I
nd
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ne
s
ia
n J
o
urna
l o
f
E
lect
rica
l En
g
ineering
a
nd
Co
m
pu
t
er
Science
Vo
l.
23
,
No
.
2
,
A
u
g
u
s
t
20
21
,
p
p
.
8
7
1
~
87
8
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23
.i
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.
pp
871
-
87
8
871
J
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:
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So
me a
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Alm
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ty
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ticle
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It
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p
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it
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t
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m
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r
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o
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wh
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lem
e
n
ts
a
re
e
q
u
a
l
to
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u
m
b
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s
.
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t
h
in
c
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g
a
sa
m
p
li
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terv
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h
a
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i
t
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m
e
s
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to
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str
u
c
t
a
G
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o
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isti
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ti
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e
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a
tu
re
o
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ich
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th
e
e
x
a
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t
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e
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o
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riati
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a
m
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o
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in
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l
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g
n
a
l
a
n
d
it
s
d
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g
it
a
l
sp
e
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tru
m
.
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h
is
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v
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ra
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y
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isti
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g
u
is
h
e
s
th
e
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lo
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F
ield
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o
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rier
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sfo
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h
e
p
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ty
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e
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o
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th
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tra,
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a
lcu
late
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u
si
n
g
,
f
o
r
e
x
a
m
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t
h
e
Walsh
b
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sis
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is
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t
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ield
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o
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iate
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h
a
rm
o
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ic
f
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c
ti
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s.
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p
a
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lar,
a
n
a
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ted
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it
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wa
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o
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d
.
On
th
is
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a
sis
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o
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,
t
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a
t
t
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si
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ty
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field
s
m
a
k
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it
p
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ss
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to
d
e
v
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lo
p
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p
lete
a
n
a
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o
f
t
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tran
sfe
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fu
n
c
ti
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t
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ly
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si
g
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ls p
re
se
n
te
d
in
d
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g
it
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l
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rm
.
K
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w
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r
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s
:
Dig
ital p
r
o
ce
s
s
in
g
Fo
u
r
ier
tr
an
s
f
o
r
m
Galo
is
f
ield
s
T
r
an
s
f
er
f
u
n
ctio
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s
T
h
is i
s
a
n
o
p
e
n
a
c
c
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ss
a
rticle
u
n
d
e
r th
e
CC B
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-
SA
li
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se
.
C
o
r
r
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s
p
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nd
ing
A
uth
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r
:
I
n
ab
at
Mo
ld
a
k
h
an
Dep
ar
tm
en
t o
f
R
ad
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E
n
g
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ee
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in
g
,
E
lectr
o
n
ics,
an
d
T
elec
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m
m
u
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icatio
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s
Alm
aty
Un
iv
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s
ity
o
f
Po
wer
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n
g
in
ee
r
in
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an
d
T
elec
o
m
m
u
n
ic
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s
1
2
6
/1
B
aitu
r
s
y
n
o
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a
Stre
et,
0
5
0
0
1
3
,
Alm
aty
,
Kaz
ak
h
s
tan
E
m
ail:
im
o
ld
ak
h
a
n
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
th
eo
r
y
o
f
Galo
is
f
ield
s
(
f
i
n
ite
co
m
m
u
tativ
e
b
o
d
ies)
is
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
to
o
ls
o
f
m
o
d
e
r
n
in
f
o
r
m
atio
n
th
e
o
r
y
[
1
]
,
[
2
]
,
in
p
ar
ticu
lar
,
th
e
th
eo
r
y
o
f
n
o
is
eless
co
d
in
g
[
3
]
,
[
4
]
.
I
n
p
ar
ti
cu
lar
,
Galo
is
f
ield
s
m
ak
e
it
p
o
s
s
ib
le
to
co
n
s
tr
u
ct
an
an
alo
g
o
f
t
h
e
Fo
u
r
ier
tr
an
s
f
o
r
m
,
w
h
ich
ap
p
licab
le
to
d
is
cr
ete
f
u
n
ctio
n
s
an
d
s
ig
n
als
(
Galo
is
Field
Fo
u
r
ier
T
r
an
s
f
o
r
m
)
,
wh
ich
cu
r
r
e
n
tly
also
ar
e
wid
ely
u
s
ed
,
in
clu
d
in
g
f
o
r
t
h
e
d
ev
elo
p
m
e
n
t o
f
al
g
o
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ith
m
s
f
o
r
en
co
d
in
g
an
d
d
ec
o
d
in
g
s
ig
n
al
s
[
5
]
-
[
8
]
.
I
n
th
e
liter
atu
r
e
m
ain
ly
u
s
in
g
th
e
b
in
ar
y
Galo
is
f
ield
s
,
m
o
r
e
p
r
ec
is
ely
,
th
e
m
o
s
t
wid
ely
u
s
ed
f
ield
s
ar
e
(
2
)
wh
er
e
is
an
in
teg
er
.
T
h
is
s
ee
m
s
q
u
ite
n
atu
r
al,
s
in
ce
i
n
th
e
o
v
e
r
wh
elm
in
g
m
ajo
r
ity
o
f
ca
s
es
u
s
in
g
b
in
ar
y
co
d
es
an
d
b
in
ar
y
lo
g
ic,
an
d
th
e
n
u
m
b
er
o
f
ele
m
en
ts
in
th
e
(
2
)
,
f
ield
ex
ac
tly
co
r
r
esp
o
n
d
s
to
th
e
n
u
m
b
er
o
f
co
d
e
b
in
ar
y
co
m
b
in
atio
n
s
o
f
len
g
th
.
R
ec
en
tly
,
h
o
wev
e
r
,
t
h
er
e
h
as
b
ee
n
a
r
en
ew
e
d
in
ter
est
[
9
]
-
[
1
1
]
in
m
u
ltiv
alu
e
d
l
o
g
ics
th
at
g
o
b
ac
k
t
o
th
e
lo
g
ic
o
f
L
u
k
asiewicz
[
1
2
]
,
wh
ich
h
e
co
n
s
id
er
e
d
as
an
alter
n
ativ
e
to
A
r
is
to
tle's
lo
g
ic,
s
in
ce
th
e
law
o
f
th
e
ex
clu
d
ed
m
i
d
d
le
d
id
n
o
t
tak
e
p
lace
in
it.
T
h
is
in
ter
est
co
n
n
ec
ted
,
a
m
o
n
g
o
th
er
th
i
n
g
s
,
with
th
e
f
ac
t
th
at
m
u
ltiv
alu
ed
lo
g
ics
ar
e
o
f
s
ig
n
if
ican
t
in
ter
est
to
th
e
d
ev
elo
p
m
en
t
o
f
ar
tific
ial
in
tellig
en
c
e
[
1
3
]
,
[
1
4
]
.
