I
nte
rna
t
io
na
l J
o
urna
l o
f
I
nfo
r
m
a
t
ics a
nd
Co
mm
u
n
ica
t
io
n T
ec
hn
o
lo
g
y
(
I
J
-
I
CT
)
Vo
l.
3
,
No
.
2
,
Ju
ne
201
4
,
p
p
.
97
~
10
2
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SS
N:
2252
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8776
97
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h
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a
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ex
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p
h
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/I
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C
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o
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Fil
ters
o
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Discre
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v
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m
s
for B
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P
riy
a
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hirud
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ro
f
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a
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a
na
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ra
bh
u*
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ter E
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KJ
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CE,
M
u
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Un
iv
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KJ
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Un
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Art
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nfo
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r
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to
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y:
R
ec
eiv
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Feb
2
1
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2
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1
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R
ev
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y
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v
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tc.
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it
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tri
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teristic
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p
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p
ro
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id
e
s
c
o
m
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s
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term
s o
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d
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S
NR
o
f
im
a
g
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s
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ey
w
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d
:
B
io
m
etr
ic
s
B
io
r
th
o
g
o
n
al
f
ilter
Dau
b
ec
h
ie
s
f
i
lter
Dis
cr
ete
w
av
ele
t d
ec
o
m
p
o
s
iti
o
n
HAAR
f
ilter
Co
p
y
rig
h
t
©
2
0
1
4
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
All
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
P
r
iy
a
B
h
ir
u
d
,
Dep
ar
t
m
en
t o
f
C
o
m
p
u
ter
E
n
g
i
n
ee
r
in
g
,
Mu
m
b
ai
U
n
i
v
er
s
it
y
.
E
m
ail
: p
an
d
u
@
y
a
h
o
o
.
co
.
in
1.
I
NT
RO
D
UCT
I
O
N
B
io
m
etr
ic
s
r
ec
o
g
n
ize
s
in
d
i
v
i
d
u
als
b
ased
o
n
th
e
f
ea
tu
r
e
s
d
er
iv
ed
f
r
o
m
t
h
eir
P
h
y
s
io
l
o
g
ical
an
d
b
eh
av
io
r
al
ch
ar
ac
ter
is
tic
s
.
B
io
m
e
tr
ic
s
y
s
te
m
s
p
r
o
v
id
e
r
eliab
le
w
a
y
o
f
r
ec
o
g
n
itio
n
to
co
n
f
ir
m
t
h
e
in
d
i
v
id
u
al
id
en
tit
y
.
A
h
i
g
h
er
d
eg
r
ee
o
f
co
n
f
id
en
ce
ca
n
b
e
ac
h
i
ev
ed
b
y
u
s
in
g
u
n
iq
u
e
p
h
y
s
ical
o
r
b
eh
a
v
io
r
al
ch
ar
ac
ter
is
tic
s
to
id
en
ti
f
y
a
p
e
r
s
o
n
[
1
]
.
Fig
u
r
e
.
1
Hu
m
a
n
e
y
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8776
IJ
-
I
C
T
Vo
l.
3
,
No
.
2
,
J
u
n
e
20
1
4
:
97
–
10
2
98
Du
e
to
th
e
v
ib
r
an
t
co
lo
r
an
d
tex
t
u
r
e
o
f
th
e
ir
is
it
is
t
y
p
ical
l
y
th
e
m
o
s
t
v
is
ib
le
an
d
d
is
ti
n
-
g
u
i
s
h
ab
le
p
ar
t o
f
th
e
h
u
m
a
n
e
y
e.
Hu
m
a
n
e
y
e
s
h
o
w
s
(
1
)
is
s
cler
a,
(
2
)
ir
is
,
(
3
)
p
u
p
il,
(
5
,
6
)
ey
elas
h
es a
n
d
(
4
,
7
)
ey
elid
s
.
Sti
ll
th
er
e
ar
e
ce
r
tain
is
s
u
es
p
ar
ticu
lar
l
y
t
h
e
s
ec
u
r
i
t
y
is
s
u
e
s
o
f
b
o
th
b
io
m
etr
ic
s
y
s
te
m
an
d
b
io
m
etr
ic
d
ata.
As
b
io
m
etr
ic
te
m
p
late
a
r
e
s
to
r
ed
in
th
e
ce
n
tr
alize
d
d
a
tab
ase,
d
u
e
to
s
ec
u
r
i
t
y
th
r
ea
t
s
b
io
m
etr
ic
te
m
p
late
m
a
y
b
e
m
o
d
if
ied
b
y
attac
k
er
[
6
]
.
I
f
b
io
m
et
r
ic
te
m
p
late
is
alter
ed
o
r
m
o
d
i
f
ies
a
u
t
h
o
r
ized
u
s
er
w
ill
n
o
t
b
e
allo
w
ed
to
ac
ce
s
s
t
h
e
r
e
s
o
u
r
c
e.
