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=
...
(
n
N
) proposed neurons, respectively. All weights, bias and input-output
signals are complex numbers. Let
Z
1
=
[
z
1
,
z
2
...
z
L
] be the vector of input signals.
w
Lm
] be the vector of weights between input layer to
m
th
Let
W
m
=
[
w
1
m
,
w
2
m
...
hidden neuron, while
W
n
w
Mn
] be the vector of weights between
hidden layer to
n
th output neuron.
w
0
is the bias weight and
z
0
is the bias input.
expressed as:
=
[
w
1
n
,
w
2
n
...
L
1
/
d
w
lm
z
l
Y
m
=
f
(
(
V
m
))
+
j
×
f
(
(
V
m
))
where
V
m
=
(4.32)
l
=
0
Similarly, the output of each neuron in output layer can be expressed as:
M
1
/
d
w
mn
Y
m
Y
n
=
f
(
(
V
n
))
+
j
×
f
(
(
V
n
))
where
V
n
=
(4.33)
m
=
0
Update equation for learning parameters in output layer:
(4.34)
V
n
(
1
−
d
)
Y
m
d
d
f
f
ʔ
w
mn
=
(
e
n
)
(
(
V
n
)
+
j
×
(
e
n
)
(
(
V
n
)
The update equation for learning parameters between input and hidden layer is as
follows. Let
AT
mn
and
VT
mn
are common terms,
AT
mn
=
(
A
1
mn
A
2
mn
+
A
3
mn
A
4
mn
)
VT
mn
=
(
A
3
mn
A
2
mn
−
A
1
mn
A
4
mn
)
Y
m
Y
m
V
n
V
n
A
1
mn
=
(
Y
m
)
+
(
Y
m
)
A
2
mn
=
(
V
n
)
+
(
V
n
)
Y
m
Y
m
V
n
V
n
A
3
mn
=
(
Y
m
)
−
(
Y
m
)
A
4
mn
=
(
V
n
)
−
(
V
n
)
2
1
V
n
f
f
and
˒
lm
=
(
e
n
)
(
(
V
n
))
(
w
mn
)
+
(
e
n
)
(
(
V
n
))
(
w
mn
)
n
f
VT
mn
f
×
(
(
V
m
))
AT
mn
+
j
×
(
(
V
m
))
j
f
f
+
(
e
n
)
(
(
V
n
))
(
w
mn
)
−
(
e
n
)
(
(
V
n
))
(
w
mn
)
f
VT
mn
f
×
(
(
V
m
))
AT
mn
+
j
×
(
(
V
m
))
(4.35)
V
m
(
1
−
d
)
ʷ
Nd
d
ʔ
w
lm
=
(
z
l
)
˒
lm
(4.36)
2
|
Y
m
|
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