I
n
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
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4
7
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2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t
20
21
:
871
-
87
8
872
liter
atu
r
e
th
er
e
ar
e
n
u
m
e
r
o
u
s
wo
r
k
s
p
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th
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ad
v
a
n
tag
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o
f
u
s
in
g
ter
n
ar
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lo
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ic
[
1
5
]
-
[
1
7
]
i
n
in
f
o
r
m
atio
n
th
eo
r
y
,
a
n
d
h
e
r
e
ap
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s
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r
al
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e
o
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h
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wid
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s
ed
b
in
ar
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f
in
f
o
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m
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m
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r
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en
t
b
its
,
ca
lled
"tr
it".
I
t
is
also
p
er
t
in
en
t
to
n
o
te
th
at
n
o
n
-
b
in
a
r
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Galo
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f
ield
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also
f
in
d
ap
p
licatio
n
f
o
r
th
e
im
p
lem
en
tatio
n
o
f
en
c
o
d
in
g
a
n
d
d
ec
o
d
in
g
p
r
o
ce
d
u
r
es [
1
8
]
-
[
21]
.
Ho
wev
er
,
th
e
p
o
s
s
ib
ilit
ies
o
f
u
s
in
g
m
u
ltiv
alu
e
d
lo
g
ics
h
a
v
e
o
n
e
m
o
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e
asp
ec
t,
w
h
ich
h
as
n
o
t
y
et
r
ec
eiv
ed
s
u
f
f
icien
t
atten
tio
n
in
th
e
liter
atu
r
e.
Nam
ely
,
m
u
lti
-
v
alu
ed
,
i
n
p
a
r
ticu
lar
,
te
r
n
ar
y
l
o
g
ic
is
a
p
r
o
m
is
in
g
m
ea
n
s
o
f
s
lo
wly
ch
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g
in
g
s
ig
n
als
[
2
2
]
an
aly
z
i
n
g
(
m
o
r
e
b
r
o
ad
ly
,
s
ig
n
als
with
a
lim
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d
er
iv
ativ
e)
.
T
h
is
lin
e
o
f
r
esear
c
h
s
ee
m
s
to
b
e
q
u
ite
im
p
o
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tan
t,
f
ir
s
tly
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s
e
m
a
n
y
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n
als,
f
o
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p
le
,
r
e
g
is
ter
ed
b
y
m
o
n
ito
r
i
n
g
s
y
s
tem
s
[
2
3
]
,
[
2
4
]
,
r
ea
lly
c
h
a
n
g
e
r
ath
er
s
lo
wly
to
th
e
p
o
in
t
th
at
th
ey
d
escr
ib
ed
b
y
f
u
n
ctio
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s
with
–
co
v
e
r
ag
e
(
th
e
d
if
f
er
en
ce
b
etwe
en
s
ig
n
a
ls
at
th
e
n
e
x
t
an
d
p
r
ev
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u
s
u
n
it
o
f
tim
e
b
y
th
e
m
o
d
u
le
d
o
es
n
o
t
ex
ce
e
d
o
n
e)
.
Seco
n
d
,
as
s
h
o
w
n
in
[
2
0
]
,
c
o
n
s
id
er
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n
o
f
s
lo
wly
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in
g
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ig
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als
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o
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to
r
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v
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r
elatio
n
s
h
ip
b
etwe
en
th
e
r
ate
o
f
s
ig
n
al
c
h
an
g
e
an
d
t
h
e
s
p
ec
tr
al
s
u
b
-
b
a
n
d
s
in
wh
ich
th
e
s
ig
n
al
ca
r
r
ies
th
e
co
r
r
esp
o
n
d
in
g
in
f
o
r
m
atio
n
.
Sp
ec
if
ically
,
in
th
e
cited
wo
r
k
,
it
is
s
h
o
wn
th
at
th
e
s
p
ec
tr
al
r
an
g
e,
in
wh
ich
co
n
ce
n
tr
ated
th
e
s
p
ec
tr
u
m
o
f
a
s
ig
n
al
wh
ich
i
s
p
o
s
s
ess
ed
o
f
-
co
v
e
r
ag
e,
is
n
atu
r
ally
d
iv
id
ed
i
n
to
th
r
ee
s
u
b
-
b
an
d
s
,
two
o
f
wh
ich
ca
r
r
y
in
f
o
r
m
atio
n
ab
o
u
t
s
ig
n
al
v
ar
iatio
n
s
with
an
a
m
p
litu
d
e
r
ed
u
ce
d
to
u
n
ity
.
T
h
is
r
ep
r
esen
tatio
n
o
f
s
ig
n
als
tu
r
n
s
o
u
t
to
b
e
clo
s
ely
r
elate
d
to
ter
n
ar
y
l
o
g
ic
[
2
2
]
,
wh
ich
s
er
v
es
as
o
n
e
m
o
r
e
ar
g
u
m
e
n
t
in
f
a
v
o
r
o
f
its
u
s
e.
T
h
is
q
u
esti
o
n
ca
n
b
e
p
o
s
ed
ev
e
n
m
o
r
e
b
r
o
ad
ly
.
Sp
ec
if
i
ca
lly
,
in
th
is
wo
r
k
s
h
o
wn
t
h
at
n
o
n
-
b
in
a
r
y
Galo
is
f
ield
s
also
h
av
e
v
e
r
y
s
ig
n
if
ic
an
t
ad
v
a
n
tag
es
f
o
r
d
ig
ital
p
r
o
ce
s
s
in
g
o
f
d
is
cr
ete
s
ig
n
als
o
f
f
i
n
ite
am
p
litu
d
e
(
wh
ich
,
s
tr
ictly
s
p
ea
k
in
g
,
in
cl
u
d
e
all
s
ig
n
als ac
tu
ally
u
s
ed
in
p
r
ac
tice)
.
2.
T
H
E
USAG
E
O
F
G
AL
O
I
S
F
I
E
L
D
S
T
O
DE
S
CRI
B
E
DIS
CR
E
T
E
SI
G
NAL
S
WI
T
H
A
F
I
NIT
E
RANG
E
O
F
AM
P
L
I
T
UD
E
S
VARIA
T
I
O
N
An
y
d
is
cr
ete
s
ig
n
als
wh
ich
u
s
in
g
in
p
r
ac
tice,
v
ar
y
o
v
er
a
f
in
ite
r
an
g
e
o
f
a
m
p
litu
d
es.
