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70
60
2.
RE
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Gab
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Har
alick
f
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em
e.
2
.
1
.
W
a
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:
a
s
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a
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t
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A
n
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p
o
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th
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itu
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tili
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co
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is
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T
h
e
g
r
ain
m
ater
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h
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A
p
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it
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h
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s
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ch
ar
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h
av
e
u
n
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ities
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wh
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ter
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r
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en
t
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m
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lti
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in
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(
MRA)
m
eth
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d
[
4
]
,
[
5
]
.
T
h
e
r
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te
wav
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ch
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g
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MRA
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m
is
s
b
r
an
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th
e
ir
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d
u
p
licate
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n
alik
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p
o
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itio
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in
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an
q
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is
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in
g
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a
n
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te
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m
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lti
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pe
r
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ten
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t
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m
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ate
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T
h
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im
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ly
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I
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ag
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if
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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Sy
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I
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N:
2089
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4
8
6
4
To
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A
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61
in
d
icato
r
f
o
n
to
th
e
p
lan
etar
y
V
J
;
in
th
eo
r
y
b
y
with
d
r
awin
g
t
h
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s
ca
lar
p
r
o
d
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ce
s
.
T
h
e
p
r
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u
r
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ec
k
less
an
d
h
as
a
lo
w
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m
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ac
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e
ass
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ly
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d
ap
ts
th
e
ass
em
b
lies
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y
ield
its
ir
is
p
ie
ce
co
d
es
[
6
]
,
[
7
]
.
I
n
d
ir
ec
t
d
iv
is
io
n
d
is
en
g
ag
ed
wa
v
elet
tr
an
s
m
u
te
[
8
]
–
[
1
3
]
.
T
h
e
p
ictu
r
e
ar
e
ess
en
tially
d
is
in
teg
r
ated
i.e
.
,
s
ep
a
r
ated
in
to
f
o
u
r
s
u
b
-
b
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d
s
an
d
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n
s
y
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p
ath
etica
lly
s
u
b
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s
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p
led
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s
m
ea
r
in
g
d
etac
h
ed
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elet
co
n
v
er
t
as
ex
p
o
s
ed
i
n
Fig
u
r
e
2
.
T
h
ese
s
u
b
-
b
a
n
d
s
b
r
an
d
ed
L
H
1
,
HL
1
,
an
d
HH
1
d
is
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g
u
is
h
th
e
s
u
p
r
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ea
s
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r
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asp
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t p
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es wh
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s
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s
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b
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d
L
L
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o
k
lik
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ev
alu
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e.
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r
d
s
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ain
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atch
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d
L
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n
aid
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r
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m
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n
ted
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d
f
r
o
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l
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ated
.
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h
e
s
e
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r
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in
two
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d
is
in
teg
r
atio
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s
h
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w
n
in
Fig
u
r
e
2
(
b
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.
C
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r
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L
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tan
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o
n
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h
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d
[
1
4
]
.
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h
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ically
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aten
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s
tr
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ctu
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I
n
a
d
d
itio
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r
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s
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p
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ices
in
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o
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o
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en
t
s
tr
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th
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s
em
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les
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is
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ctiv
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ex
p
lain
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n
s
is
ten
cy
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T
h
e
s
tr
u
ctu
r
es
g
r
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wn
af
te
r
th
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eh
ab
ilit
ated
im
ag
es a
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s
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e
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ed
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o
r
co
n
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ten
cy
tag
g
in
g
[
1
5
]
–
[
1
7
]
.
Fig
u
r
e
2
.
T
wo
l
ev
el
d
ec
o
m
p
o
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n
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y
u
s
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g
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is
cr
ete
wav
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an
s
f
o
r
m
f
o
r
(
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n
ew
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g
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,
(
b
)
f
ir
s
t sectio
n
b
r
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k
d
o
wn
,
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d
(
c)
s
ec
o
n
d
s
e
ctio
n
b
r
ea
k
d
o
wn
[
1
8
]
2
.
2
.
F
a
s
t
wa
v
elet
t
r
a
ns
f
o
rm
T
h
e
f
ast
wav
elet
tr
an
s
f
o
r
m
(
FW
T
)
is
m
ath
em
atica
l
wh
ich
is
tech
n
iq
u
e
p
lan
n
ed
f
o
r
th
e
s
ig
n
al
o
r
wav
e.