B
ec
au
s
e
o
f
t
h
ese
ca
u
s
e
s
r
es
ea
r
ch
es
h
av
e
b
ee
n
m
ad
e
to
p
r
o
tect
th
e
b
io
m
etr
ic
d
ata
an
d
te
m
p
late
in
t
h
e
s
y
s
te
m
b
y
u
s
i
n
g
cr
y
p
to
g
r
ap
h
y
,
s
te
n
o
g
r
ap
h
y
a
n
d
w
ater
m
ar
k
in
g
.
So
to
im
p
le
m
e
n
t
s
ec
u
r
it
y
f
o
r
ir
is
i
m
ag
e
s
its
e
m
b
ed
d
ed
in
co
v
er
i
m
a
g
e/i
m
ag
e
s
.
f
o
r
th
is
r
ea
s
o
n
s
ize
o
f
ir
is
i
m
ag
e
s
h
o
u
ld
b
e
4
0
%
o
f
c
o
v
er
i
m
a
g
e
.
T
h
is
i
s
ac
h
iev
ed
b
y
d
ec
o
m
p
o
s
in
g
I
r
is
i
m
a
g
e
b
y
w
a
v
elet
tr
an
s
f
o
r
m
an
d
th
e
n
e
m
b
ed
d
ed
in
to
co
v
er
i
m
a
g
e.
Dis
cr
ete
W
av
el
et
tr
an
s
f
o
r
m
h
a
v
e
v
ar
io
u
s
f
iler
s
as
s
o
ciate
d
w
it
h
it
s
u
c
h
as
H
AAR
f
ilter
,
B
io
r
th
o
g
o
n
al
f
ilter
,
C
o
if
lets
,
Da
u
b
ec
h
ies
f
ilter
.
I
n
t
h
e
p
r
o
p
o
s
ed
co
m
p
ar
i
s
o
n
o
f
p
er
f
o
r
m
a
n
ce
o
f
t
h
ese
f
i
lter
s
w
ith
r
esp
ec
t to
I
r
is
i
m
a
g
e
h
a
s
b
ee
n
ca
r
r
ied
o
u
t f
o
r
o
b
tain
in
g
b
e
s
t
f
ilter
ca
n
b
e
u
s
ed
to
e
m
b
ed
in
co
v
er
i
m
a
g
e.
T
h
e
p
ap
er
is
o
r
g
an
ized
as
f
o
ll
o
w
s
:
Sectio
n
2
d
is
cu
s
s
es
th
e
W
av
elet
T
r
an
s
f
o
r
m
s
.
Sectio
n
3
ex
p
lain
s
w
h
at
ar
e
d
if
f
er
e
n
t
t
y
p
e
s
o
f
f
ilt
er
s
ass
o
ciate
d
w
it
h
DW
T
(
Dis
cr
ete
W
av
elet
T
r
an
s
f
o
r
m
)
.
Se
ctio
n
4
ex
p
lai
n
s
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
.
T
h
e
ex
p
er
i
m
e
n
ts
co
n
d
u
c
ted
an
d
s
i
m
u
la
tio
n
r
esu
lt
s
ar
e
p
r
esen
ted
in
s
ec
tio
n
5
.
Fin
all
y
,
co
n
clu
s
io
n
s
ar
e
g
iv
e
n
i
n
s
ec
tio
n
6
.
2.
WAVE
L
E
T
T
RANSF
O
RM
T
h
er
e
ar
e
m
a
n
y
d
i
f
f
er
en
t
t
y
p
e
s
o
f
w
a
v
elet
s
tr
an
s
f
o
r
m
.
Mo
s
t
o
f
d
ata
an
al
y
s
is
ap
p
licatio
n
s
ar
e
u
s
i
n
g
C
o
n
ti
n
u
o
us
-
ti
m
e
w
a
v
elet
tr
a
n
s
f
o
r
m
s
(
C
W
T
)
.
Ho
w
e
v
er
,
t
h
e
m
o
s
t
p
o
p
u
lar
t
y
p
e
w
h
ic
h
a
f
f
ec
ted
th
e
p
r
o
p
er
ties
o
f
m
an
y
r
ea
l
s
i
g
n
a
ls
is
d
i
s
cr
ete
w
av
ele
t
tr
a
n
s
f
o
r
m
(
DW
T
)
[
1
3
]
.
T
h
e
w
a
v
elet
tr
an
s
f
o
r
m
i
s
s
i
m
ilar
to
t
h
e
Fo
u
r
ier
tr
an
s
f
o
r
m
w
i
th
a
co
m
p
letel
y
d
i
f
f
er
en
t
m
er
it
f
u
n
cti
o
n
.
T
h
e
m
ain
d
i
f
f
er
en
ce
in
b
o
th
is
Fo
u
r
ier
tr
an
s
f
o
r
m
d
ec
o
m
p
o
s
es
th
e
s
i
g
n
al
i
n
to
s
i
n
es
an
d
co
s
in
e
s
,
i.e
.
th
e
f
u
n
ctio
n
s
lo
ca
lized
in
Fo
u
r
ier
s
p
ac
e;
in
co
n
tr
ast
w
i
th
th
a
t
w
a
v
elet
tr
an
s
f
o
r
m
u
s
es
f
u
n
c
tio
n
s
t
h
at
ar
e
lo
ca
lized
in
b
o
th
t
h
e
r
ea
l
a
n
d
Fo
u
r
ier
s
p
ac
e.