Fo
r
ex
am
p
le,
th
e
n
u
m
b
er
o
f
s
ig
n
al
lev
els
(
wh
ich
ar
e
h
a
n
d
led
b
y
s
tan
d
ar
d
m
icr
o
p
r
o
ce
s
s
o
r
s
th
at
ca
r
r
y
o
u
t
an
alo
g
-
to
-
d
ig
ital
co
n
v
er
s
io
n
)
is
eq
u
al
to
2
5
6
l
ev
els,
wh
ich
co
r
r
esp
o
n
d
s
to
th
e
s
tan
d
ar
d
an
alo
g
-
to
-
d
ig
ital
co
n
v
er
ter
(
ADC
)
ca
p
ac
ity
o
f
8
,
alth
o
u
g
h
in
s
o
m
e
ca
s
es u
s
in
g
ADC o
f
lar
g
e
ca
p
ac
ity
[
2
5
]
.
Acc
o
r
d
in
g
ly
,
in
p
r
ac
tice
u
s
in
g
d
ig
ital
s
ig
n
als th
at
co
r
r
esp
o
n
d
to
a
f
in
ite
s
et
o
f
lev
els.
E
ac
h
o
f
t
h
ese
lev
els
ca
n
b
e
as
s
o
ciate
d
wit
h
an
elem
en
t
o
f
s
o
m
e
Galo
is
f
ield
,
o
n
co
n
d
itio
n
s
th
at
th
e
n
u
m
b
er
o
f
s
ig
n
al
lev
els
co
r
r
esp
o
n
d
s
to
th
e
n
u
m
b
er
o
f
elem
e
n
ts
o
f
th
is
f
ield
.
I
t
i
s
im
p
o
r
tan
t
to
em
p
h
asize
th
at
th
e
tr
an
s
itio
n
ch
ar
ac
ter
f
r
o
m
a
co
n
tin
u
o
u
s
s
ig
n
al
to
a
d
is
cr
et
e
s
ig
n
al
is
a
m
atter
o
f
a
g
r
ee
m
en
t,
i.e
.
,
th
e
s
ca
le
o
f
lev
els an
d
th
eir
n
u
m
b
er
,
s
tr
ictly
s
p
ea
k
in
g
,
ca
n
b
e
s
elec
ted
b
a
s
ed
o
n
co
n
s
id
er
atio
n
s
o
f
c
o
n
v
en
ien
ce
.
I
n
p
ar
ticu
lar
,
as
will
b
e
clea
r
f
r
o
m
wh
at
f
o
llo
ws,
th
er
e
is
a
ce
r
tain
s
co
p
e
o
f
f
u
n
ctio
n
s
,
f
o
r
wh
ich
it
is
ex
p
ed
ien
t
to
c
h
o
o
s
e
t
h
e
n
u
m
b
er
o
f
n
o
n
ze
r
o
lev
els
eq
u
al
to
s
o
m
e
p
r
im
e
n
u
m
b
er
p
.
I
n
th
is
ca
s
e,
it
is
p
er
m
is
s
ib
le
to
estab
li
s
h
a
co
r
r
esp
o
n
d
e
n
ce
b
etwe
en
th
e
s
et
o
f
d
is
cr
ete
s
ig
n
al
lev
els
an
d
th
e
Galo
is
f
ield
(
)
.
W
e
em
p
h
asize
th
at
a
h
o
m
o
m
o
r
p
h
is
m
o
f
th
e
r
in
g
o
f
in
teg
er
s
in
to
r
es
id
u
e
-
class
r
in
g
s
g
e
n
er
ates
a
f
ield
(
s
p
ec
if
ically
,
a
Galo
is
f
ield
)
o
n
ly
if
is
a
p
r
im
e
n
u
m
b
e
r
.
In
t
h
is
ca
s
e,
a
d
is
cr
ete
s
ig
n
al
ca
n
b
e
co
n
s
id
er
e
d
as
a
f
u
n
ctio
n
o
f
tim
e
(
)
,
tak
in
g
v
alu
es
in
th
e
(
)
f
ield
o
r
,
wh
en
d
iv
i
d
in
g
th
e
s
ig
n
al
in
to
u
n
ite
o
f
ti
m
e,
as
an
o
r
d
er
e
d
,
ea
ch
p
ar
t o
f
wh
ich
is
an
elem
en
t o
f
th
e
Galo
is
f
ield
,
an
d
is
th
e
u
n
it o
f
tim
e
n
u
m
b
er
.
E
s
tab
lis
h
in
g
th
e
s
p
ec
if
ied
co
r
r
esp
o
n
d
en
c
e
b
etwe
en
th
e
s
ig
n
al
lev
els
an
d
th
e
elem
e
n
ts
o
f
th
e
Galo
is
f
ield
is
s
u
f
f
icien
t
to
c
o
n
s
tr
u
ct
th
e
Galo
is
Field
Fo
u
r
ier
T
r
a
n
s
f
o
r
m
.
I
n
d
ee
d
,
f
o
r
a
n
y
elem
en
t
o
f
an
a
r
b
itra
r
y
Galo
is
f
ield
co
n
tain
in
g
+
1
elem
e
n
ts
,
we
h
av
e
(
1
)
.
+
1
−
=
0
an
d
−
1
=
0
(
1
)
Fu
r
th
er
,
o
n
e
h
as a
g
e
n
er
al
th
e
o
r
em
to
th
e
s
u
m
o
f
p
r
im
al
ele
m
en
t d
eg
r
ee
.
1
+
+
2
+
⋯
+
−
1
=
{
"n
"
,
=
1
0
,
≠
1
(
2
)
wh
er
e
n
is
th
e
n
u
m
b
er
o
f
n
o
n
z
er
o
elem
en
ts
in
th
e
g
iv
en
Galo
is
f
ield
.
T
h
is
th
eo
r
em
is
ap
p
licab
le
t
o
an
y
elem
e
n
t
f
r
o
m
an
y
Galo
is
f
ield
,
s
in
ce
f
o
r
≠
1
o
n
e
h
as
th
e
r
elatio
n
,
wh
ich
f
o
llo
ws f
r
o
m
th
e
f
o
r
m
u
la
f
o
r
th
e
g
eo
m
etr
ic
p
r
o
g
r
ess
io
n
.
1
+
+
2
+
⋯
+
−
1
=
1
−
1
−
(
3
)
W
e
em
p
h
asize
th
at
in
(
3
)
,
th
e
n
u
m
b
er
n
ap
p
ea
r
s
o
n
ly
f
o
r
m
ally
,
s
in
ce
th
e
s
u
m
m
atio
n
s
h
o
u
ld
b
e
p
er
f
o
r
m
ed
p
r
ec
is
ely
in
th
e
s
en
s
e
o
f
ad
d
itio
n
in
th
is
p
ar
ticu
l
ar
f
ield
,
an
d
n
is
f
ar
f
r
o
m
n
ec
e
s
s
ar
ily
its
elem
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
S
o
me
a
d
v
a
n
ta
g
es
o
f n
o
n
-
b
in
a
r
y
Ga
lo
is
field
s
fo
r
d
ig
ita
l sig
n
a
l p
r
o
ce
s
s
in
g
(
I
n
a
b
a
t Mo
ld
a
k
h
a
n
)
873
T
h
e
n
u
m
b
er
n
in
(
3
)
,
ac
co
r
d
i
n
g
ly
,
is
n
o
th
in
g
m
o
r
e
th
a
n
a
s
y
m
b
o
l
im
p
ly
in
g
th
e
s
u
m
m
ati
o
n
o
f
n
u
n
its
.
