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ased
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m
a
x
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m
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m
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ig
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C
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to
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eter
m
i
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th
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n
t
r
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e.
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h
is
w
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k
m
ad
e
ex
ten
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v
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u
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f
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h
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m
u
lat
io
n
s
o
f
t
w
ar
e
P
S
C
A
D/
E
MT
DC
[
1
6
]
w
h
ic
h
r
es
u
lted
i
n
t
h
e
f
au
lt
o
f
th
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m
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latio
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n
t
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a
l
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is
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io
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li
n
e
p
ar
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n
u
m
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er
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f
d
ata
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r
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k
in
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o
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lt,
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e
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ata
w
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tr
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s
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ed
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MA
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B
w
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elp
o
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l
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ed
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1
7
]
s
u
ch
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Db
4
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y
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4
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C
o
il4
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d
Db
8
w
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m
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ip
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lated
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r
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p
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tio
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f
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an
s
m
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io
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2.
B
ASI
C
P
RINC
I
P
L
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CL
ARK
E
’
S AN
D
W
AVE
L
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T
T
RANSF
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RM
AT
I
O
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2
.
1
.
Cla
rk
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s
T
ra
ns
f
o
r
m
a
t
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C
lar
k
e
's
T
r
an
s
f
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n
(
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β0
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is
a
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s
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l
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n
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tical
ap
p
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t
s
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ts
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0
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t
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m
o
f
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n
d
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le
x
n
u
m
b
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s
.
A
t
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ee
-
p
h
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s
e
cu
r
r
en
t
w
h
ic
h
h
a
s
a
d
ig
ital
r
ep
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tatio
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s
as
s
u
m
ed
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av
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t
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f
o
r
m
[
1
8
]
,
[
1
9
]
.
T
h
er
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o
r
e,
th
e
ab
o
v
e
co
m
p
o
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e
n
t
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ca
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e
f
o
r
m
ed
in
t
o
a
m
atr
i
x
[
2
0
]
=
αβ
=C
[
]
[
]
(
1
)
w
h
er
e
C
is
t
h
e
w
ell
-
k
n
o
w
n
tr
a
n
s
f
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m
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n
in
tr
o
d
u
ce
d
b
y
E
d
i
th
C
lar
k
e
[
2
1
]
.
2
.2
.
F
a
ult
Cha
ra
ct
er
iza
t
io
n in Cla
rk
e’
s
T
ra
ns
f
o
r
m
a
t
io
n
2
.
2
.
1
.
Sin
g
le
L
i
ne
o
f
G
ro
un
d F
a
ult
P
ha
s
e
A
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p
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f
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to
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f
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A
G)
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m
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n
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ar
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it
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w
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e:
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d
0
(
2
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T
h
en
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b
o
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n
d
ar
y
co
n
d
it
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n
in
s
ta
n
ta
n
eo
u
s
w
ill b
e:
[
]
[
]
(
3
)
2
.
2
.
2
.
L
ine t
o
L
ine F
a
ult
in P
ha
s
e
A
-
B
A
s
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p
p
o
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e
f
o
r
th
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l
in
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to
li
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f
au
l
t
(
A
B
)
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ass
u
m
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g
t
h
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g
r
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d
in
g
r
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s
tan
ce
is
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r
o
,
th
en
t
h
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in
s
ta
n
ta
n
eo
u
s
b
o
u
n
d
ar
y
co
n
d
it
io
n
s
w
ill b
e:
0
,
-
an
d
(
4
)
T
h
en
,
th
e
b
o
u
n
d
ar
y
co
n
d
it
io
n
in
s
ta
n
ta
n
eo
u
s
w
ill b
e:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
lg
o
r
ith
m
fo
r
F
a
u
lt Lo
ca
tio
n
a
n
d
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la
s
s
ifica
tio
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P
a
r
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a
n
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mis
s
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n
Lin
e
….
(
Ma
km
u
r
S
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in
i)
701
[
]
[
]
(
5
)
2
.
2
.
3
.