I
n
th
e
tim
e
r
an
g
e
,
it
will
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n
v
er
t
o
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s
ess
ed
b
y
a
s
eq
u
en
ce
o
f
m
ea
s
u
r
em
e
n
ts
co
n
s
tr
u
cted
s
ch
ed
u
led
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o
r
th
o
g
o
n
al
b
asis
o
f
s
m
all
f
in
ite
wav
es
o
r
wa
v
elets
.
T
h
e
co
n
v
er
t
ca
n
b
e
ef
f
o
r
tles
s
ly
p
r
o
tr
ac
ted
t
o
m
u
lti
-
d
im
en
s
io
n
al
s
ig
n
als
s
u
c
h
as
p
ictu
r
es.
T
h
is
alg
o
r
ith
m
w
as
p
r
esen
ted
in
[
1
9
]
,
h
y
p
o
th
etica
l
b
ase
o
f
th
is
alg
o
r
ith
m
is
to
p
r
o
d
u
ce
th
e
o
r
th
o
g
o
n
al
MRA
f
in
itely
.
T
h
e
Ma
llat
alg
o
r
ith
m
is
a
n
av
er
a
g
e
m
eth
o
d
f
o
r
d
is
tin
ct
wav
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n
v
er
t
wh
ic
h
is
b
r
an
d
ed
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two
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ch
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n
n
el
s
u
b
-
g
r
o
u
p
co
d
e
r
.
T
h
e
r
ef
o
r
e,
th
is
co
n
v
er
s
io
n
co
m
p
r
is
es
o
f
two
p
ar
ts
as
[
2
0
]
:
i)
T
h
e
d
is
in
teg
r
atio
n
p
r
o
ce
d
u
r
e
ju
m
p
s
with
s
ig
n
al
s
,
n
ex
t
d
eter
m
in
es
th
e
h
ar
m
o
n
izes
o
f
A
1
an
d
D
1
an
d
b
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o
r
e
p
er
s
o
n
s
o
f
A
2
an
d
D
2
an
d
s
o
o
n
an
d
ii)
T
h
e
r
en
ewa
l
tech
n
iq
u
e
ca
lled
t
h
e
in
v
er
s
e
d
etac
h
ed
wav
elet
tr
an
s
f
o
r
m
s
tar
ts
f
r
o
m
th
e
m
a
n
ag
es
o
f
A
J
a
n
d
D
J
n
ex
t
d
eter
m
in
es
th
e
o
r
g
a
n
iz
es
o
f
A
J
–
1
an
d
th
e
n
co
m
p
lete
th
e
s
y
n
ch
r
o
n
izes
o
f
A
J
–
1
an
d
D
J
–
1
an
aly
s
es
in
d
iv
id
u
als
o
f
A
J
–
2
an
d
s
o
o
n
[
2
1
]
.
I
n
th
e
m
u
lti
-
d
eter
m
in
atio
n
a
g
en
d
a,
an
o
r
th
o
g
o
n
al
wav
elet
twitch
es
th
r
o
u
g
h
th
e
ascen
d
in
g
task
φ
th
en
t
h
e
wav
elet
p
u
r
p
o
s
e
ψ.
On
e
o
f
th
e
ess
en
tial
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s
tan
d
s
th
e
id
en
tical
-
r
u
ler
r
elativ
e
wh
ich
is
d
ef
in
ed
i
n
(
1
)
an
d
t
h
e
wav
elet
f
u
n
ctio
n
is
in
(
2
)
as
[
2
2
]
,
[
2
3
]
.
ϕ
(
)
=
∑
(
ϕ
(
2
−
)
=
−
)
(
1
)
ψ
(
)
=
∑
(
(
−
1
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1
−
ψ
(
2
−
)
)
=
−
(
2
)
Alto
g
eth
er
th
e
f
ilter
s
u
s
ed
in
d
is
s
im
ilar
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elet
co
n
v
er
t
an
d
in
v
er
s
e
d
is
tin
ct
wav
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tially
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ciate
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s
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(
3
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[
2
4
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(
)
∈
(
3
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Ob
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φ
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im
ly
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r
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ate
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eg
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ilter
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ain
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ich
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ca
lle
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th
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m
e
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el
o
n
g
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g
s
s
u
ch
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ix
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o
m
p
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ls
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n
r
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F
C
R
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,
d
is
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ce
2
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am
o
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ar
d
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r
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o
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N
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d
o
f
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r
m
1
eq
u
ip
p
ed
as u
n
p
r
o
tect
ed
in
Fig
u
r
e
3
[
2
5
]
–
[
2
7
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
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62
Fig
u
r
e
3.