W
e
co
n
s
tr
u
ct
th
e
f
o
llo
win
g
s
eq
u
e
n
ce
s
,
s
tar
tin
g
f
r
o
m
s
o
m
e
p
r
im
itiv
e
elem
en
t
,
th
e
d
eg
r
ee
s
o
f
wh
ich
in
clu
s
iv
e
to
(
−
1
)
-
th
g
iv
e
all
n
o
n
ze
r
o
elem
en
ts
o
f
th
e
co
n
s
id
er
ed
Galo
is
f
ie
ld
.
1
=
(
1
,
,
2
,
3
,
…
,
−
1
)
2
=
(
1
,
2
,
2
∙
2
,
2
∙
3
,
…
,
2
∙
(
−
1
)
)
(
4
)
−
1
=
(
1
,
(
−
1
)
,
(
−
1
)
∙
2
,
(
−
1
)
∙
3
,
…
,
(
−
1
)
∙
(
−
1
)
)
T
h
ese
s
eq
u
en
ce
s
ca
n
also
b
e
v
iewe
d
as f
u
n
ctio
n
s
o
f
d
is
cr
ete
tim
e.
W
e
em
p
h
asize
th
at
f
o
r
th
e
f
ie
ld
(
)
,
b
y
v
ir
t
u
e
o
f
(
1
)
,
all
th
e
d
e
g
r
ee
s
ap
p
ea
r
in
g
in
(
1
2
)
,
d
e
f
a
cto
,
d
o
n
o
t
e
x
ce
ed
.
Oth
er
wis
e,
in
clu
d
ed
in
th
em
p
r
o
d
u
cts
o
f
in
teg
er
s
(
d
eg
r
ee
s
)
ar
e
ca
lc
u
lated
b
y
(
+
1
)
.
Su
ch
s
eq
u
en
ce
s
,
as
f
o
llo
ws
f
r
o
m
(
4
)
,
ar
e
p
r
ec
is
ely
=
−
1
,
wh
er
e
is
th
e
n
u
m
b
er
o
f
n
o
n
ze
r
o
elem
e
n
ts
in
th
e
u
s
ed
Galo
is
f
ield
.
L
et
u
s
s
u
p
p
lem
en
t t
h
e
s
et
o
f
th
ese
s
eq
u
en
ce
s
with
a
s
eq
u
en
ce
c
o
n
s
is
tin
g
o
n
ly
o
f
o
n
es
.
0
=
(
1
,
1
,
1
,
1
,
…
,
1
)
(
5
)
E
ac
h
s
eq
u
e
n
ce
(
4
)
f
o
r
m
ed
in
ac
co
r
d
an
ce
with
t
h
e
f
o
llo
win
g
r
u
le.
Ho
ld
f
ix
e
d
s
o
m
e
d
e
g
r
ee
o
f
th
e
elem
en
t
.
Acc
o
r
d
in
g
ly
,
th
e
-
th
ter
m
o
f
th
e
-
th
s
eq
u
e
n
ce
will
b
e
eq
u
al
to
,
if
we
ass
u
m
e
th
at
th
e
f
ir
s
t
ter
m
co
r
r
esp
o
n
d
s
to
th
e
v
alu
e
=
0
.
Seq
u
en
ce
(
5
)
also
m
ee
ts
th
is
r
u
le
if
we
p
u
t
=
0
.
E
x
am
p
les
o
f
th
e
f
o
r
m
(
4
)
s
eq
u
en
ce
s
f
o
r
=
17
s
h
o
wn
in
Fig
u
r
e
1.
W
h
en
in
clu
d
in
g
(
5
)
in
to
t
h
e
s
et
(
4
)
,
o
b
v
io
u
s
ly
,
th
e
n
u
m
b
er
o
f
s
eq
u
en
ce
s
o
f
th
e
co
n
s
id
er
e
d
ty
p
e
will
b
e
eq
u
al
to
-
th
e
n
u
m
b
er
o
f
elem
en
ts
o
f
th
e
co
n
s
id
er
ed
Galo
is
f
ield
.
Fo
r
ea
c
h
o
f
t
h
e
s
eq
u
en
ce
s
(
4
)
,
th
er
e
is
o
n
e
a
n
d
o
n
l
y
o
n
e
s
eq
u
en
ce
f
r
o
m
th
is
s
et
f
o
r
wh
ich
t
h
e
co
n
d
itio
n
:
∑
1
(
)
2
(
)
=
−
1
=
0
=
1
(
6
)
Fig
u
r
e
1
.
E
x
am
p
les o
f
s
eq
u
en
ce
th
at
allo
w
th
e
in
ter
p
r
etatio
n
as a
g
en
er
aliza
tio
n
o
f
th
e
R
ad
em
ac
h
er
f
u
n
ctio
n
s
f
o
r
d
if
f
er
en
t
v
alu
es
o
f
(
th
e
n
u
m
b
er
s
o
f
s
eq
u
en
ce
a
r
e
in
d
icate
d
o
n
th
e
g
r
ap
h
s
)
Su
ch
s
eq
u
en
ce
s
ca
n
b
e
ca
lle
d
co
n
ju
g
ate;
eq
u
ality
(
6
)
is
v
ali
d
f
o
r
s
eq
u
en
ce
s
with
n
u
m
b
er
s
s
atis
f
y
in
g
th
e
co
n
d
itio
n
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t
20
21
:
871
-
87
8
874
1
≡
2
(
(
+
1
)
)
(
7
)
R
elatio
n
(
6
)
f
o
llo
ws f
r
o
m
th
e
f
ac
t th
at
th
e
d
ir
ec
t
p
r
o
d
u
ct
o
f
s
eq
u
en
ce
s
(
4
)
b
y
ea
ch
o
t
h
er
h
a
s
th
e
f
o
r
m
:
1
∗
2
=
(
1
,
(
1
+
2
)
,
2
(
1
+
2
)
,
…
,
(
−
1
)
(
1
+
2
)
)
(
8
)
Ass
u
m
in
g
=
(
1
+
2
)
(
9
)
an
d
ap
p
ly
in
g
(
3
)
,
we
o
b
tain
(
1
0
)
.
