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ctio
n
al
f
o
r
m
,
y
et
co
n
ta
in
s
s
ev
er
al
p
ar
a
m
eter
s
t
h
at
ca
n
n
o
t
b
e
in
ter
p
r
eted
as
in
th
e
p
ar
a
m
etr
ic
m
o
d
el
[
1
5
]
.
T
h
e
ap
p
licatio
n
o
f
th
e
NN
m
o
d
el
f
o
r
ti
m
e
s
er
ie
s
p
r
ed
ictio
n
s
co
n
tai
n
i
n
g
s
ea
s
o
n
al
ele
m
en
ts
an
d
tr
en
d
i
n
g
ele
m
e
n
ts
i
s
d
o
n
e
b
y
Z
h
an
g
a
n
d
Qi
[
1
6
]
.
Mu
lti
-
la
y
er
p
er
ce
p
tr
o
n
(
ML
P
)
ar
ch
itectu
r
e
i
s
w
id
el
y
u
s
ed
f
o
r
n
o
n
-
lin
ea
r
an
d
n
o
n
-
s
tat
io
n
ar
y
t
i
m
e
s
er
ies
d
ata
p
r
ed
ictio
n
,
w
h
il
e
th
e
co
m
m
o
n
l
y
u
s
ed
lear
n
in
g
m
e
th
o
d
is
f
ee
d
-
f
o
r
w
ar
d
N
N
(
F
FNN)
a
s
d
id
b
y
Kaj
itan
i
et
a
l
.
[
1
7
]
.
T
h
e
r
ad
ial
b
ases
f
u
n
ctio
n
NN
(
R
B
FNN)
ar
ch
i
tectu
r
e
r
ese
m
b
les
M
L
P
b
u
t it
ap
p
lies
t
h
e
cl
u
s
ter
i
n
g
m
et
h
o
d
o
n
t
h
e
h
i
d
d
en
la
y
er
u
n
it.
T
h
e
R
B
FNN
ca
n
al
s
o
b
e
u
s
ed
to
f
o
r
ec
ast n
o
n
-
s
tatio
n
a
r
y
ti
m
e
s
er
ies
w
i
th
s
h
o
r
ter
tr
ain
i
n
g
p
r
o
ce
s
s
es
[
1
8
]
.
Sev
er
al
s
t
u
d
ies
w
i
th
w
av
ele
t
an
d
NN
co
m
b
i
n
atio
n
s
w
er
e
in
itiated
b
y
t
h
e
r
esear
c
h
co
m
m
u
n
it
y
o
f
w
a
v
elet
a
n
d
NN.
O
n
e
o
f
t
h
e
m
aj
o
r
p
r
o
b
lem
s
in
NN
m
o
d
el
in
g
in
t
i
m
e
s
er
ies
d
ata
i
s
th
e
n
ee
d
f
o
r
s
elec
ti
n
g
a
p
r
o
p
e
r
in
itial
d
ata
p
r
o
ce
s
s
in
g
.
T
h
e
co
m
b
in
atio
n
o
f
w
a
v
elet
s
,
as
an
i
n
itial
p
r
o
ce
s
s
i
n
g
m
e
th
o
d
an
d
NN
as
a
m
et
h
o
d
th
at
p
r
o
ce
s
s
e
s
i
n
p
u
ts
in
to
an
o
u
tp
u
t,
p
r
o
d
u
ce
s
a
h
y
b
r
id
m
o
d
el
k
n
o
w
n
as
W
a
v
ele
t
Neu
r
al
n
et
w
o
r
k
s
(
W
NN)
[
1
9
]
-
[
2
5
]
.
T
h
e
ap
p
li
ca
tio
n
o
f
t
h
e
W
NN
m
o
d
el
f
o
r
ti
m
e
s
er
ies
f
o
r
ec
asti
n
g
i
s
o
n
e
o
f
t
h
e
m
o
s
t
in
ter
esti
n
g
r
esear
ch
to
p
ics
i
n
th
e
f
ield
s
o
f
m
at
h
e
m
atic
s
,
s
tati
s
tics
,
an
d
co
m
p
u
ter
s
cie
n
ce
.
I
n
g
e
n
er
al,
W
NN
is
n
eu
r
al
n
et
w
o
r
k
s
w
i
th
w
a
v
elet
f
u
n
c
tio
n
s
u
s
ed
i
n
p
r
o
ce
s
s
i
n
g
in
tr
an
s
f
er
f
u
n
ct
io
n
s
.