Ho
w
t
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m
p
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te
f
o
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r
f
ilter
s
Ass
u
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ed
a
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ig
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o
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d
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e
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e
d
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elet
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ts
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m
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r
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o
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at
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ig
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I
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ir
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t
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ets
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io
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:
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p
r
o
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am
o
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n
ts
cA
1
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d
f
ea
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r
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n
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m
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er
s
cD
1
.
T
h
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tr
ajec
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ar
e
p
r
o
l
o
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g
e
d
b
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n
v
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lv
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n
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th
r
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u
g
h
th
e
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w
-
p
ass
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tr
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er
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o
r
ca
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latio
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d
with
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e
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ig
h
-
p
ass
s
tr
ain
er
f
o
r
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r
e
ar
e
m
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ito
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ed
b
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d
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Ad
d
itio
n
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r
atel
y
th
e
f
ir
s
t step
is
s
h
o
w
n
in
Fig
u
r
e
4
[
2
8
]
,
[
2
9
]
.
Fig
u
r
e
4.
First p
h
ase
o
f
d
is
cr
et
e
wav
elet
tr
an
s
f
o
r
m
T
h
e
ex
ten
t
o
f
ev
e
r
y
s
tr
ain
er
is
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tical
to
2
L
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T
h
e
p
r
o
d
u
ct
o
f
co
n
v
o
lv
in
g
a
d
im
e
n
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io
n
N
in
d
icato
r
with
a
d
im
en
s
io
n
2
L
f
ilter
is
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2
L
–
1
.
Hen
ce
,
th
e
in
d
icato
r
s
F
an
d
G
ar
e
o
f
m
ea
s
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r
e
m
en
t
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2
L
–
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.
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ater
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o
wn
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n
b
y
2
,
th
e
c
o
n
s
tan
t
v
ec
to
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s
cA
1
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d
cD
1
ar
e
o
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⌊
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1
2
+
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.
T
h
en
s
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cc
ee
d
in
g
s
tep
s
p
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th
e
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u
m
b
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r
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cA
1
in
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o
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co
n
s
u
m
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g
th
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s
am
e
ar
r
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g
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en
t
tr
a
n
s
ac
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n
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by
cA
1
an
d
m
an
u
f
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tu
r
in
g
cA
2
a
n
d
cD
2
w
h
ich
d
is
p
lay
s
in
Fig
u
r
e
5
[
3
0
]
,
[
3
1
]
.
Fig
u
r
e
5
.
1
-
D
s
ep
ar
ate
wav
ele
t tr
an
s
f
o
r
m
f
o
r
d
is
in
teg
r
atio
n
s
tag
e
E
q
u
ally
,
p
r
elim
in
ar
y
f
r
o
m
cA
j
an
d
cD
j
th
e
o
p
p
o
s
ite
d
is
co
n
n
ec
ted
wav
elet
co
n
v
er
t
r
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o
v
ates
cA
j
–
1
,
u
p
s
ettin
g
th
e
d
ec
o
m
p
o
s
itio
n
p
h
ase
th
r
o
u
g
h
im
p
lan
tin
g
ze
r
o
s
a
n
d
co
n
v
o
lv
in
g
th
e
c
o
n
s
eq
u
e
n
ce
s
b
y
t
h
e
r
eb
u
ild
in
g
f
ilter
s
[
3
2
]
.
Fig
u
r
e
6
s
h
o
ws th
e
r
en
o
v
atio
n
s
tep
o
f
1
-
D
s
ep
ar
ate
wav
elet
tr
an
s
f
o
r
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
R
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f
ig
u
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a
b
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&
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4
To
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63
Fig
u
r
e
6.
1
-
D
d
is
cr
ete
wav
elet
tr
an
s
f
o
r
m
f
o
r
r
en
o
v
atio
n
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ase
On
b
eh
al
f
o
f
i
m
ag
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a
co
m
p
ar
ab
le
alg
o
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ith
m
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o
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ce
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ab
le
f
o
r
2
-
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wav
elets
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d
ascen
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g
m
ea
n
in
g
s
in
cr
ea
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ed
af
ter
1
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D
wav
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b
y
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s
o
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ial
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n
s
tr
u
ctio
n
.
