Digital Signal Processing Reference
In-Depth Information
¢
()
=+
()
(
)
(
()
)
fx
1
fs
1
-
fs
Then
(
)
(
(
)
)
(
(
)
)
=-
e
0
=-
0
0 894
.
1
+
tanh 1.44
1
-
tanh 1.44
0 18
.
Similarly,
e
1
=
0.399. Based on this output error, the contribution to the error by each
hidden layer node is to be found. The weights are then adjusted based on this error
using
D
we x
kj
=h
k
j
where
can
cause instability, and a very small one can make the learning process much too slow.
Then
h
is the network learning rate constant, chosen as 0.3. A large value of
h
=
()
-
(
)(
)
=-
D
w
00
0 3
.
0 18
.
0 664
.
0 036
.
Similarly,
D
w
01
=-
0.046,
D
w
10
=
0.08, and
D
w
11
=
0.103. The error associated with the
hidden layer is
1
=
()
Â
0
ef
s ew
j
j
k
kj
k
Then
{
}
=-
(
()
)
(
()
)
(
)(
)
+
(
)(
)
e
0
=+
1
tanh 0.8
1
-
tanh
08
.
-
018 10
.
.
0399 04
.
.
0011
.
Similarly,
e
1
=-
0.011. Changing the weights between layers
i
and
j
,
D
we x
ji
=h
j
i
Then
=
()
-
(
)( )
=-
D
w
00
0 3
.
0 011 1
.
0 0033
.
Similarly,
0. This
gives an indication of by how much to change the original set of weights chosen.
For example, the new set of coefficients becomes
D
w
01
=-
0.0033,
D
w
02
=
0,
D
w
10
=-
0.0033,
D
w
11
=-
0.0033, and
D
w
12
=
ww w
00
=+
D
=-
0 5
.
0 0033
.
=
0 4967
.
00
00
and
w
01
=
0.2967,
w
02
=
0.1, and so on.
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