L
ine t
o
L
ine t
o
g
ro
un
d F
a
ult
in P
ha
s
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AB
t
o
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A
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lt
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ar
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it
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w
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e:
0
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0
(
6
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en
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th
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b
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n
d
ar
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d
it
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n
in
s
ta
n
ta
n
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s
w
ill b
e:
[
]
[
]
(
7
)
2
.
2
.
4
.
T
hree
P
ha
s
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F
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ult
in P
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A
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s
w
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e:
+
+
0
an
d
+
+
0
(8
)
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h
en
,
th
e
b
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u
n
d
ar
y
co
n
d
it
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n
in
s
ta
n
ta
n
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u
s
w
ill b
e:
[
]
[
]
(
9
)
B
ased
o
n
th
e
ab
o
v
e
an
al
y
s
is
,
th
e
ch
ar
ac
ter
is
tics
o
f
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ar
io
u
s
f
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lts
b
a
s
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C
lar
k
e’
s
tr
an
s
f
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m
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n
-
Mo
d
al,
-
Mo
d
al
an
d
m
o
d
al
γ
ca
n
b
e
p
r
o
p
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s
ed
.
2
.
3
.
Wa
v
elet
T
ra
ns
f
o
r
m
a
t
io
n
W
av
elet
tr
an
s
f
o
r
m
atio
n
is
th
e
d
ec
o
m
p
o
s
itio
n
o
f
a
s
ig
n
a
l
b
y
a
f
u
n
c
tio
n
w
h
ich
is
d
elete
d
an
d
tr
an
s
lated
b
y
th
e
s
o
-
ca
lled
m
o
th
er
w
a
v
elet.
T
h
e
f
u
n
ctio
n
o
f
th
e
m
o
t
h
er
w
av
ele
t
ca
n
b
e
w
r
itte
n
a
s
f
o
llo
w
s
[
2
2
]
,
[
2
3
]
:
(
)
(
1
0
)
W
h
er
e
a
is
th
e
d
ilat
io
n
p
ar
am
eter
(
a
R
ea
l
)
a
n
d
b
is
a
tr
an
s
latio
n
p
ar
a
m
eter
(
b
R
ea
l
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p
ar
am
eter
a
in
d
icate
s
th
e
w
id
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o
f
th
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w
av
elet
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r
v
e,
w
h
en
th
e
v
a
lu
e
o
f
a
w
id
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m
a
g
n
if
ied
w
av
e
let
c
u
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v
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i
s
d
i
m
in
i
s
h
ed
a
s
th
e
c
u
r
v
e
g
ets
s
m
aller
,
w
h
ile
th
e
w
a
v
elet
p
ar
a
m
eter
cu
r
v
e
b
s
h
o
w
s
th
e
lo
ca
lizatio
n
o
f
w
a
v
elet
ce
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ter
ed
at
t
b
.
T
h
e
d
etec
tio
n
o
f
th
e
d
is
cr
ete
w
av
e
let
tr
an
s
f
o
r
m
ed
(
DW
T
)
f
au
lt
i
s
r
eq
u
ir
ed
s
o
th
at
t
h
e
eq
u
at
io
n
b
ec
o
m
e
s
[
2
4
]
,
[
25]
⁄
(
1
1
)
Var
iab
les
j
a
n
d
k
ar
e
i
n
te
g
er
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t
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s
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i
f
t
s
o
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e
m
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v
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f
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to
p
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ce
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o
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m
o
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a
v
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ch
a
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S
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s
an
d
Haa
r
w
a
v
elets.
T
h
e
w
id
t
h
o
f
a
w
av
e
let
is
s
h
o
w
n
b
y
t
h
e
s
ca
le
,
an
d
th
e
p
o
s
itio
n
is
i
n
d
i
ca
ted
b
y
t
h
e
w
a
v
elet
s
ca
le
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
p
r
il 2
0
1
8
:
6
9
9
–
7
1
0
702
Dis
cr
ete
W
av
elet
T
r
an
s
f
o
r
m
at
io
n
s
(
DW
T
)
ar
e
m
eth
o
d
s
u
s
ed
to
d
ec
o
m
p
o
s
e
th
e
i
n
p
u
t
s
ig
n
a
l,
an
d
th
e
s
ig
n
al
is
a
n
al
y
ze
d
b
y
g
iv
i
n
g
t
r
ea
t
m
en
t
to
th
e
w
a
v
elet
co
ef
f
i
cien
ts
.