Gen
er
all
y
,
t
h
e
w
a
v
elet
tr
an
s
f
o
r
m
ca
n
b
e
ex
p
r
ess
ed
b
y
t
h
e
f
o
l
lo
w
i
n
g
eq
u
atio
n
:
W
h
er
e
th
e
*
is
th
e
co
m
p
le
x
c
o
n
j
u
g
ate
s
y
m
b
o
l
an
d
f
u
n
ctio
n
ψ
is
s
o
m
e
f
u
n
ctio
n
.
T
h
is
f
u
n
ctio
n
ca
n
b
e
ch
o
s
en
ar
b
itra
r
ily
p
r
o
v
id
ed
th
at
o
b
e
y
s
ce
r
tain
r
u
les.
T
h
e
W
av
elet
tr
an
s
f
o
r
m
i
s
i
n
f
ac
t
an
i
n
f
in
i
te
s
et
o
f
v
ar
io
u
s
t
r
an
s
f
o
r
m
s
,
d
ep
en
d
i
n
g
o
n
t
h
e
m
er
it
f
u
n
ctio
n
u
s
ed
f
o
r
its
co
m
p
u
ta
tio
n
.
T
h
e
d
iv
is
io
n
b
ased
o
n
th
e
w
a
v
elet
o
r
th
o
g
o
n
alit
y
is
to
u
s
e
o
r
th
o
g
o
n
a
l
w
a
ve
lets
f
o
r
d
is
cr
ete
w
av
ele
t
tr
an
s
f
o
r
m
d
ev
elo
p
m
e
n
t
a
n
d
n
on
-
o
r
th
o
g
o
n
a
l
w
a
ve
lets
f
o
r
co
n
ti
n
u
o
u
s
w
a
v
elet
tr
an
s
f
o
r
m
d
ev
elo
p
m
en
t.
T
h
ese
t
w
o
tr
an
s
f
o
r
m
s
h
a
v
e
th
e
f
o
llo
w
in
g
p
r
o
p
er
ties
:
1.
T
h
e
d
is
cr
ete
w
a
v
elet
tr
an
s
f
o
r
m
r
etu
r
n
s
a
d
ata
v
ec
to
r
o
f
th
e
s
a
m
e
len
g
t
h
as
t
h
e
in
p
u
t
is
.
Usu
al
l
y
,
ev
e
n
i
n
th
is
v
ec
to
r
m
an
y
d
ata
ar
e
al
m
o
s
t
ze
r
o
.
T
h
is
co
r
r
esp
o
n
d
s
to
th
e
f
ac
t
t
h
at
it
d
ec
o
m
p
o
s
e
s
in
to
a
s
et
o
f
w
a
v
elet
s
(
f
u
n
c
tio
n
s
)
t
h
at
ar
e
o
r
th
o
g
o
n
al
to
it
s
tr
an
s
latio
n
s
an
d
s
ca
li
n
g
.
T
h
er
ef
o
r
e
w
e
d
ec
o
m
p
o
s
e
s
u
c
h
a
s
ig
n
al
to
a
s
a
m
e
o
r
lo
w
er
n
u
m
b
er
o
f
t
h
e
w
a
v
elet
co
ef
f
icie
n
t
s
p
ec
tr
u
m
as
i
s
th
e
n
u
m
b
er
o
f
s
ig
n
al
d
ata
p
o
in
ts
.
S
u
c
h
a
w
av
ele
t
s
p
ec
tr
u
m
i
s
v
er
y
g
o
o
d
f
o
r
s
i
g
n
al
p
r
o
ce
s
s
i
n
g
an
d
co
m
p
r
ess
io
n
,
f
o
r
e
x
a
m
p
le,
as
w
e
g
et
n
o
r
ed
u
n
d
an
t i
n
f
o
r
m
atio
n
h
er
e.
2.
T
h
e
co
n
tin
u
o
u
s
w
av
elet
tr
an
s
f
o
r
m
i
n
co
n
tr
ar
y
r
etu
r
n
s
a
n
ar
r
a
y
o
n
e
d
i
m
en
s
io
n
lar
g
er
th
a
t
t
h
e
in
p
u
t
d
ata.
Fo
r
a
1
D
d
ata
w
e
o
b
tain
a
n
i
m
ag
e
o
f
t
h
e
ti
m
e
-
f
r
eq
u
e
n
c
y
p
l
an
e.
W
e
ca
n
ea
s
i
l
y
s
ee
th
e
s
i
g
n
al
f
r
eq
u
en
cie
s
ev
o
lu
tio
n
d
u
r
i
n
g
t
h
e
d
u
r
atio
n
o
f
th
e
s
i
g
n
al
a
n
d
c
o
m
p
ar
e
th
e
s
p
ec
tr
u
m
w
it
h
o
t
h
er
s
i
g
n
a
ls
s
p
ec
tr
a.