T
h
is
g
en
er
o
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s
o
f
2
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D
d
is
cr
ete
wav
elet
co
n
v
er
ts
in
d
icatio
n
s
to
a
p
u
tr
e
f
ac
tio
n
o
f
esti
m
ate
q
u
a
n
titi
es
at
eq
u
al
j
in
f
o
u
r
wo
r
k
i
n
g
s
:
th
e
ev
alu
atio
n
at
lev
el
j
+1
an
d
th
e
d
etails
in
th
r
ee
alig
n
m
en
ts
s
u
ch
as
s
tr
aig
h
t,
u
p
r
ig
h
t
an
d
d
iag
o
n
al
[
3
3
]
.
T
h
e
d
is
cr
ete
wav
elet
tr
an
s
m
u
te
o
f
a
d
is
cr
ete
s
ig
n
al
=
[
[
0
]
,
…
,
[
−
1
]
]
is
th
e
p
r
o
ce
s
s
o
f
g
ettin
g
th
e
c
o
ef
f
icien
ts
as
in
(
4
)
an
d
(
5
)
[
3
4
]
.
[
0
,
]
=
1
√
∑
[
]
0
,
[
]
−
1
=
0
=
1
√
∑
[
]
2
0
/
2
[
2
0
−
]
−
1
=
0
,
∀
(
4
)
[
,
]
=
1
√
∑
[
]
,
[
]
−
1
=
0
=
1
√
∑
[
]
2
/
2
[
2
−
]
−
1
=
0
,
∀
>
0
(
5
)
W
h
ile
th
e
s
o
u
r
ce
s
ca
lin
g
an
d
wav
elet
m
ea
n
in
g
s
ar
e
c
o
r
r
esp
o
n
d
in
g
l
y
f
o
r
m
u
lated
i
n
(
6
)
as m
o
n
ito
r
s
[
3
5
]
.
{
,
[
]
=
2
/
2
[
2
−
]
,
[
]
=
2
/
2
[
2
−
]
(
6
)
R
em
em
b
er
th
at
b
o
t
h
th
e
s
cr
a
b
b
lin
g
a
n
d
wav
elet
m
ea
n
in
g
s
ca
n
b
e
p
r
o
lo
n
g
ed
i
n
ter
m
s
o
f
b
asis
m
o
u
n
tin
g
p
u
r
p
o
s
es o
f
th
e
n
e
x
t h
ig
h
e
r
p
u
r
p
o
s
e
wh
ich
s
h
o
ws in
(
7
)
as
[
3
5
]
,
[
3
6
]
.
{
[
]
=
∑
ℎ
[
]
√
2
[
2
−
]
[
]
=
∑
ℎ
[
]
√
2
[
2
−
]
(
7
)
C
u
r
r
en
tly
s
ee
in
g
th
e
alg
o
r
ith
m
as
a
wild
o
r
ig
i
n
atio
n
to
g
e
t
th
e
co
n
s
tan
ts
[
,
]
an
d
[
,
]
o
f
d
if
f
er
en
t
s
ca
les
j.
C
o
n
s
id
er
f
ir
s
t
th
e
clim
b
in
g
f
u
n
ctio
n
[
]
.
T
r
ad
in
g
m
b
y
2
−
(
s
ca
led
b
y
2
an
d
d
ec
r
y
p
ted
b
y
k
)
,
th
en
th
e
m
o
u
n
tin
g
f
u
n
ctio
n
d
ev
elo
p
s
lik
e
in
(
8
)
[
3
7
]
,
[
3
8
]
.
[
2
−
]
=
∑
ℎ
[
]
√
2
[
2
(
2
−
)
−
]
=
∑
ℎ
[
]
√
2
[
2
+
1
−
2
−
]
(
8
)
No
w
th
e
r
ep
lace
m
en
t
o
f
n
=2
k
+l a
n
d
l=n
-
2k
,
th
en
(
8
)
b
ec
o
m
es ju
s
t a
s
(
9
)
[
3
8
]
.
[
2
−
]
=
∑
ℎ
[
−
2
]
√
2
[
2
+
1
−
]
(
9
)
L
ik
ew
is
e,
th
e
wav
elet
p
u
r
p
o
s
e
ca
n
also
b
e
lo
n
g
-
d
r
awn
-
o
u
t ju
s
t a
s
in
(
10
)
[
3
9
]
.