T
h
e
d
ec
o
m
p
o
s
itio
n
p
r
o
ce
s
s
in
v
o
lv
e
s
t
w
o
f
ilter
s
,
w
h
ic
h
ar
e
lo
w
-
p
as
s
f
ilt
er
an
d
a
h
ig
h
-
p
ass
f
ilter
[
2
6
]
.
T
h
is
is
ac
h
ie
v
ed
b
y
s
u
cc
es
s
i
v
e
h
ig
h
p
as
s
an
d
lo
w
p
ass
f
il
ter
in
g
o
f
t
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e
ti
m
e
d
o
m
a
in
s
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al
an
d
is
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e
f
in
ed
b
y
t
h
e
f
o
llo
w
in
g
eq
u
at
io
n
:
[
]
∑
[
]
[
]
(
1
2
)
[
]
∑
[
]
[
]
(
1
3
)
w
h
er
e
[
]
o
u
tp
u
t h
ig
h
-
p
ass
f
ilter
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d
[
]
o
u
tp
u
t lo
w
-
p
ass
f
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ter
.
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h
e
s
ig
n
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is
f
ir
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t p
ass
ed
t
h
r
o
u
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h
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e
h
i
g
h
-
p
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w
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ilter
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t
h
en
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al
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o
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ch
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u
tp
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t
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tak
e
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s
a
m
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li
n
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d
o
w
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r
o
u
g
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e
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a
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o
p
er
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n
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e
s
i
g
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a
l o
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r
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e
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m
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t c
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n
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e
o
b
tain
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r
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o
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tio
n
s
a
s
s
h
o
w
n
b
y
Fig
u
r
e
1
[
2
7
]
.
Fig
u
r
e
1.
T
h
e
p
r
o
ce
s
s
d
ec
o
m
p
o
s
itio
n
o
f
d
is
cr
ete
w
a
v
elet
tr
a
n
s
f
o
r
m
T
h
is
is
ca
lled
a
d
ec
o
m
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o
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itio
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ir
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le
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el
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r
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ce
s
s
i
n
t
h
e
f
r
eq
u
en
c
y
r
a
n
g
e
o
f
2
5
0
-
5
0
0
k
Hz.
T
h
e
o
u
tp
u
t
f
r
o
m
t
h
e
lo
w
-
p
as
s
f
ilter
is
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s
e
d
as th
e
in
p
u
t o
f
t
h
e
n
e
x
t
d
ec
o
m
p
o
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itio
n
s
ec
o
n
d
lev
e
l
,
w
ith
a
f
r
eq
u
en
c
y
r
an
g
e
o
f
125
-
2
5
0
k
Hz.
T
h
is
p
r
o
ce
s
s
is
r
ep
ea
ted
ag
ain
u
n
t
il it r
ea
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e
t
h
ir
d
lev
el
o
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d
ec
o
m
p
o
s
it
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it
h
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f
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eq
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en
c
y
o
f
6
2
.
5
-
1
2
5
k
Hz,
an
d
s
o
f
o
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th
,
ac
co
r
d
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g
to
th
e
lev
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l d
esire
d
.
I
n
th
i
s
s
t
u
d
y
,
it is
c
h
o
s
e
n
to
r
ea
ch
lev
el
4
,
w
it
h
a
f
r
eq
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en
c
y
r
an
g
e
o
f
3
1
.
2
5
-
6
2
.
5
k
Hz
an
d
a
lev
el
8
w
it
h
f
r
eq
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e
n
c
y
r
a
n
g
e
o
f
7
.
8
1
2
5
-
1
5
.
6
2
5
k
Hz
[
2
8
]
.