As
h
er
e
is
u
s
ed
t
h
e
n
o
n
-
o
r
th
o
g
o
n
al
s
e
t
o
f
w
a
v
elet
s
,
d
ata
ar
e
co
r
r
elate
d
h
i
g
h
l
y
,
s
o
b
ig
r
ed
u
n
d
a
n
c
y
is
s
ee
n
h
er
e.
T
h
is
h
elp
s
to
s
ee
th
e
r
es
u
lt
s
i
n
a
m
o
r
e
h
u
m
a
n
e
f
o
r
m
.
2
.
1
.
Co
ntinuo
us
Wa
v
elet
T
ra
ns
f
o
r
m
C
o
n
ti
n
u
o
u
s
w
a
v
elet
tr
a
n
s
f
o
r
m
(
C
W
T
)
is
an
i
m
p
le
m
e
n
tatio
n
o
f
th
e
w
a
v
elet
tr
a
n
s
f
o
r
m
u
s
i
n
g
ar
b
itra
r
y
s
ca
les
an
d
al
m
o
s
t
ar
b
itra
r
y
wav
elets.
T
h
e
w
av
ele
ts
u
s
ed
ar
e
n
o
t
o
r
th
o
g
o
n
al
a
n
d
th
e
d
at
a
o
b
tain
ed
b
y
t
h
is
tr
an
s
f
o
r
m
ar
e
h
i
g
h
l
y
co
r
r
elate
d
.
Fo
r
th
e
d
i
s
cr
ete
ti
m
e
s
er
i
es
w
e
ca
n
u
s
e
t
h
is
tr
an
s
f
o
r
m
as
w
e
ll,
w
it
h
th
e
li
m
ita
tio
n
t
h
at
t
h
e
s
m
alles
t
w
a
v
elet
tr
an
s
latio
n
s
m
u
s
t
b
e
eq
u
al
to
th
e
d
ata
s
a
m
p
li
n
g
.
T
h
is
is
s
o
m
et
i
m
e
s
ca
lled
Dis
cr
ete
T
im
e
C
o
n
ti
n
u
o
u
s
W
av
elet
T
r
an
s
f
o
r
m
(
DT
-
C
W
T
)
a
n
d
it
is
th
e
m
o
s
t
u
s
ed
w
a
y
o
f
co
m
p
u
ti
n
g
C
W
T
in
r
ea
l a
p
p
licatio
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
T
I
SS
N:
2252
-
8776
P
erfo
r
ma
n
ce
E
va
lu
a
tio
n
o
f F
i
lter
s
o
f …
(
P
r
iya
B
h
ir
u
d
)
99
A
co
n
ti
n
u
o
u
s
w
a
v
elet
tr
an
s
f
o
r
m
(
C
W
T
)
is
u
s
ed
to
d
i
v
id
e
a
co
n
ti
n
u
o
u
s
-
ti
m
e
f
u
n
ctio
n
in
t
o
w
a
v
elet
s
.
Un
li
k
e
Fo
u
r
ier
tr
an
s
f
o
r
m
,
t
h
e
co
n
ti
n
u
o
u
s
w
av
ele
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tr
an
s
f
o
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p
o
s
s
e
s
s
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t
h
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ab
i
lit
y
to
co
n
s
tr
u
ct
a
ti
m
e
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f
r
eq
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en
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y
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ep
r
esen
tat
io
n
o
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a
s
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g
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a
l
th
at
o
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er
s
v
er
y
g
o
o
d
ti
m
e
an
d
f
r
eq
u
en
c
y
lo
ca
lizatio
n
.
I
n
m
at
h
e
m
a
tics
,
t
h
e
co
n
ti
n
u
o
u
s
w
a
v
elet
tr
an
s
f
o
r
m
o
f
a
co
n
tin
u
o
u
s
,
s
q
u
ar
e
-
i
n
te
g
r
ab
le
f
u
n
ctio
n
at
a
s
ca
le
an
d
tr
an
s
latio
n
al
v
al
u
e
is
ex
p
r
ess
ed
b
y
th
e
f
o
llo
w
i
n
g
i
n
t
eg
r
al.
W
h
er
e
Ψ
(
t)
is
a
co
n
tin
u
o
u
s
f
u
n
ct
io
n
in
b
o
th
t
h
e
ti
m
e
d
o
m
ain
an
d
th
e
f
r
eq
u
en
c
y
d
o
m
ai
n
ca
lled
th
e
m
o
th
er
w
a
v
elet
a
n
d
r
ep
r
esen
ts
o
p
er
atio
n
o
f
co
m
p
lex
co
n
j
u
g
ate
I
n
p
r
in
cip
le
t
h
e
co
n
tin
u
o
u
s
wav
elet
tr
a
n
s
f
o
r
m
w
o
r
k
s
b
y
u
s
i
n
g
d
ir
ec
tl
y
t
h
e
d
e
f
i
n
itio
n
o
f
t
h
e
w
a
v
ele
t
t
r
an
s
f
o
r
m
,
i.e
.
w
e
ar
e
co
m
p
u
ti
n
g
a
co
n
v
o
l
u
tio
n
o
f
th
e
s
ig
n
al
w
it
h
t
h
e
s
ca
led
w
a
v
elet.