∑
1
(
)
2
(
)
=
−
1
=
0
=
{
1
,
1
≡
2
(
(
+
1
)
)
0
,
1
≢
2
(
(
+
1
)
)
(
1
0
)
B
ased
o
n
(
1
0
)
,
o
n
e
ca
n
im
m
e
d
iately
g
o
to
th
e
s
p
ec
tr
al
r
ep
r
es
en
tatio
n
o
f
t
h
e
s
ig
n
al
in
th
e
f
o
r
m
⃗
=
∑
⃗
⃗
=
−
1
=
0
(
1
1
)
Mu
ltip
licatio
n
o
f
r
elatio
n
(
1
1
)
b
y
th
e
v
ec
to
r
⃗
⃗
co
n
ju
g
ate
(
in
t
h
e
s
en
s
e
o
f
(
6
)
with
⃗
⃗
,
b
y
v
ir
tu
e
o
f
(
1
0
)
,
g
iv
es
(
1
2
)
.
(
,
⃗
⃗
⃗
⃗
⃗
)
=
∑
(
⃗
⃗
,
⃗
⃗
)
=
−
1
=
0
=
(
1
2
)
I
t
f
o
llo
ws
f
r
o
m
r
elatio
n
(
1
2
)
th
at
th
e
o
b
tain
ed
s
eq
u
e
n
ce
s
ca
n
b
e
i
n
ter
p
r
eted
as
g
en
er
alize
d
R
ad
em
ac
h
er
f
u
n
ctio
n
s
[
2
1
]
-
[
2
3
]
th
at
m
a
k
e
u
p
a
co
m
p
lete
s
y
s
tem
o
n
ly
f
o
r
th
e
ca
s
e
o
f
th
e
m
in
im
u
m
n
u
m
b
er
s
o
f
u
n
it
o
f
tim
e.
I
n
d
ee
d
,
r
elatio
n
(
1
0
)
ca
n
b
e
in
ter
p
r
eted
b
y
an
al
o
g
y
with
th
e
co
n
d
itio
n
o
f
f
u
n
ctio
n
s
o
r
th
o
g
o
n
ality
o
f
a
co
m
p
lex
v
ar
iab
le
u
n
d
er
co
n
d
itio
n
th
at
co
n
s
id
er
ed
p
iece
wis
e
co
n
tin
u
o
u
s
f
u
n
ctio
n
s
,
t
h
at
ar
e
r
e
d
u
cib
le
t
o
s
eq
u
en
ce
s
co
n
tain
in
g
p
u
n
it o
f
tim
e,
wh
ich
co
r
r
esp
o
n
d
s
to
th
e
u
s
e
o
f
th
e
f
ield
(
)
.
I
t
ca
n
b
e
s
e
en
th
at
s
u
ch
f
u
n
ctio
n
s
f
o
r
m
in
g
a
co
m
p
lete
b
asis
,
i.e
.
,
th
er
eth
r
o
u
g
h
ca
n
b
e
r
ep
r
esen
ted
an
y
f
u
n
ctio
n
d
ef
in
ed
in
u
n
ite
o
f
tim
e,
as we
ll a
s
an
y
-
p
er
io
d
ic
f
u
n
ctio
n
.
I
n
th
is
ca
s
e,
th
e
elem
en
ts
o
f
th
e
f
ield
th
at
ca
lcu
lated
b
y
(
1
2
)
h
a
v
e
th
e
s
am
e
m
ea
n
in
g
as
th
e
s
p
ec
tr
al
co
m
p
o
n
en
ts
ca
lcu
lat
ed
u
s
in
g
o
n
e
o
r
an
o
t
h
er
b
asis
o
f
co
m
p
lex
-
v
alu
ed
f
u
n
ctio
n
s
.
T
h
e
o
n
ly
o
n
e
d
if
f
er
en
ce
is
th
at
wh
en
u
s
in
g
t
h
e
o
r
th
o
g
o
n
al
b
asis
o
f
co
m
p
le
x
-
v
alu
ed
f
u
n
ctio
n
s
,
th
e
am
p
litu
d
es o
f
th
e
s
p
ec
tr
al
co
m
p
o
n
en
ts
ar
e
also
ap
p
ea
r
e
d
co
m
p
lex
q
u
an
titi
es,
an
d
w
h
e
n
u
s
in
g
th
e
s
p
ec
tr
al
r
ep
r
esen
t
atio
n
in
n
o
n
-
b
in
ar
y
Galo
is
f
ield
s
,
th
ey
ar
e
elem
en
t
s
o
f
th
e
s
am
e
f
ield
.
I
t
is
ess
en
tial
th
at
d
u
e
to
th
i
s
,
th
e
am
o
u
n
t
o
f
d
ata
th
at
n
e
ed
ed
to
tr
an
s
m
it
in
f
o
r
m
atio
n
ab
o
u
t
th
e
s
p
ec
tr
u
m
tu
r
n
o
u
t
to
b
e
s
ig
n
if
ican
tly
less
th
an
,
f
o
r
e
x
am
p
le
,
wh
en
u
s
in
g
t
h
e
W
alsh
b
asis
[
2
4
]
,
[
2
5
]
.
I
n
d
ee
d
,
th
e
am
p
litu
d
e
o
f
th
e
s
p
ec
tr
al
co
m
p
o
n
en
ts
ca
lc
u
lated
b
y
u
s
in
g
th
e
W
alsh
b
asis
ca
n
v
ar
y
o
v
er
a
v
er
y
wid
e
r
an
g
e,
a
n
d
in
t
h
e
ca
s
e
u
n
d
er
c
o
n
s
id
er
atio
n
,
it
k
n
o
win
g
ly
lies
in
th
e
s
am
e
r
an
g
e
as th
e
o
r
ig
i
n
al
s
ig
n
al.
3.
DE
SCR
I
P
T
I
O
N
O
F
T
H
E
D
I
G
I
T
A
L
SPEC
T
RU
M
O
F
T
H
E
SI
G
N
AL
DE
R
I
VA
T
I
V
E
I
N
T
E
R
M
S
O
F
NO
N
-
B
I
NARY
G
A
L
O
I
S
F
I
E
L
DS
T
h
e
f
u
n
ctio
n
s
p
r
esen
ted
ab
o
v
e,
wh
ich
ca
n
b
e
in
ter
p
r
ete
d
as
g
en
e
r
alize
d
R
ad
em
ac
h
e
r
f
u
n
ctio
n
s
,
m
ak
e
it
p
o
s
s
ib
le
to
o
b
tain
a
r
esu
lt
th
at
is
a
d
ir
ec
t
an
alo
g
u
e
o
f
th
e
well
-
k
n
o
wn
p
r
o
p
e
r
ty
o
f
h
ar
m
o
n
ic
s
ig
n
als,
wh
ich
co
n
s
is
ts
in
th
e
f
ac
t
th
at
th
e
Fo
u
r
ier
tr
an
s
f
o
r
m
o
f
a
s
ig
n
al,
wh
ich
tim
e
tr
an
s
lated
,
d
i
f
f
er
s
f
r
o
m
th
e
in
itial
o
n
e
o
n
l
y
b
y
th
e
p
h
ase
f
ac
to
r
.