T
h
e
co
m
b
in
at
io
n
o
f
t
h
e
o
u
t
p
u
t
f
r
o
m
t
h
e
h
i
g
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-
p
a
s
s
f
ilte
r
an
d
lo
w
-
p
as
s
f
i
lter
o
u
tp
u
t
is
ca
lled
C
o
ef
f
icie
n
t
W
a
v
elet
tr
a
n
s
f
o
r
m
ed
(
C
W
T
)
,
w
h
i
ch
co
n
tai
n
s
i
n
f
o
r
m
atio
n
o
n
t
h
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e
s
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l
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at
h
av
e
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n
co
m
p
r
es
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ed
an
d
tr
an
s
f
o
r
m
ed
.
I
n
th
i
s
s
tu
d
y
,
th
e
h
i
g
h
p
ass
f
il
ter
an
d
lo
w
-
p
as
s
f
ilter
ar
e
co
u
p
led
an
d
b
ec
o
m
i
n
g
a
Qu
ad
r
atu
r
e
Mir
r
o
r
Fil
ter
(
QM
F),
in
w
h
ich
t
h
e
co
u
p
les
m
e
et
th
e
f
o
llo
w
i
n
g
[
2
9
]
eq
u
atio
n
:
[
]
[
]
(
1
4
)
w
h
er
e
[
]
h
i
g
h
-
p
ass
f
il
ter
,
[
]
lo
w
-
p
ass
f
ilter
,
L
len
g
t
h
o
f
ea
ch
f
i
lter
.
Su
cc
e
s
s
f
u
l
to
th
e
d
o
w
n
s
a
m
p
li
n
g
o
p
er
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n
th
at
r
e
m
o
v
es
r
ed
u
n
d
an
t
in
f
o
r
m
at
io
n
s
i
g
n
al,
w
av
ele
t
tr
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s
f
o
r
m
h
a
s
b
ec
o
m
e
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n
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f
t
h
e
m
o
s
t r
eliab
le
an
d
a
cc
u
r
ate
co
m
p
o
s
itio
n
m
et
h
o
d
s
[
3
0
]
.
3.
T
H
E
P
RO
P
O
SE
D
AL
G
O
RI
T
H
M
I
n
t
h
is
s
t
u
d
y
,
th
e
s
i
m
u
latio
n
s
w
er
e
p
er
f
o
r
m
ed
u
s
i
n
g
P
S
C
A
D,
a
n
d
t
h
e
s
i
m
u
latio
n
r
esu
lt
s
w
er
e
o
b
tain
e
d
f
r
o
m
th
e
f
a
u
lt c
u
r
r
en
t
s
ig
n
al
.
T
h
e
s
tep
s
p
er
f
o
r
m
ed
i
n
th
i
s
s
t
u
d
y
w
er
e
:
a.
Fin
d
i
n
g
t
h
e
in
p
u
t
to
th
e
C
lar
k
e’
s
tr
an
s
f
o
r
m
atio
n
an
d
w
a
v
ele
t
tr
an
s
f
o
r
m
.
T
h
e
s
ig
n
al
f
lo
w
o
f
P
SC
A
D
w
a
s
t
h
e
n
co
n
v
er
ted
i
n
to
m
.
f
i
les
(
*
.
M)
a
n
d
t
h
en
co
n
v
er
ted
in
to
m
a
t.
Fil
e
s
(
*
m
at)
w
it
h
a
s
a
m
p
lin
g
r
ate
o
f
an
d
f
r
eq
u
en
c
y
d
ep
en
d
en
t o
f
0
.
5
Hz
-
1
MH
z.
L
e
v
el
3
C
o
ef
f
icie
n
t
L
e
v
el
2
C
o
ef
f
icie
n
t
h
[
n
]
2
g
[
n
]
2
h
[
n
]
2
g
[
n
]
2
L
e
v
el
1
C
o
ef
f
icie
n
t
h
[
n
]
2
g
[
n
]
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
lg
o
r
ith
m
fo
r
F
a
u
lt Lo
ca
tio
n
a
n
d
C
la
s
s
ifica
tio
n
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P
a
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a
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a
n
s
mis
s
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Lin
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(
Ma
km
u
r
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a
in
i)
703
b.