Fo
r
ea
ch
s
ca
le
w
e
o
b
tai
n
b
y
th
i
s
w
a
y
an
ar
r
a
y
o
f
t
h
e
s
a
m
e
le
n
g
th
N
as
th
e
s
i
g
n
al
h
a
s
.
B
y
u
s
in
g
M
ar
b
itra
r
il
y
ch
o
s
e
n
s
ca
le
s
w
e
o
b
tain
a
f
ield
N
×M
th
at
r
ep
r
esen
ts
t
h
e
ti
m
e
-
f
r
eq
u
en
c
y
p
la
n
e
d
ir
ec
tl
y
.
T
h
e
alg
o
r
ith
m
u
s
ed
f
o
r
t
h
is
c
o
m
p
u
tatio
n
ca
n
b
e
b
ased
o
n
a
d
ir
ec
t
co
n
v
o
lu
tio
n
o
r
o
n
a
co
n
v
o
lu
tio
n
b
y
m
ea
n
s
o
f
m
u
ltip
licatio
n
i
n
Fo
u
r
ier
s
p
ac
e
(
th
is
i
s
s
o
m
eti
m
es c
al
led
Fas
t W
av
ele
t T
r
an
s
f
o
r
m
)
.
T
h
e
ch
o
ice
o
f
th
e
w
a
v
elet
t
h
at
is
u
s
ed
f
o
r
ti
m
e
-
f
r
eq
u
e
n
c
y
d
ec
o
m
p
o
s
itio
n
is
t
h
e
m
o
s
t
i
m
p
o
r
ta
n
t
th
i
n
g
.
B
y
th
i
s
ch
o
ice
w
e
ca
n
i
n
f
lu
e
n
ce
t
h
e
ti
m
e
an
d
f
r
eq
u
e
n
c
y
r
eso
lu
t
io
n
o
f
th
e
r
es
u
lt.
W
e
ca
n
n
o
t
c
h
an
g
e
t
h
e
m
ai
n
f
ea
tu
r
e
s
o
f
W
T
b
y
th
i
s
w
a
y
(
lo
w
f
r
eq
u
e
n
cies
h
a
v
e
g
o
o
d
f
r
eq
u
en
c
y
a
n
d
b
ad
ti
m
e
r
eso
lu
tio
n
;
h
ig
h
f
r
eq
u
en
c
ies
h
a
v
e
g
o
o
d
ti
m
e
a
n
d
b
ad
f
r
eq
u
en
c
y
r
eso
l
u
tio
n
)
,
b
u
t
w
e
ca
n
s
o
m
eh
o
w
i
n
cr
ea
s
e
th
e
to
tal
f
r
eq
u
e
n
c
y
o
f
to
tal
ti
m
e
r
eso
lu
tio
n
.
T
h
is
is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
th
e
w
id
th
o
f
t
h
e
u
s
ed
w
a
v
elet
i
n
r
ea
l
an
d
Fo
u
r
ier
s
p
ac
e.
I
f
w
e
u
s
e
t
h
e
Mo
r
let
w
a
v
ele
t
f
o
r
ex
a
m
p
le
(
r
ea
l
p
ar
t
–
d
am
p
ed
co
s
in
e
f
u
n
ctio
n
)
w
e
ca
n
e
x
p
ec
t
h
ig
h
f
r
eq
u
en
c
y
r
eso
l
u
tio
n
a
s
s
u
ch
a
w
a
v
elet
is
v
er
y
w
e
ll
lo
ca
lize
d
in
f
r
eq
u
e
n
cies.
I
n
co
n
tr
ar
y
,
u
s
i
n
g
Der
iv
ati
v
e
o
f
Gau
s
s
ia
n
(
DOG)
w
a
v
elet
w
i
ll
r
esu
lt i
n
g
o
o
d
ti
m
e
lo
ca
lizat
io
n
,
b
u
t p
o
o
r
o
n
e
in
f
r
eq
u
e
n
cies.
2
.
2
.
Dis
cr
et
e
Wa
v
elet
T
ra
ns
f
o
r
m
I
n
n
u
m
er
ical
an
al
y
s
is
an
d
f
u
n
ctio
n
al
an
al
y
s
i
s
,
a
d
is
cr
ete
w
av
elet
tr
an
s
f
o
r
m
(
DW
T
)
is
an
y
w
a
v
elet
tr
an
s
f
o
r
m
f
o
r
w
h
ic
h
t
h
e
w
a
v
e
lets
ar
e
d
is
cr
etel
y
s
a
m
p
led
.
As
w
it
h
o
th
er
w
a
v
elet
tr
a
n
s
f
o
r
m
s
,
a
k
e
y
ad
v
a
n
tag
e
it
h
as
o
v
er
Fo
u
r
ier
tr
an
s
f
o
r
m
s
is
te
m
p
o
r
al
r
eso
lu
t
io
n
:
it
c
ap
tu
r
es
b
o
th
f
r
eq
u
e
n
c
y
a
n
d
l
o
ca
tio
n
in
f
o
r
m
atio
n
(
lo
ca
tio
n
in
ti
m
e)
.