[
2
−
]
=
∑
ℎ
[
−
2
]
√
2
[
2
+
1
−
]
(
1
0
)
T
h
is
wav
elet
p
u
r
p
o
s
e
wh
ich
lab
ele
d
in
(
10
)
is
in
d
is
tin
g
u
is
h
ab
le
to
th
e
u
n
iq
u
e
s
ec
o
n
d
h
an
d
in
c
o
m
p
ar
is
o
n
5
.
So
,
s
u
p
er
n
u
m
er
ar
y
(
10
)
in
to
(
5
)
th
en
it c
o
n
v
e
r
ts
lik
e
(
11
)
[
4
0
]
.
[
,
]
:
1
√
∑
[
]
2
2
[
2
−
]
−
1
=
0
=
1
√
∑
[
]
2
2
[
∑
ℎ
[
−
2
]
√
2
[
2
+
1
−
]
]
−
1
=
0
:
∑
ℎ
[
−
2
]
[
1
√
∑
[
]
2
(
+
1
)
/
2
(
2
+
1
−
)
−
1
=
0
]
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
11
,
No
.
1
,
M
ar
c
h
20
22
:
59
-
70
64
T
h
e
ap
p
ea
r
an
ce
1
√
∑
[
]
2
(
+
1
)
/
2
(
2
+
1
−
)
−
1
=
0
m
ater
ializes
to
b
e
th
e
wav
elet
ch
a
n
g
e
f
o
r
t
h
e
q
u
a
n
tity
o
f
s
ca
le
j+1
in
(
12
)
[
4
1
]
.
[
+
1
,
]
=
1
√
∑
[
]
2
(
+
1
)
/
2
(
2
+
1
−
)
−
1
=
0
(
1
2
)
C
o
n
s
eq
u
en
tly
,
a
r
ec
u
r
s
iv
e
r
ela
tio
n
am
o
n
g
t
h
e
wav
elet
tr
a
n
s
f
o
r
m
s
co
n
s
tan
ts
o
f
two
u
n
in
ter
r
u
p
ted
s
ca
le
h
ei
g
h
ts
j
an
d
j+1
s
h
o
wn
in
(
13
)
a
n
d
t
h
e
s
im
ilar
is
tr
u
e
to
th
e
m
o
u
n
tin
g
m
ea
n
in
g
wh
ich
is
also
ex
p
o
s
ed
in
(
14
)
[
3
9
]
–
[
4
1
]
.
[
,
]
=
∑
ℎ
[
−
2
]
[
+
1
,
]
(
1
3
)
[
,
]
=
∑
ℎ
[
−
2
]
[
+
1
,
]
(
1
4
)
On
ce
ass
o
ciatin
g
(
13
)
an
d
(
14
)
with
a
d
is
cr
ete
d
if
f
icu
lty
t
h
en
we
g
et
th
e
co
n
s
eq
u
en
ce
as
a
f
o
r
m
o
f
(
15
)
as
[
4
2
]
–
[
4
4
]
.
[
]
=
ℎ
[
]
∗
[
]
=
∑
ℎ
[
−
]
[
]
(
1
5
)
Acc
o
r
d
in
g
ly
,
th
e
wav
elet
r
e
n
o
v
ate
co
n
s
tan
ts
[
,
]
an
d
[
,
]
at
th
e
j
th
s
ca
le
ca
n
is
ter
s
tan
d
attain
ed
f
r
o
m
th
e
q
u
a
n
titi
es
[
+
1
,
]
an
d
[
+
1
,
]
at
th
e
(
j+1
)
th
s
ca
le
b
y
t
wo
b
elo
n
g
i
n
g
s
s
u
ch
as
co
m
p
licatio
n
with
tim
e
r
e
v
e
r
s
ed
ℎ
o
r
ℎ
an
d
s
u
b
-
s
am
p
lin
g
to
g
et
ev
er
y
o
th
e
r
illu
s
tr
atio
n
s
in
th
e
co
n
v
o
l
u
tio
n
.
T
h
er
e
f
o
r
e,
wav
e
l
et
tr
an
s
m
u
te
an
d
s
ca
lin
g
m
ea
n
in
g
will
b
ec
o
m
e
th
e
s
h
ap
e
as
g
iv
en
in
(
16
)
as
[
4
5
]
,
[
4
6
]
.