[
(
−
0
)
]
=
−
0
∫
−
1
(
)
=
−
0
[
(
)
]
(
1
3
)
wh
er
e
an
d
ar
e
tim
e
an
d
f
r
eq
u
en
cy
v
ar
iab
les,
[
(
)
]
is
th
e
d
esig
n
atio
n
o
f
th
e
Fo
u
r
ier
tr
an
s
f
o
r
m
o
f
th
e
f
u
n
ctio
n
(
)
,
0
is
th
e
s
h
if
t
in
ter
v
a
l
alo
n
g
t
h
e
tim
e
ax
is
.
W
e
o
b
t
ain
a
d
ir
ec
t
an
alo
g
u
e
o
f
p
r
o
p
er
ty
(
1
3
)
f
o
r
s
p
ec
tr
a,
wh
ich
o
b
tain
ed
f
r
o
m
g
en
er
alize
d
R
ad
em
ac
h
e
r
f
u
n
ct
io
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
S
o
me
a
d
v
a
n
ta
g
es
o
f n
o
n
-
b
in
a
r
y
Ga
lo
is
field
s
fo
r
d
ig
ita
l sig
n
a
l p
r
o
ce
s
s
in
g
(
I
n
a
b
a
t Mo
ld
a
k
h
a
n
)
875
T
h
e
an
alo
g
y
with
th
e
tim
e
tr
a
n
s
latio
n
f
o
r
p
er
i
o
d
ic
s
ig
n
als,
th
at
s
atis
f
y
to
th
e
r
ep
o
r
tin
g
s
y
s
tem
u
n
d
er
co
n
s
id
er
atio
n
,
t
h
e
am
p
litu
d
e
v
alu
es
o
f
wh
ich
d
is
p
lay
ed
in
a
ce
r
tain
Galo
is
f
ield
,
is
as
f
o
llo
ws.
T
h
er
e
is
an
o
r
ig
in
al
s
eq
u
e
n
ce
.
(
0
)
=
(
0
,
1
,
2
,
3
,
…
,
−
1
)
(
1
4
)
C
y
clic
p
er
m
u
tatio
n
b
y
o
n
e
p
o
s
itio
n
co
r
r
esp
o
n
d
s
to
a
tim
e
s
h
i
f
t b
y
o
n
e
cy
cle.
(
1
)
=
(
−
1
,
0
,
1
,
2
,
…
,
−
2
)
(
1
5
)
(
2
)
=
(
−
2
,
−
1
,
0
,
1
,
…
,
−
3
)
(
1
6
)
L
et
u
s
f
o
r
m
a
d
ir
ec
t
p
r
o
d
u
ct.
⃗
⃗
∗
(
1
)
=
(
1
∙
−
1
,
∙
0
,
2
∙
1
,
…
,
(
−
1
)
∙
−
2
)
(
1
7
)
W
h
en
s
u
m
m
in
g
(
th
e
o
p
er
atio
n
o
f
ca
lcu
latin
g
t
h
e
elem
en
t
o
f
th
e
Galo
is
f
ield
co
r
r
esp
o
n
d
i
n
g
to
th
e
am
p
litu
d
e
o
f
an
in
d
iv
id
u
al
s
p
ec
tr
al
c
o
m
p
o
n
en
t)
,
o
n
e
ca
n
m
ak
e
a
p
er
m
u
tatio
n
.
(
⃗
⃗
,
(
1
)
)
=
0
+
1
2
+
⋯
+
−
2
(
−
1
)
+
−
1
(
1
8
)
T
ak
in
g
th
e
f
ac
to
r
o
u
ts
id
e
th
e
b
r
ac
k
et,
we
o
b
tain
(
⃗
⃗
,
(
1
)
)
=
(
,
(
0
)
)
(
1
9
)
wh
er
e
it is
co
n
s
id
er
ed
th
at
(
−
1
)
=
=
1
.
T
h
e
s
am
e
way
,
(
⃗
⃗
,
(
)
)
=
(
⃗
⃗
,
(
0
)
)
(
2
0
)
I
t
can
b
e
s
ee
n
th
at
th
e
o
b
tain
e
d
(
2
0
)
is
a
d
ir
ec
t
an
alo
g
u
e
o
f
p
r
o
p
er
t
y
(
1
3
)
in
h
e
r
en
t
in
s
p
ec
tr
a,
th
at
ca
lcu
lated
b
ased
o
n
t
h
e
d
ec
o
m
p
o
s
itio
n
o
f
th
e
s
ig
n
al
b
y
h
ar
m
o
n
ic
f
u
n
ctio
n
s
.
T
h
is
f
o
r
m
u
la
will
b
e
n
ee
d
ed
b
elo
w
t
o
d
escr
ib
e
th
e
s
p
ec
tr
a
o
f
th
e
n
u
m
er
ical
d
er
iv
ativ
es o
f
s
ig
n
als th
at
r
ep
r
esen
ted
i
n
d
is
cr
ete
f
o
r
m
.
A
s
p
ec
ial
ca
s
e
o
f
s
u
ch
an
o
p
er
atio
n
is
th
e
n
u
m
e
r
ical
s
ea
r
ch
o
f
th
e
f
ir
s
t
d
er
iv
ativ
e
th
at
r
ed
u
ce
s
to
ca
lcu
latin
g
th
e
d
if
f
er
en
ce
.
Δ
(
)
=
(
)
−
(
−
0
)
(
2
1
)
wh
er
e
is
th
e
d
u
r
atio
n
o
f
o
n
e
c
y
cle,
d
u
r
i
n
g
wh
ich
th
e
s
ig
n
al
r
em
ain
s
co
n
s
tan
t.
W
h
en
p
ass
in
g
to
p
e
r
io
d
ic
o
r
ar
tific
ially
p
er
io
d
ic
s
ig
n
als,
th
at
r
ep
r
esen
ted
b
y
s
eq
u
e
n
ce
s
o
f
th
e
f
o
r
m
(
1
4
)
,
t
h
e
o
p
er
atio
n
(
2
1
)
co
r
r
es
p
o
n
d
s
to
ca
lc
u
latin
g
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
two
s
eq
u
en
c
es
.
⃗
(
0
)
=
(
0
,
1
,
2
,
…
,
−
1
)
(
2
2
)
⃗
(
1
)
=
(
−
1
,
0
,
1
,
…
,
−
2
)
(
2
3
)
L
et
u
s
s
h
o
w
th
at
in
th
e
s
p
ec
tr
al
r
ep
r
esen
tatio
n
it
d
escr
ib
e
d
th
r
o
u
g
h
th
e
a
n
alo
g
u
e
o
f
th
e
tr
an
s
f
er
f
u
n
ctio
n
.