Dete
r
m
i
n
i
n
g
t
h
e
d
ata
s
tr
ea
m
i
n
ter
f
er
e
n
ce
,
w
h
er
e
t
h
e
s
i
g
n
al
w
a
s
tr
an
s
f
o
r
m
ed
b
y
u
s
i
n
g
th
e
C
lar
k
e
’
s
tr
an
s
f
o
r
m
atio
n
to
co
n
v
er
t
t
h
e
tr
a
n
s
ie
n
t
s
i
g
n
al
s
i
n
to
t
h
e
b
asic
c
u
r
r
en
t
m
o
d
e
s
i
g
n
a
l
in
u
s
i
n
g
E
q
u
atio
n
(
1
)
.
c.
T
r
an
s
f
o
r
m
i
n
g
th
e
m
o
d
e
c
u
r
r
e
n
t
s
ig
n
al
s
a
g
ai
n
b
y
u
s
i
n
g
DW
T
an
d
W
T
C
,
w
h
ic
h
w
er
e
t
h
e
g
en
er
ated
co
ef
f
icie
n
t
s
,
an
d
th
e
n
s
q
u
ar
ed
to
b
e
in
o
r
d
er
to
o
b
tain
th
e
m
ax
i
m
u
m
s
i
g
n
a
l
a
m
p
lit
u
d
e
t
o
d
eter
m
in
e
t
h
e
ti
m
e
o
f
t
h
e
in
ter
r
u
p
tio
n
[
3
1
]
,
[
3
2
]
.
d.
P
r
o
ce
s
s
in
g
t
h
e
g
r
o
u
n
d
m
o
d
e
an
d
ae
r
ial
m
o
d
e
an
d
(
WT
C
)
2
u
s
i
n
g
th
e
B
e
w
le
y
L
a
ttice
d
ia
g
r
a
m
[
3
2
]
,
[
3
3
]
o
f
th
e
in
itial
w
a
v
e
to
d
eter
m
in
e
t
h
e
f
au
l
t lo
ca
tio
n
an
d
d
e
tectio
n
.
e.
A
d
d
in
g
t
h
e
m
a
g
n
itu
d
e
o
f
t
h
e
cu
r
r
en
t
g
a
m
m
a
to
m
ak
e
th
e
f
au
lt
cla
s
s
i
f
icat
io
n
al
g
o
r
ith
m
w
h
ic
h
t
h
e
n
b
ec
am
e
m
o
d
al
th
at
ca
n
b
e
p
r
o
p
o
s
ed
.
W
h
ile
th
e
m
ag
n
i
tu
d
e
o
f
th
e
c
u
r
r
en
t
g
a
m
m
a
o
f
ea
c
h
d
if
f
er
e
n
t t
y
p
e
s
o
f
f
a
u
lt c
a
n
b
e
s
ee
n
i
n
T
ab
le
1
.
(
1
5
)
f.
Dete
r
m
i
n
i
n
g
w
h
e
th
er
th
e
in
te
r
n
al
f
au
lt
in
b
o
th
C
ir
cu
i
t
1
o
r
C
ir
c
u
it
2
a
n
d
e
x
ter
n
al
f
au
l
t
u
s
in
g
t
h
e
f
o
llo
w
in
g
e
q
u
at
io
n
:
I
f
|
|
o
r
|
|
Fau
lt I
n
ter
n
al
C
ir
c
u
it 1
(
1
6
)
I
f
|
|
|
|
Fau
lt I
n
ter
n
al
C
ir
cu
it
2
(
1
7
)
I
f
|
|
|
|
Fau
lt E
x
t
er
n
al
(
1
8
)
g.
T
h
e
p
r
o
tectio
n
tech
n
iq
u
e
s
h
o
u
ld
b
e
ab
le
to
class
if
y
th
e
f
a
u
lted
p
h
ase
f
o
r
s
in
g
le
-
p
h
a
s
e
-
to
-
g
r
o
u
n
d
f
au
lts
.