{
[
,
]
=
ℎ
[
−
]
∗
[
+
1
,
]
|
=
2
,
≤
0
[
,
]
=
ℎ
[
−
]
∗
[
+
1
,
]
|
=
2
,
≤
0
(
1
6
)
C
r
ea
ted
o
n
(
16
)
,
all
wa
v
elet
th
en
s
cr
ab
b
lin
g
n
u
m
b
e
r
s
[
,
]
an
d
[
,
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o
f
a
a
g
r
ee
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in
d
icatio
n
X
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n
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tten
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ec
u
r
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iv
ely
f
r
o
m
th
e
co
n
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tan
ts
[
,
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d
[
,
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at
th
e
h
ig
h
est
d
eter
m
in
atio
n
le
v
el
j=J
with
all
co
n
ce
n
tr
ated
in
f
o
r
m
at
io
n
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d
t
h
e
N
d
ata
p
o
in
ts
[
]
(
=
0
,
…
,
−
1
)
s
tr
ai
g
h
t
tr
ied
af
ter
t
h
e
s
ig
n
al
(
)
.
As
a
n
ass
o
ciate
o
f
s
p
ac
e
,
th
ese
s
ep
ar
ate
s
am
p
les
ca
n
b
e
wr
itten
as
a
r
ec
tili
n
ea
r
m
i
x
tu
r
e
o
f
th
e
clim
b
in
g
s
o
u
r
ce
p
u
r
p
o
s
es
,
[
]
wh
i
ch
s
h
o
ws in
(
17
)
as
[
4
7
]
,
[
4
8
]
.
Fig
u
r
e
7
p
r
esen
t w
av
elet
tr
an
s
f
o
r
m
.
Fig
u
r
e
7
.
Diag
r
a
m
o
f
f
ast wa
v
elet
tr
an
s
f
o
r
m
with
its
o
p
er
ati
o
n
al
[
4
9
]
2
.
3
.
G
a
bo
r
f
ilte
r
In
im
ag
e
p
r
o
ce
s
s
in
g
a
Gab
o
r
f
ilter
is
a
lin
ea
r
f
ilter
u
s
ed
f
o
r
tex
tu
r
e
an
aly
s
is
.
As
a
lin
e
ar
f
ilter
,
it
r
ef
lects th
e
ac
co
u
n
t a
s
m
o
n
ito
r
s
:
[
(
)
→
(
)
]
Su
b
ject
to
lin
ea
r
ity
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
ec
o
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
To
w
a
r
d
s
mo
r
e
a
cc
u
r
a
te
ir
is
r
e
co
g
n
itio
n
s
ystem
b
y
u
s
in
g
h
yb
r
id
a
p
p
r
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ch
fo
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fea
tu
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… (
A
r
if Ulla
h
)
65
W
h
er
e
lin
ea
r
ity
is
a
s
tu
f
f
w
h
ich
r
ev
e
n
u
es
th
at
it
ca
n
b
e
ex
p
licitly
ch
a
r
ac
ter
ized
as
a
tr
ad
itio
n
al
lin
e.
C
o
n
f
er
r
in
g
to
th
e
lin
ea
r
f
u
n
ctio
n
f(
x)
th
at
f
u
n
ctio
n
m
u
s
t
in
d
u
lg
es
th
e
two
ef
f
ec
ts
.
First
p
r
o
p
er
t
y
is
th
e
co
n
s
er
v
in
g
s
tu
f
f
as
{
(
+
)
=
(
)
+
(
)
}
an
d
th
e
s
ec
o
n
d
is
eq
u
ality
o
f
d
eg
r
ee
1
wh
ich
is
{
(
)
=
(
)
,
∀
}
[
3
8
]
.
I
t
m
o
s
tly
s
cr
u
tin
izes
wh
eth
er
n
ea
r
b
y
an
y
ex
p
licit
r
e
g
u
lar
ity
p
leased
tr
en
d
y
th
e
p
i
ctu
r
es
in
p
lain
d
ir
ec
tiv
es
in
a
co
n
s
tr
ain
ed
d
iv
is
io
n
ev
er
y
wh
er
e
th
e
th
em
e
o
r
p
itch
o
f
in
v
esti
g
atio
n
.
I
n
th
e
latitu
d
in
a
l
ar
ea
,
a
2
D
Gab
o
r
f
ilter
is
a
Ga
u
s
s
ian
K
er
n
el
f
u
n
ctio
n
alter
e
d
b
y
a
s
in
u
s
o
id
al
p
la
n
e
wav
e
.
