)
+
a
⋅
x
(
n
)
⋅
e
(
n
)
2
2
2
So we can obtain output signal and error signal. That is, the following equations
hold
that
. (8)
yn wn x n w n x n
()
=
()
⋅
()
+
()
⋅
()
1
1
2
2
e
(
n
)
=
d
(
n
)
−
y
(
n
)
. (9)
4 Simulation Results
We know that adaptive notch filter based on LMS algorithm can filter very well noise
from noise added sinusoidal signal by setting
proper parameter
a
whether using
Matlab language programming to realize or using Simulink direct modeling to realize.
Further, we can observe
a
influence on filter performance by choosing different
a
values in the model.
N
o
ise add
ed
sinuso
i
dal signa
l
10
0
-10
0
200
400
600
800
1000
T he out p ut signal of adap t ive not ch filt er
10
0
-10
0
200
400
600
800
1000
Samp ling number
Fig. 4.
The simulation results in Matlab
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