T
h
e
d
is
cr
ete
w
a
v
elet
tr
an
s
f
o
r
m
(
DW
T
)
is
an
i
m
p
le
m
e
n
tati
o
n
o
f
t
h
e
w
av
e
let
tr
an
s
f
o
r
m
u
s
in
g
a
d
is
cr
ete
s
et
o
f
t
h
e
w
a
v
elet
s
ca
les
an
d
t
r
an
s
latio
n
s
w
h
ic
h
f
o
llo
w
s
s
o
m
e
d
ef
in
ed
r
u
les.
T
h
is
tr
a
n
s
f
o
r
m
d
ec
o
m
p
o
s
es
t
h
e
s
ig
n
al
i
n
to
m
u
t
u
all
y
o
r
t
h
o
g
o
n
al
s
et
o
f
w
av
e
lets
,
w
h
ic
h
is
t
h
e
m
ai
n
d
i
f
f
er
e
n
ce
f
r
o
m
t
h
e
co
n
tin
u
o
u
s
w
av
e
let
tr
an
s
f
o
r
m
(
C
W
T
)
,
o
r
its
i
m
p
le
m
e
n
tat
io
n
f
o
r
th
e
d
is
cr
ete
ti
m
e
s
er
ies
s
o
m
eti
m
es
ca
lled
d
is
cr
ete
-
ti
m
e
co
n
tin
u
o
u
s
w
av
e
let
tr
an
s
f
o
r
m
(
DT
-
C
W
T
)
.
T
h
e
w
av
ele
t
ca
n
b
e
co
n
s
tr
u
cted
f
r
o
m
a
s
ca
li
n
g
f
u
n
ctio
n
w
h
ic
h
d
escr
ib
es
its
s
ca
li
n
g
p
r
o
p
er
ties
.
T
h
e
r
estrictio
n
t
h
at
th
e
s
ca
l
in
g
f
u
n
ctio
n
s
m
u
s
t
b
e
o
r
th
o
g
o
n
al
to
its
d
is
cr
ete
tr
an
s
latio
n
s
i
m
p
lie
s
s
o
m
e
m
a
th
e
m
atica
l
co
n
d
itio
n
s
o
n
th
e
m
w
h
ich
ar
e
m
en
t
io
n
ed
ev
er
y
w
h
er
e,
e.
g
.
t
h
e
d
ilatio
n
eq
u
atio
n
w
h
er
e
S
is
a
s
ca
lin
g
f
ac
to
r
(
u
s
u
all
y
c
h
o
s
e
n
as
2
)
.
T
h
e
ar
ea
b
etw
ee
n
t
h
e
f
u
n
c
tio
n
m
u
s
t
b
e
n
o
r
m
al
ized
an
d
s
ca
lin
g
f
u
n
ctio
n
m
u
s
t
b
e
o
r
t
h
o
g
o
n
al
to
its
i
n
teg
e
r
tr
an
s
latio
n
s
,
i.e
.
Af
ter
in
tr
o
d
u
ci
n
g
s
o
m
e
m
o
r
e
co
n
d
itio
n
s
(
as
th
e
r
estrictio
n
s
ab
o
v
e
d
o
es
n
o
t
p
r
o
d
u
ce
u
n
iq
u
e
s
o
lu
tio
n
)
r
esu
lt
s
ca
n
b
e
o
b
tain
ed
o
f
all
th
ese
eq
u
a
tio
n
s
,
i.e
.
t
h
e
f
in
i
te
s
et
o
f
co
ef
f
icie
n
t
s
ak
t
h
at
d
ef
in
e
t
h
e
s
ca
l
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8776
IJ
-
I
C
T
Vo
l.
3
,
No
.
2
,
J
u
n
e
20
1
4
:
97
–
10
2
100
f
u
n
ctio
n
an
d
also
th
e
w
a
v
elet
.
T
h
e
w
a
v
elet
is
o
b
tain
ed
f
r
o
m
th
e
s
ca
lin
g
f
u
n
ctio
n
as
N
w
h
er
e
N
is
an
e
v
en
in
te
g
er
.
T
h
e
s
et
o
f
w
av
e
lets
t
h
en
f
o
r
m
s
a
n
o
r
th
o
n
o
r
m
al
b
a
s
is
w
h
ich
w
e
u
s
e
to
d
ec
o
m
p
o
s
e
th
e
s
i
g
n
al.
No
te
th
at
u
s
u
all
y
o
n
l
y
f
e
w
o
f
th
e
co
ef
f
icien
ts
ar
e
n
o
n
ze
r
o
,
w
h
ic
h
s
i
m
p
li
f
ie
s
th
e
ca
lc
u
latio
n
s
.
3.
F
I
L
T
E
R
S O
F
DIS
CR
E
T
E
WAVE
L
E
T
T
RANSF
O
RM
T
h
er
e
ar
e
v
ar
io
u
s
f
ilter
s
as
s
o
ciate
d
w
i
th
Di
s
cr
ete
W
av
elet
T
r
an
s
f
o
r
m
.