I
t
s
im
p
u
ls
e
r
esp
o
n
s
e
is
well
-
d
ef
in
ed
b
y
a
s
in
u
s
o
id
al
wav
e
wh
ich
au
g
m
en
ted
b
y
a
Gau
s
s
ian
f
u
n
ctio
n
[
5
0
]
,
[
5
1
]
.
Owin
g
to
th
e
d
ev
elo
p
m
e
n
t
in
tr
icac
y
s
tu
f
f
,
t
h
e
tr
an
s
f
o
r
m
atio
n
o
f
a
Gab
o
r
f
ilter
'
s
o
b
lig
atio
n
r
ejo
in
d
e
r
is
th
e
co
n
v
o
lu
tio
n
o
f
th
e
ch
o
r
al
d
eter
m
in
atio
n
w
h
ich
is
id
en
tifie
d
as
s
in
u
s
o
id
al
m
ea
n
in
g
an
d
th
e
Gau
s
s
ian
f
u
n
ctio
n
.
T
h
e
f
ilter
h
as
a
m
ater
ial
an
d
a
m
ak
e
-
b
eliev
e
e
s
s
en
tial
o
n
b
e
h
alf
o
f
o
r
th
o
g
o
n
al
r
em
its
[
5
2
]
,
[
5
3
]
.
T
h
ese
t
w
o
wo
r
k
in
g
s
m
ay
b
e
d
esig
n
ed
in
to
a
m
u
ltifa
r
io
u
s
n
u
m
b
er
o
r
u
s
ed
in
d
ep
e
n
d
en
tly
.
As
a
co
m
p
lex
m
eth
o
d
o
f
Gab
o
r
f
ilter
is
ex
p
o
s
ed
in
E
q
u
iv
alen
ce
1
8
as:
(
,
;
,
,
,
,
)
=
(
−
́
2
+
2
́
2
2
2
)
(
(
2
́
+
)
)
(
1
7
)
Ma
ter
ial
an
d
in
v
e
n
ted
p
ar
ts
o
f
(
18
)
r
ev
ea
led
i
n
(
19
)
as:
{
(
,
;
,
,
,
,
)
=
(
−
́
2
+
2
́
2
2
2
)
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os
(
2
́
+
)
,
(
,
;
,
,
,
,
)
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(
−
́
2
+
2
́
2
2
2
)
s
in
(
2
́
+
)
(
1
8
)
W
h
er
e
:
-
x
=
́
x
co
s
θ+
y
s
in
θ
an
d
y
=
́
y
co
s
θ
–
x
s
in
θ
ar
e
th
e
co
m
p
o
n
en
ts
-
λ
C
h
ar
ac
ter
izes th
e
wav
elen
g
th
o
f
th
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s
in
u
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id
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in
s
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ir
atio
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Den
o
tes th
e
alig
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t o
f
t
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e
u
s
u
al
to
th
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eq
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iv
alen
t strip
es
o
f
a
Gab
o
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m
ea
n
in
g
-
ѱ
is
th
e
s
tag
e
o
f
f
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et,
is
th
e
s
tan
d
ar
d
d
e
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iatio
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o
f
th
e
Gau
s
s
ian
co
v
er
in
g
-
is
th
e
lo
n
g
itu
d
i
n
al
f
ac
et
r
elati
o
n
an
d
r
eq
u
ir
es th
e
ellip
ticity
o
f
th
e
s
u
s
ten
an
ce
o
f
th
e
Ga
b
o
r
f
u
n
ctio
n
A
f
ix
ed
o
f
Gab
o
r
f
ilter
s
wit
h
d
iv
e
r
s
e
o
cc
u
r
r
en
ce
s
a
n
d
b
ea
r
in
g
s
ca
n
s
tay
co
o
p
er
ativ
e
aim
ed
at
ex
ca
v
atin
g
c
o
n
v
e
n
ien
t
s
tr
u
ctu
r
es
af
ter
an
im
ag
e
(
Hag
h
ig
h
a
t
et
a
l
.
,
2
0
1
3
)
.
I
n
t
h
e
d
is
tin
c
t
f
ield
,
2
D
Gab
o
r
f
ilter
s
ar
e
g
iv
en
by
[
5
4
]
,
[
5
5
]
.
{
[
,
]
=
−
(
2
+
2
)
2
2
c
os
(
2
(
c
os
+
s
in
)
)
[
,
]
=
−
(
2
+
2
)
2
2
s
in
(
2
(
c
os
+
s
in
)
)
(
1
9
)
W
h
er
e
B
an
d
C
ar
e
r
eg
u
latin
g
f
ac
to
r
s
to
b
e
d
eter
m
in
e
d
,
f
d
ef
in
es
th
e
f
r
e
q
u
en
c
y
.