I
n
t
h
e
ca
s
e
o
f
ti
m
e
s
er
ie
s
f
o
r
ec
asti
n
g
,
t
h
e
in
p
u
ts
u
s
ed
i
n
W
NN
ar
e
w
a
v
elet
co
ef
f
ic
ie
n
ts
at
a
g
iv
e
n
r
eso
l
u
tio
n
.
T
o
d
ate,
s
o
m
e
ar
ticle
s
h
av
e
b
ee
n
d
is
c
u
s
s
ed
in
d
etail
w
it
h
r
eg
ar
d
to
W
NN
m
o
d
eli
n
g
f
o
r
n
o
n
-
s
tatio
n
ar
y
t
i
m
e
s
er
ie
s
f
o
r
ec
asti
n
g
,
s
o
m
e
o
f
w
h
ich
ar
e
C
h
e
n
et
a
l
.
[
1
9
]
,
Su
b
a
n
ar
an
d
Su
h
ar
to
n
o
[
2
0
]
,
an
d
El
-
So
u
s
y
[
2
1
]
.
T
h
e
ar
ticles
u
s
e
th
e
FF
N
N
tr
ain
i
n
g
al
g
o
r
ith
m
s
o
t
h
at
th
e
r
esu
lt
in
g
m
o
d
el
is
s
p
ec
if
ica
ll
y
ca
lled
W
FF
NN.
I
n
an
o
t
h
er
h
a
n
d
,
s
o
m
e
r
esear
c
h
er
s
w
h
o
h
a
v
e
i
m
p
le
m
e
n
ted
t
h
e
h
y
b
r
id
m
et
h
o
d
b
et
w
ee
n
wav
elet
a
n
d
NN,
o
r
h
y
b
r
id
a
m
o
n
g
m
ac
h
i
n
e
lear
n
in
g
m
et
h
o
d
s
f
o
r
ti
m
e
s
er
ies
f
o
r
ec
asti
n
g
ie
B
u
n
n
o
o
n
[
2
2
]
h
as
f
o
r
ec
asted
th
e
elec
tr
icit
y
p
ea
k
lo
ad
d
e
m
an
d
,
P
o
o
r
an
i
an
d
Mu
r
u
g
an
[
2
3
]
h
av
e
f
o
r
ec
asted
th
e
r
is
i
n
g
d
em
a
n
d
f
o
r
elec
tr
ic
v
eh
ic
les
ap
p
licab
le
to
I
n
d
ian
r
o
ad
co
n
d
itio
n
s
,
Ka
m
le
y
,
et
a
l
.
[2
4
]
h
av
e
m
ea
s
u
r
ed
t
h
e
p
er
f
o
r
m
an
ce
f
o
r
ec
ast
in
g
o
f
t
h
e
s
h
ar
e
m
ar
k
et,
a
n
d
th
e
e
n
ab
lin
g
e
x
ter
n
al
f
ac
to
r
s
f
o
r
i
n
f
latio
n
r
ate
f
o
r
ec
asti
n
g
w
er
e
c
o
n
d
u
cted
b
y
Sar
i,
et
al
.
[
2
5
]
.
I
n
th
e
p
r
ev
io
u
s
h
y
b
r
id
m
et
h
o
d
s
t
h
at
w
er
e
n
o
t
a
h
y
b
r
id
b
et
w
ee
n
w
a
v
elet
a
n
d
R
B
FNN.
B
o
th
i
n
B
u
r
n
o
o
n
[
2
2
]
,
an
d
in
P
o
o
r
an
i&
M
u
r
u
g
a
n
[
2
3
]
co
m
b
i
n
ed
b
et
w
ee
n
w
a
v
elet
an
d
FF
NN,
m
ea
n
w
h
i
le
b
o
th
in
Ka
m
le
y
,
et
a
l
.
[
2
4
]
an
d
in
Sar
i,
et
a
l
.
[
2
5
]
c
o
m
b
i
n
ed
b
et
w
ee
n
NN,
an
d
f
u
zz
y
i
n
f
er
en
ce
s
s
y
s
te
m
.
F
u
r
th
er
m
o
r
e,
m
o
d
eli
n
g
th
e
h
y
b
r
id
b
et
w
ee
n
w
a
v
elet
a
n
d
R
B
FNN
is
f
o
c
u
s
o
n
th
i
s
r
esear
ch
.