W
e
o
u
tli
n
e
th
e
b
asic
d
ev
elo
p
m
en
t o
f
d
is
cr
ete
w
av
e
l
et
tr
an
s
f
o
r
m
atio
n
s
as
f
o
llo
w
s
.
3
.
1
.
H
AAR
T
ra
ns
f
o
r
m
An
y
d
is
c
u
s
s
io
n
o
f
w
a
v
elets
b
eg
in
s
w
it
h
Haa
r
w
a
v
elet,
t
h
e
f
ir
s
t
a
n
d
s
i
m
p
les
t.
Haa
r
w
a
v
elet
i
s
d
is
co
n
ti
n
u
o
u
s
,
an
d
r
ese
m
b
les
a
s
tep
f
u
n
ctio
n
.
W
e
m
o
tiv
ate
t
h
is
tr
a
n
s
f
o
r
m
atio
n
as
f
o
llo
w
s
:
Su
p
p
o
s
e
w
e
w
i
s
h
to
tr
a
n
s
m
it
a
lis
t
(
v
ec
to
r
)
o
f
N
n
u
m
b
er
s
,
N
ev
e
n
,
to
a
f
r
ie
n
d
v
ia
th
e
I
n
ter
n
et.
T
o
r
ed
u
ce
tr
an
s
f
er
ti
m
e,
w
e
d
ec
id
e
to
s
en
d
o
n
l
y
a
le
n
g
th
N
/2
ap
p
r
o
x
i
m
atio
n
o
f
t
h
e
d
ata.
On
e
w
a
y
to
f
o
r
m
t
h
e
ap
p
r
o
x
im
a
tio
n
is
to
s
en
d
p
air
w
i
s
e
av
er
ag
e
s
o
f
th
e
n
u
m
b
er
s
.
Fo
r
ex
am
p
le,
th
e
v
ec
to
r
[
6
,
1
2
,
1
5
,
1
5
,
1
4
,
1
2
,
1
2
0
,
1
1
6
]
T
ca
n
b
e
ap
p
r
o
x
i
m
ated
b
y
th
e
v
ec
to
r
[
9
,
1
5
,
1
3
,
1
1
8
]
T
.
Of
co
u
r
s
e,
it
is
i
m
p
o
s
s
ib
le
to
d
eter
m
i
n
e
t
h
e
o
r
ig
i
n
al
N
n
u
m
b
er
s
f
r
o
m
t
h
is
ap
p
r
o
x
i
m
atio
n
,
b
u
t
i
f
,
i
n
ad
d
itio
n
,
w
e
tr
an
s
m
it
t
h
e
N/2
av
er
ag
ed
d
ir
ec
ted
d
is
tan
ce
s
,
t
h
en
o
u
r
f
r
ie
n
d
co
u
ld
co
m
p
le
te
l
y
r
ec
o
v
er
t
h
e
o
r
ig
i
n
al
d
ata.
F
o
r
o
u
r
ex
a
m
p
le,
t
h
e
av
er
ag
ed
d
ir
ec
ted
d
is
tan
ce
s
ar
e
[
3
,
0
,
−
1
,
−2
]
T
.
W
e
d
ef
i
n
e
t
h
e
o
n
e
–
d
i
m
e
n
s
io
n
al
d
is
cr
ete
Haa
r
w
a
v
elet
tr
an
s
f
o
r
m
atio
n
as t
h
e
lin
ea
r
tr
a
n
s
f
o
r
m
atio
n
.
x
→[
a/d
]
a
k
= (
x
2
k−
1
+x
2k
)
/2
,
d
k
=(
−x
2
k−
1
+x
2k
)
/2
,
Fo
llo
w
i
n
g
f
i
g
u
r
e
g
i
v
es b
eh
a
v
i
o
r
o
f
w
a
v
elet
f
u
n
ctio
n
[
1
1
]
Fig
u
r
e
2
.
W
av
elet
Fu
n
ctio
n
3
.
2
.
Da
ub
ec
hies
O
rt
ho
g
o
na
l
F
ilte
r
T
h
e
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
s
et
o
f
d
is
cr
ete
w
av
e
let
tr
an
s
f
o
r
m
s
w
a
s
f
o
r
m
u
lated
b
y
t
h
e
B
elg
ian
m
at
h
e
m
a
ticia
n
I
n
g
r
id
Da
u
b
ec
h
ies
in
1
9
8
8
.
T
h
is
f
o
r
m
u
latio
n
i
s
b
ased
o
n
t
h
e
u
s
e
o
f
r
ec
u
r
r
en
ce
r
elatio
n
s
to
g
en
er
ate
p
r
o
g
r
es
s
i
v
el
y
f
i
n
er
d
is
cr
ete
s
a
m
p
l
in
g
s
o
f
a
n
i
m
p
licit
m
o
t
h
er
w
a
v
elet
f
u
n
c
tio
n
;
ea
ch
r
eso
l
u
tio
n
is
t
w
ice
t
h
at
o
f
t
h
e
p
r
ev
io
u
s
s
ca
le.