I
n
th
e
ca
s
e
o
f
s
i
n
g
le
-
p
h
ase
-
to
-
g
r
o
u
n
d
f
au
lts
,
t
w
o
o
f
th
e
m
o
d
al
co
m
p
o
n
en
ts
th
at
i
n
clu
d
e
th
e
f
au
lted
p
h
ase
s
h
o
u
ld
h
av
e
al
m
o
s
t
t
h
e
s
a
m
e
a
m
p
li
tu
d
e
an
d
th
e
o
th
er
m
o
d
al
co
m
p
o
n
e
n
t
s
h
o
u
ld
b
e
ze
r
o
,
as f
o
llo
w
s
:
|
|
|
|
|
|
⇒
AG
f
a
u
lt
(
1
9
)
|
|
|
|
|
|
|
|
⇒
B
G
f
au
lt
(
2
0
)
|
|
|
|
|
|
|
|
⇒
C
G
f
au
lt
(
2
1
)
T
h
e
alg
o
r
ith
m
w
i
ll c
o
n
ti
n
u
e
to
d
eter
m
i
n
e
t
h
e
f
a
u
lted
p
h
ase
s
i
n
v
o
l
v
ed
in
a
m
u
l
tip
le
-
p
h
ase
f
a
u
lt.
I
n
th
e
ca
s
e
o
f
li
n
e
to
li
n
e
f
a
u
lt
s
,
th
e
cr
iter
ia
ar
e
as g
i
v
en
i
n
(
2
2
)
-
(
2
4
)
:
|
|
|
|
|
|
|
|
⇒
A
B
f
au
lt
(
2
2
)
|
|
|
|
|
|
|
|
⇒
A
C
f
a
u
lt
(
2
3
)
|
|
|
|
|
|
⇒
B
C
f
au
lt
(
2
4
)
I
n
th
e
ca
s
e
o
f
d
o
u
b
le
lin
e
to
g
r
o
u
n
d
f
a
u
lt
s
,
th
e
cr
iter
ia
ar
e
as
g
iv
e
n
i
n
(
2
5
)
-
(
2
7
)
:
|
|
|
|
|
|
|
|
⇒
A
B
G
f
au
lt
(
2
5
)
|
|
|
|
|
|
|
|
|
|
⇒
A
C
G
f
a
u
lt
(
2
6
)
|
(
|
|
|
|
)
|
|
|
|
|
⇒
B
C
G
f
au
lt
(
2
7
)
h.
Dete
r
m
i
n
i
n
g
t
h
e
f
a
u
lt
C
las
s
i
f
icatio
n
w
h
er
e
t
h
e
f
a
u
lt
cla
s
s
i
f
icatio
n
w
a
s
d
iv
id
ed
in
to
2
ca
teg
o
r
ies
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
p
r
il 2
0
1
8
:
6
9
9
–
7
1
0
704
g
r
o
u
n
d
a
n
d
u
n
g
r
o
u
n
d
.
T
h
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cu
r
r
en
t
ap
p
r
o
ac
h
h
ad
ze
r
o
g
iv
e
n
th
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RE
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[1
]
IEE
E
G
u
id
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f
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r
De
ter
m
in
in
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a
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IEE
E
S
td
C
3
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.
1
1
4
,
(2
0
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)
.
[2
]
J.
S
o
n
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a
n
d
Y.G
.
S
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o
n
a
n
,
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n
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term
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ta,
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p
p
.
1
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4
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1
2
9
,
2
0
0
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.
[3
]
J.
Iz
y
k
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,
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t.
,
“
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ts
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,
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o
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In
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ra
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Distrib
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1
5
1
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.
[4
]
S
.
H.
Ka
n
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,
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2
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.
1
8
5
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6
,
2
0
0
9
.
[5
]
J.
S
u
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t.
,
“
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rre
n
ts,
”
El
e
c
t
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