C
alcu
latin
g
th
e
s
p
ec
tr
a
o
f
s
eq
u
en
ce
s
(
2
2
)
a
n
d
(
2
3
)
,
s
u
b
tr
ac
tin
g
th
e
o
b
tain
ed
r
esu
lt
f
r
o
m
ea
c
h
o
t
h
er
an
d
u
s
in
g
r
elatio
n
(
2
0
)
,
we
o
b
t
ain
(
2
4
)
.
(
⃗
⃗
,
⃗
(
1
)
−
⃗
(
0
)
)
=
(
−
1
)
(
⃗
⃗
,
⃗
(
0
)
)
(
2
4
)
i.e
.
,
a
d
is
cr
ete
an
alo
g
o
f
th
e
d
if
f
er
en
tiatio
n
o
p
er
atio
n
in
s
p
e
ctr
a
ter
m
s
,
th
at
co
n
s
tr
u
cted
b
a
s
ed
o
n
g
en
er
alize
d
R
ad
em
ac
h
er
f
u
n
ctio
n
s
is
in
d
e
ed
d
escr
ib
ed
t
h
r
o
u
g
h
th
e
an
alo
g
o
f
th
e
tr
an
s
f
er
f
u
n
ctio
n
.
T
h
is
f
o
r
m
u
la
(
2
5
)
clea
r
ly
co
r
r
elate
s
with
th
e
well
-
k
n
o
wn
f
ac
t
th
at,
in
th
e
f
r
eq
u
en
cy
r
e
p
r
esen
tatio
n
th
e
d
if
f
er
e
n
tiatio
n
o
p
er
atio
n
al
s
o
r
ed
u
ce
d
t
o
th
e
a
p
p
ea
r
an
ce
o
f
th
e
s
im
p
lest
ty
p
e
o
f
tr
an
s
f
er
f
u
n
ctio
n
.
E
x
ac
tly
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t
20
21
:
871
-
87
8
876
[
]
=
∫
−
=
−
∫
(
)
=
∫
(
)
=
[
]
(
2
5
)
T
h
is
f
o
r
m
o
f
th
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
d
if
f
e
r
en
tiatio
n
o
p
er
atio
n
,
in
p
ar
ticu
lar
,
d
eter
m
i
n
es
th
e
well
-
k
n
o
wn
f
o
r
m
o
f
th
e
f
o
r
m
u
la
f
o
r
th
e
im
p
ed
an
ce
o
f
a
ca
p
ac
it
o
r
with
C
ca
p
ac
itan
ce
.
=
1
(
2
6
)
Gen
er
alize
d
R
ad
em
ac
h
er
f
u
n
c
tio
n
s
ar
e
v
al
u
ab
le
b
ec
au
s
e
th
e
y
allo
w
u
s
to
d
ev
elo
p
a
s
im
ila
r
ap
p
r
o
ac
h
but
ap
p
lied
to
d
ig
itized
s
ig
n
als.
I
n
p
a
r
ticu
lar
,
f
o
r
≠
0
,
(
2
7
)
is
v
alid
.
(
⃗
⃗
,
⃗
)
=
1
(
−
1
)
(
⃗
⃗
,
Δ
⃗
)
,
≠
0
(
2
7
)
T
h
e
co
n
d
itio
n
≠
0
m
ea
n
s
th
at
all
co
m
p
o
n
en
ts
ca
n
b
e
r
esto
r
ed
,
e
x
ce
p
t f
o
r
th
e
co
n
s
tan
t.
T
h
e
r
esu
ltin
g
r
elatio
n
(
2
7
)
o
p
en
s
u
p
a
n
u
m
b
er
o
f
a
d
d
itio
n
al
p
o
s
s
ib
ilit
ies
f
o
r
b
o
th
d
ig
ital
s
ig
n
al
p
r
o
ce
s
s
in
g
an
d
f
o
r
th
eir
t
r
an
s
m
is
s
io
n
.
I
n
p
ar
ticu
lar
,
th
e
n
u
m
er
ical
d
er
iv
ativ
e
o
f
a
s
ig
n
al
with
an
-
c
o
v
er
i
n
g
ca
n
tak
e
o
n
ly
th
r
ee
v
alu
es
b
y
d
ef
in
itio
n
(
wh
ich
co
r
r
esp
o
n
d
s
to
ter
n
ar
y
lo
g
ic)
.
Ob
v
io
u
s
ly
,
th
at
if
tr
an
s
m
it
o
n
ly
in
f
o
r
m
atio
n
ab
o
u
t
th
e
d
er
iv
at
iv
e
th
en
f
o
r
th
is
will
r
eq
u
ir
e
less
b
an
d
wid
th
.
Ho
wev
er
,
t
h
is
ap
p
r
o
ac
h
is
n
o
t
ac
ce
p
tab
le
f
o
r
p
r
ac
tical
u
s
e
d
u
e
to
th
e
in
ev
it
ab
le
ac
cu
m
u
latio
n
o
f
er
r
o
r
s
.
On
th
e
co
n
tr
ar
y
,
th
e
n
o
ted
cir
cu
m
s
tan
ce
ca
n
b
e
u
s
ed
if
tr
an
s
m
it
th
e
in
f
o
r
m
atio
n
ab
o
u
t
th
e
s
p
ec
tr
a
-
ea
ch
s
p
ec
tr
al
co
m
p
o
n
en
t
(
m
o
r
e
p
r
ec
is
ely
,
th
e
co
r
r
esp
o
n
d
in
g
elem
en
t
o
f
th
e
Galo
is
f
ield
)
is
ca
lcu
lated
b
ased
o
n
in
f
o
r
m
ati
o
n
ab
o
u
t
th
e
en
tire
s
ig
n
al
p
r
o
f
ile
o
v
er
th
e
all
-
in
te
r
v
al,
an
d
th
e
n
u
m
b
er
ca
n
b
e
m
ad
e
lar
g
e
e
n
o
u
g
h
.
Fu
r
th
er
,
th
e
f
u
n
ctio
n
s
,
in
ter
p
r
eted
as
g
en
er
alize
d
R
ad
em
ac
h
er
f
u
n
ctio
n
s
,
m
ak
e
it
p
o
s
s
ib
le
to
d
ev
elo
p
a
d
ig
ital
an
alo
g
u
e
o
f
th
e
tr
an
s
f
er
f
u
n
ctio
n
a
p
p
ar
at
u
s
f
o
r
an
y
l
in
ea
r
r
ad
io
-
e
n
g
in
ee
r
in
g
n
etwo
r
k
s
(
m
o
r
e
b
r
o
ad
ly
,
f
o
r
a
n
y
lin
ea
r
s
y
s
tem
s
)
.