I
n
h
er
s
e
m
i
n
al
p
ap
er
,
Dau
b
ec
h
ies
d
er
iv
es
a
f
a
m
i
l
y
o
f
wav
elets,
t
h
e
f
ir
s
t
o
f
w
h
ic
h
is
t
h
e
Haa
r
w
a
v
elet.
I
n
t
er
est
in
th
is
f
ield
h
as
e
x
p
lo
d
ed
s
in
ce
t
h
e
n
,
a
n
d
m
a
n
y
v
ar
ia
ti
o
n
s
o
f
Dau
b
ec
h
ies
'
o
r
ig
in
al
w
a
v
elet
s
w
er
e
d
ev
elo
p
ed
[
3
]
.
I
n
g
r
id
Da
u
b
ec
h
ies,
o
n
e
o
f
t
h
e
b
r
ig
h
te
s
t
s
tar
s
in
th
e
w
o
r
ld
o
f
w
av
ele
t
r
esear
ch
,
i
n
v
en
te
d
w
h
at
ar
e
ca
lled
co
m
p
ac
tl
y
s
u
p
p
o
r
ted
o
r
th
o
n
o
r
m
a
l
w
av
e
lets
—
th
u
s
m
ak
in
g
d
is
cr
ete
w
av
elet
an
al
y
s
i
s
p
r
ac
ticab
le.
T
h
e
n
a
m
e
s
o
f
t
h
e
Da
u
b
ec
h
ie
s
f
a
m
i
l
y
w
a
v
elet
s
ar
e
w
r
it
ten
d
b
N,
w
h
er
e
N
is
th
e
o
r
d
er
,
an
d
d
b
th
e
"
s
u
r
n
a
m
e"
o
f
th
e
w
a
v
elet.
T
h
e
d
b
1
w
a
v
elet,
as
m
en
tio
n
ed
ab
o
v
e,
is
t
h
e
s
a
m
e
as Ha
ar
w
a
v
elet.
3
.
3
.
B
io
rt
ho
g
o
na
l F
ilte
r
T
h
is
f
a
m
il
y
o
f
w
a
v
elet
s
e
x
h
i
b
its
th
e
p
r
o
p
er
t
y
o
f
lin
ea
r
p
h
ase,
w
h
ich
i
s
n
ee
d
ed
f
o
r
s
ig
n
al
an
d
i
m
a
g
e
r
ec
o
n
s
tr
u
ct
io
n
.
B
y
u
s
i
n
g
t
w
o
w
a
v
elet
s
,
o
n
e
f
o
r
d
ec
o
m
p
o
s
itio
n
(
o
n
t
h
e
le
f
t
s
id
e)
an
d
t
h
e
o
th
er
f
o
r
r
ec
o
n
s
tr
u
ctio
n
(
o
n
th
e
r
ig
h
t s
id
e)
in
s
tead
o
f
t
h
e
s
a
m
e
s
in
g
le
o
n
e,
i
n
ter
esti
n
g
p
r
o
p
e
r
ties
ar
e
d
er
iv
ed
.
I
n
th
e
B
io
r
th
o
g
o
n
al
ca
s
e
[
5
]
,
th
er
e
ar
e
t
w
o
s
ca
lin
g
f
u
n
ctio
n
s
,
w
h
ic
h
m
a
y
g
en
er
ate
d
i
f
f
er
en
t
m
u
l
tire
s
o
lu
tio
n
an
al
y
s
es,
an
d
ac
co
r
d
in
g
l
y
t
w
o
d
if
f
er
en
t
w
a
v
elet
f
u
n
ctio
n
s
.
So
th
e
n
u
m
b
er
s
M
an
d
N
o
f
co
ef
f
icie
n
t
s
in
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
T
I
SS
N:
2252
-
8776
P
erfo
r
ma
n
ce
E
va
lu
a
tio
n
o
f F
i
lter
s
o
f …
(
P
r
iya
B
h
ir
u
d
)
101
s
ca
lin
g
s
eq
u
en
ce
s
m
a
y
d
if
f
er
.
T
h
e
s
ca
lin
g
s
eq
u
e
n
ce
s
th
e
m
u
s
t
s
atis
f
y
th
e
f
o
llo
w
in
g
B
io
r
th
o
g
o
n
alit
y
co
n
d
itio
n
.
T
h
en
th
e
w
av
e
let
s
eq
u
e
n
ce
s
ca
n
b
e
d
eter
m
in
ed
as
4.
P
RO
P
O
SE
D
WO
RK
I
n
th
e
P
r
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p
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w
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g
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e
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t
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b
y
t
h
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p
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er
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I
r
is
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m
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g
e
wh
ich
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to
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e
e
m
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ed
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e
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o
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p
o
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ed
b
y
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a
v
elet
tr
a
n
s
f
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u
s
in
g
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ar
io
u
s
f
ilter
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k
e
Da
u
b
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h
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s
Or
th
o
g
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n
a
l
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il
ter
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HAAR
f
ilter
a
n
d
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io
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th
o
g
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n
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l
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ilter
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s
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g
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.
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r
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er
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o
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ar
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atab
ase[
9
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d
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6.
CO
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Fro
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t
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