B
ased
o
n
th
e
ab
o
v
e
d
escr
ip
tio
n
th
at
ti
m
e
s
er
ie
s
d
ata
in
th
e
r
ea
l
w
o
r
ld
is
g
en
er
all
y
n
o
n
-
li
n
ea
r
an
d
n
o
n
s
tatio
n
ar
y
,
cu
r
r
e
n
tl
y
,
t
h
er
e
is
n
o
t
t
h
e
h
y
b
r
id
m
o
d
el
co
m
b
i
n
ed
b
et
w
ee
n
w
a
v
elet
an
d
R
B
FN
N
f
o
r
n
o
n
s
tatio
n
ar
y
ti
m
e
s
er
ies
f
o
r
e
ca
s
tin
g
,
s
o
t
h
is
s
t
u
d
y
p
r
o
p
o
s
es
an
d
in
v
e
s
ti
g
ates
t
h
e
p
er
f
o
r
m
an
ce
o
f
a
h
y
b
r
id
m
o
d
el
ca
l
led
w
a
v
elet
r
ad
ial
b
ases
f
u
n
ctio
n
NN
(
W
R
B
FNN
)
.
T
h
e
m
o
d
el
w
ill
b
e
co
m
p
ar
ed
its
p
er
f
o
r
m
an
ce
w
it
h
th
e
W
FF
N
N
m
o
d
el
b
y
d
ev
elo
p
ed
a
f
o
r
ec
ast
in
g
s
y
s
te
m
th
at
co
n
s
id
er
s
t
w
o
t
y
p
es
o
f
i
n
p
u
t
f
o
r
m
at
s
:
i
n
p
u
t9
an
d
in
p
u
t1
7
in
o
r
d
er
to
in
v
es
tig
ate
t
h
e
e
f
f
ec
t
o
f
t
h
e
n
u
m
b
er
o
f
in
p
u
t
s
o
n
t
h
e
m
o
d
el
p
er
f
o
r
m
a
n
ce
,
an
d
also
4
ty
p
es
o
f
n
o
n
-
s
tatio
n
ar
y
d
at
asets
w
it
h
d
if
f
er
e
n
ce
p
atter
n
an
d
ch
ar
ac
ter
is
tic
t
h
at
p
o
p
u
la
r
l
y
d
is
cu
s
s
ed
in
t
h
e
n
o
n
li
n
ea
r
ti
m
e
s
er
ies li
ter
atu
r
e
as c
ase
s
t
u
d
ies.
2.
M
A
X
I
M
A
L
O
V
E
R
L
A
P
D
I
S
C
R
E
T
W
A
V
E
L
E
T
T
R
A
N
S
F
R
O
M
(
M
O
D
W
T
)
Su
p
p
o
s
e
th
er
e
i
s
a
ti
m
e
s
er
ie
s
d
ata
x
,
s
ize
N,
t
h
e
n
th
e
M
ODW
T
tr
an
s
f
o
r
m
w
ill
p
r
o
d
u
c
e
a
co
lu
m
n
v
ec
to
r
w
1
,
w
2
,
.
.
.
,
w
Jo
an
d
v
Jo
ea
ch
o
f
t
h
e
m
is
N.
T
h
e
v
ec
to
r
co
n
tain
s
th
e
M
ODW
T
w
av
el
et
co
ef
f
ic
ien
t,
w
h
ile
w
Jo
co
n
tai
n
s
t
h
e
s
ca
le
co
ef
f
ici
en
t.
T
h
e
MO
DW
T
w
a
v
elet
f
il
ter
{
̃
}
is
o
b
tai
n
ed
t
h
r
o
u
g
h
̃
⁄
an
d
t
h
e
MO
DW
T
s
ca
le
*
̃
+
o
b
tain
ed
th
r
o
u
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̃
⁄
.
T
h
u
s
t
h
e
co
n
d
itio
n
o
f
a
MO
DW
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w
av
e
let
f
il
ter
m
u
s
t
s
atis
f
y
th
e
f
o
llo
w
in
g
eq
u
at
io
n
[
9
]
:
∑
̃
∑
̃
⁄
∑
̃
̃
(
1
)
Si
m
i
lar
l
y
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t
h
e
s
ca
le
f
ilter
m
u
s
t
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f
y
t
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f
o
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w
in
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eq
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n
:
∑
̃
∑
̃
⁄
∑
̃
̃
(
2
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W
h
er
e
(
⁄
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tr
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h
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in
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af
ter
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n
th
e
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ase
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d
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5
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2
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O
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o
f
WRB
F
NN
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ll f
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d
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B
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Hea
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Stati
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n
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let
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t
h
e
r
esear
ch
.