B
y
ch
a
n
g
in
g
is
u
s
ed
f
o
r
co
n
s
is
ten
cy
o
r
ien
tatio
n
i
n
a
ce
r
tain
b
ea
r
in
g
wh
ile
th
r
o
u
g
h
th
e
v
ar
iatio
n
o
f
,
d
is
s
im
ilar
ity
[
5
6
]
–
[
5
8
]
.
3.
E
XP
E
R
I
M
E
N
T
A
L
RE
SUL
T
S AN
D
CO
M
P
AR
I
SO
N
Ass
es
s
in
g
th
ese
p
r
esen
tatio
n
s
o
f
b
io
m
etr
ic
tec
h
n
iq
u
e
is
a
p
r
o
b
lem
atic
p
r
o
d
u
ctio
n
.
Fo
r
th
e
d
eter
m
in
atio
n
o
f
ju
d
g
m
en
t;
w
e
co
n
tr
iv
a
n
ce
th
ese
a
p
p
r
o
ac
h
e
s
in
ter
p
r
etatio
n
t
o
th
e
r
ep
r
o
d
u
ce
d
d
o
c
u
m
en
ts
.
T
o
ass
is
tan
t
th
eir
r
ec
ital,
we
ca
s
t
-
o
f
f
th
r
ee
ca
teg
o
r
ies
o
f
s
tatis
t
ics
wh
ich
ar
e
U
B
I
R
I
S,
C
ASI
A
,
an
d
MM
U.
I
r
is
d
atab
ase
co
v
er
s
2
8
0
ey
e
im
ag
es
f
r
o
m
2
8
o
b
jects
an
d
ea
ch
p
er
s
o
n
h
as
1
0
im
ag
es
o
f
ey
e.
Alto
g
eth
er
h
ea
r
in
g
s
wer
e
ac
h
iev
ed
b
y
MA
T
L
AB
v
er
s
io
n
R
2
0
1
0
b
o
n
th
e
co
r
e
p
r
o
ce
s
s
o
r
.
W
e
u
s
e
th
e
u
s
u
al
tech
n
iq
u
e
to
g
en
er
ate
an
d
n
o
r
m
alize
i
r
is
ex
ten
ts
an
d
u
s
e
th
e
am
alg
am
atio
n
o
f
th
r
ee
m
eth
o
d
s
ac
k
n
o
wled
g
ed
o
v
er
h
ea
d
to
m
i
n
e
th
e
q
u
an
tity
.
C
o
n
s
eq
u
en
tly
,
we
i
n
d
iv
id
u
al
i
n
s
p
ec
t
an
d
c
o
m
p
an
i
o
n
th
e
ex
ac
t
n
ess
an
d
co
m
p
u
ta
tio
n
al
ap
p
licatio
n
o
f
ch
in
ex
tr
ac
tio
n
.
Su
b
s
eq
u
en
tly
p
iece
co
n
s
tr
u
ct,
we
u
s
ag
e
h
y
b
r
id
class
if
ier
f
o
r
c
o
r
r
esp
o
n
d
in
g
p
er
io
d
(
i.e
)
h
ar
d
-
to
-
test
f
au
lts
(
HT
T
F
)
an
d
f
als
e
ac
ce
p
tan
ce
r
ate
(
FAR
)
/
f
alse
r
e
jectio
n
r
ate
(
FR
R
)
ar
e
u
s
ed
f
o
r
ap
p
r
aisi
n
g
th
e
o
u
tco
m
e.
4.
ACCURACY
RAT
E
O
F
PREPRO
CE
SS
S
E
C
T
I
O
N
T
h
e
p
r
ec
is
io
n
o
f
th
e
p
lan
n
e
d
tech
n
iq
u
e
is
ch
ar
te
d
in
T
a
b
le
1
s
h
o
ws
th
at
th
e
alg
o
r
ith
m
m
ec
h
an
is
m
well
ev
en
with
th
e
r
etin
al
im
ag
es
with
co
m
p
lain
ts
.
Fro
m
T
ab
le
1
,
T
a
b
le
2
an
d
Fig
u
r
e
8
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RE
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NC
E
S
[
1
]
D
.
P
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smi
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Evaluation Warning : The document was created with Spire.PDF for Python.