RE
F
E
R
E
NC
E
S
[1
]
H.
T
o
n
g
,
“
No
n
-
li
n
e
a
r
T
ime
S
e
rie
s: A
D
y
n
a
m
i
c
a
l
S
y
ste
m
s
A
p
p
ro
a
c
h
”
,
Ox
f
o
rd
Un
iv
e
rsity
P
re
ss
.
Ox
fo
rd
.
1
9
9
0
.
[2
]
P
.
J.
Bro
c
k
w
e
ll
,
a
n
d
R.
A
.
Da
v
is
,
"
No
n
sta
ti
o
n
a
ry
a
n
d
se
a
so
n
a
l
ti
m
e
se
ries
m
o
d
e
ls
"
,
In
tro
d
u
c
ti
o
n
t
o
T
ime
S
e
rie
s
a
n
d
Fo
re
c
a
stin
g
,
S
p
rin
g
e
r
In
tern
a
ti
o
n
a
l
P
u
b
li
sh
i
n
g
,
2
0
1
6
,
p
p
.
1
5
7
-
1
9
3
.
[3
]
N.E
.
Hu
a
n
g
,
e
t
a
l
.
,
"
T
h
e
e
m
p
iri
c
a
l
m
o
d
e
d
e
c
o
m
p
o
siti
o
n
a
n
d
th
e
Hilb
e
rt
sp
e
c
tru
m
f
o
r
n
o
n
li
n
e
a
r
a
n
d
n
o
n
-
sta
ti
o
n
a
ry
ti
m
e
se
ries
a
n
a
l
y
sis
"
,
Pro
c
e
e
d
in
g
s
o
f
th
e
Ro
y
a
l
S
o
c
iety
o
f
L
o
n
d
o
n
A:
ma
th
e
ma
ti
c
a
l,
p
h
y
sic
a
l
a
n
d
e
n
g
i
n
e
e
rin
g
sc
ien
c
e
s
,
T
h
e
Ro
y
a
l
S
o
c
iet
y
,
v
o
l.
4
5
4
,
no
.
1
9
7
1
,
1
9
9
8
.
[4
]
C.
V
e
las
c
o
,
"
G
a
u
ss
i
a
n
S
e
m
ip
a
ra
m
e
tri
c
Esti
m
a
ti
o
n
o
f
No
n
-
sta
ti
o
n
a
r
y
T
i
m
e
S
e
rie
s"
,
J
o
u
rn
a
l
o
f
T
im
e
S
e
rie
s A
n
a
lys
is
,
v
o
l.
20
,
n
o
.
1
,
1
9
9
9
,
p
p
.
87
-
1
2
7
.
[5
]
J.
F
a
n
a
n
d
Q.
Ya
o
,
“
No
n
li
n
e
a
r
T
i
m
e
S
e
ries
:
n
o
n
p
a
ra
m
e
tri
c
a
n
d
p
a
ra
m
e
tri
c
m
e
th
o
d
s
”
,
S
p
rin
g
e
r
-
V
e
rl
a
g
,
Ne
w
Yo
rk
,
2
0
0
3
.
[6
]
S
.
Ha
n
d
o
y
o
,
e
t
a
l
.
,
“
I
m
p
le
m
e
n
tatio
n
Of
P
a
rti
c
le S
w
a
r
m
Op
ti
m
iz
a
ti
o
n
(
P
so
)
A
lg
o
rit
h
m
F
o
r
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m
a
ti
n
g
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a
ra
m
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ter
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f
A
r
m
a
M
o
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l
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ia
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m
u
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h
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d
M
e
th
o
d
”
,
F
a
r
Ea
st
J
o
u
r
n
a
l
o
f
M
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t
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ma
ti
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c
ien
c
e
s
,
vol
.
1
0
2
,
n
o
.
7
,
2
0
1
7
,
p
p
.
1
3
3
7
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3
6
3
.
[7
]
C.
K.
P
e
n
g
,
e
t
a
l
.
,
"
Qu
a
n
ti
f
ica
ti
o
n
o
f
sc
a
li
n
g
e
x
p
o
n
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n
ts
a
n
d
c
ro
ss
o
v
e
r
p
h
e
n
o
m
e
n
a
in
n
o
n
sta
ti
o
n
a
r
y
h
e
a
rtb
e
a
t
ti
m
e
se
ries
"
,
Ch
a
o
s: A
n
In
ter
d
isc
i
p
li
n
a
ry
J
o
u
rn
a
l
o
f
No
n
li
n
e
a
r S
c
ien
c
e
,
v
o
l.
5
,
no
.
1
,
1
9
9
5
,
p
p
.
82
-
87.
[8
]
S
.
P
o
o
ra
n
i
,
a
n
d
R.
M
u
r
u
g
a
n
,
"
A
No
n
-
L
in
e
a
r
Co
n
tro
ll
e
r
f
o
r
F
o
re
c
a
stin
g
th
e
Risin
g
De
m
a
n
d
f
o
r
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e
c
tri
c
V
e
h
icle
s
A
p
p
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c
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b
le
to
I
n
d
ian
Ro
a
d
Co
n
d
it
io
n
s"
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
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e
c
trica
l
a
n
d
Co
mp
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ter
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n
g
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.
6
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5
,
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0
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6
,
p
p
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2
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7
4
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1
.
[9
]
A
.
Bru
c
e
a
n
d
H.Y.
G
a
o
,
“
A
p
p
li
e
d
W
a
v
e
let
A
n
a
l
y
sis
w
it
h
S
-
P
L
US
”
,
S
p
ri
n
g
e
r
-
V
e
rlag
,
Ne
w
Yo
rk
,
US
A
,
1
9
9
6
.
[1
0
]
L
.
De
b
n
a
th
,
“
W
a
v
e
let
T
ra
n
s
f
o
rm
a
n
d
T
h
e
ir
A
p
p
li
c
a
ti
o
n
”
,
Birk
h
h
a
u
se
r,
Bo
sto
n
,
2
0
0
2
.
[1
1
]
H.
S
a
b
ro
l,
a
n
d
S
.
K
u
m
a
r
,
"
Re
c
o
g
n
it
io
n
o
f
T
o
m
a
to
L
a
te
Bli
g
h
t
b
y
u
sin
g
DWT
a
n
d
Co
m
p
o
n
e
n
t
A
n
a
ly
sis
"
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
7
,
n
o
.
1
,
2
0
1
7
,
p
p
.
1
9
4
-
1
9
9
.
[1
2
]
V
.
A
.
Ku
m
a
r,
C.
Dh
a
rm
a
ra
j,
a
n
d
C.
S
.
Ra
o
,
"
A
H
y
b
rid
Dig
it
a
l
W
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ter
m
a
rk
in
g
A
p
p
ro
a
c
h
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in
g
W
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v
e
lets
a
n
d
L
S
B"
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
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lec
trica
l
a
n
d
C
o
mp
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ter
En
g
in
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rin
g
,
V
o
l
.
7
,
N
o
.
5
,
2
0
1
7
,
p
p
.
2
4
8
3
-
2
4
9
5
.
[1
3
]
S.
S
o
lt
a
n
i
,
"
On
th
e
u
se
o
f
th
e
w
a
v
e
let
d
e
c
o
m
p
o
siti
o
n
f
o
r
ti
m
e
se
ri
e
s
p
re
d
ictio
n
"
,
Ne
u
ro
c
o
mp
u
ti
n
g
,
V
o
l
.
48
,
No
.1
,
2
0
0
2
,
p
p
.
2
6
7
-
2
7
7
.
[1
4
]
O.
Re
n
a
u
d
,
J.L
.
S
tark
,
a
n
d
F
.
M
u
rtag
h
,
“
P
re
d
icti
o
n
Ba
se
d
o
n
M
u
lt
isc
a
le
De
c
o
m
p
o
siti
o
n
”,
In
t.
J
o
u
rn
a
l
o
f
W
a
v
e
lets,
M
u
lt
ire
so
lu
ti
o
n
a
n
d
I
n
fo
rm
a
ti
o
n
Pro
c
e
ss
i
n
g
,
v
o
l
.
1
, n
o
.
2
,
2
0
0
3
,
p
p
.
2
1
7
-
2
3
2
.
[1
5
]
L
.
F
a
u
se
tt
,
“
Fo
u
n
d
a
me
n
ta
ls
o
f
Ne
u
ra
l
Ne
two
rk
s:
Arc
h
it
e
c
tu
re
,
Al
g
o
rit
h
m,
a
n
d
Ap
p
li
c
a
t
io
n
”
,
F
l
o
rid
a
In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
,
P
re
n
ti
c
e
Ha
ll
In
c
.
E
n
g
lew
o
o
d
s Cli
f
fs,
Ne
w
Je
rse
y
,
1
9
9
4
.
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