T
h
is
f
o
llo
ws
f
r
o
m
th
e
f
ac
t
th
at
a
n
y
lin
ea
r
o
p
er
atio
n
s
p
er
f
o
r
m
ed
o
n
f
u
n
ctio
n
s
in
t
h
e
d
ig
ital
r
ep
r
esen
tatio
n
(
if
t
h
ey
h
av
e
th
e
p
r
o
p
er
ty
o
f
i
n
v
ar
ian
c
e
with
r
esp
ec
t
to
tim
e
tr
an
s
la
tio
n
)
in
th
e
s
p
ec
tr
a
l
r
ep
r
esen
tatio
n
tak
e
t
h
e
f
o
r
m
.
(
⃗
⃗
,
⃗
)
=
(
)
(
⃗
⃗
,
Δ
⃗
)
(
2
8
)
wh
ich
ca
n
b
e
s
h
o
wn
in
t
h
e
s
am
e
way
in
wh
ich
r
elatio
n
(
2
7
)
was o
b
tain
ed
.
T
h
e
ex
p
ed
ien
c
y
o
f
u
s
in
g
f
o
r
m
u
las
o
f
th
e
f
o
r
m
(
2
8
)
f
o
r
r
ad
io
-
tech
n
ical
cir
cu
its
o
f
th
is
ty
p
e
ca
n
o
b
v
io
u
s
l
y
b
e
d
is
p
u
ted
.
Ho
we
v
er
,
th
ey
ca
n
ce
r
tain
ly
b
e
u
s
ef
u
l,
f
o
r
ex
a
m
p
le,
f
o
r
s
o
lv
in
g
p
r
o
b
lem
s
o
f
f
in
d
in
g
eq
u
iv
alen
t
r
ad
io
cir
cu
its
o
f
v
ar
io
u
s
k
in
d
s
o
f
p
r
o
ce
s
s
es
(
f
o
r
ex
am
p
le,
eq
u
i
v
alen
t
cir
c
u
its
o
f
elec
tr
o
c
h
em
ical
ce
lls
,
etc.
)
.
I
n
t
h
is
ca
s
e,
th
e
ta
s
k
ca
n
b
e
f
o
r
m
u
lated
as
f
o
llo
ws.
T
h
er
e
is
a
d
ef
in
ite
f
u
n
cti
o
n
o
f
tim
e
(
s
ig
n
al)
,
wh
ich
ap
p
ea
r
s
as
a
r
esp
o
n
s
e
t
o
s
o
m
e
in
f
lu
e
n
ce
s
o
n
th
e
s
y
s
tem
,
wh
ich
s
tu
d
ied
e
x
p
er
im
e
n
ta
lly
.
I
t
is
r
eq
u
ir
e
d
to
estab
lis
h
wh
eth
er
th
er
e
ar
e
r
ad
io
-
tech
n
ical
cir
c
u
its
th
at
is
eq
u
iv
alen
t
to
th
e
s
y
s
tem
u
n
d
er
co
n
s
id
er
atio
n
in
ter
m
s
o
f
s
ig
n
al
co
n
v
er
s
io
n
.
An
d
if
s
o
,
wh
ic
h
o
n
e?
T
o
s
o
lv
e
p
r
o
b
lem
s
o
f
th
is
k
in
d
,
th
e
tr
a
n
s
itio
n
to
d
ig
ital
r
e
p
r
esen
tatio
n
is
o
b
v
io
u
s
ly
u
s
ef
u
l,
s
in
ce
it
s
ig
n
if
ican
tly
s
im
p
lifie
s
co
m
p
u
tatio
n
al
p
r
o
ce
d
u
r
es,
in
m
an
y
r
esp
ec
ts
it
tu
r
n
s
o
u
t
to
r
em
o
v
e
th
e
q
u
esti
o
n
o
f
m
ea
s
u
r
em
en
t e
r
r
o
r
s
,
etc.
4.
CO
NCLU
SI
O
N
T
h
e
u
s
in
g
o
f
n
o
n
-
b
in
a
r
y
Galo
is
f
ield
s
in
d
ee
d
cr
ea
tes
q
u
ite
d
ef
in
ite
ad
v
a
n
tag
es
f
o
r
p
r
o
ce
s
s
in
g
d
ig
ital
s
ig
n
als
th
at
v
ar
y
in
g
in
a
f
in
ite
r
an
g
e
o
f
am
p
litu
d
es.
I
n
th
is
c
ase,
it
b
ec
o
m
es
p
o
s
s
ib
le
a
ce
r
t
ain
elem
en
t
o
f
th
e
Galo
is
f
ield
p
u
t
in
co
r
r
esp
o
n
d
en
ce
to
ea
ch
o
f
th
e
s
ig
n
al
am
p
litu
d
e
lev
els.
T
h
is
ap
p
r
o
ac
h
allo
ws,
f
ir
s
tly
,
to
co
n
s
tr
u
ct
a
wid
e
v
ar
iety
o
f
an
alo
g
s
o
f
o
r
t
h
o
g
o
n
al
b
ases
,
d
if
f
er
in
g
in
th
at
t
h
e
o
p
e
r
atio
n
s
wh
ich
n
ec
ess
ar
y
f
o
r
d
ig
ital
s
ig
n
al
p
r
o
ce
s
s
in
g
ar
e
ca
r
r
ied
o
u
t
in
th
e
s
en
s
e
o
f
m
u
ltip
licatio
n
,
ad
d
itio
n
,
etc.
Galo
is
f
ield
s
.
An
illu
s
tr
atio
n
o
f
th
e
ad
d
itio
n
al
p
o
s
s
ib
ilit
ie
s
th
at
ar
is
e
i
s
,
in
p
ar
ticu
lar
,
th
e
co
n
s
tr
u
ctio
n
o
f
a
b
asis
in
wh
ich
th
e
f
u
n
ctio
n
s
th
at
in
cl
u
d
ed
in
it,
c
an
b
e
in
ter
p
r
eted
as
g
en
er
aliz
ed
R
ad
em
ac
h
er
f
u
n
ctio
n
s
.
I
t
i
s
ess
en
tial
th
at
s
u
ch
f
u
n
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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d
o
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J
E
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E
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g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
S
o
me
a
d
v
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I
n
a
b
a
t Mo
ld
a
k
h
a
n
)
877
RE
F
E
R
E
NC
E
S
[1
]
M
.
P
o
o
la
k
k
a
p
a
ra
m
b
il
,
J.
M
a
t
h
e
w,
A.
M
.
Ja
b
ir,
a
n
d
S
.
P
.
M
o
h
a
n
ty
,
“
An
In
v
e
sti
g
a
ti
o
n
o
f
Co
n
c
u
rre
n
t
Err
o
r
De
tec
ti
o
n
o
v
e
r
Bi
n
a
ry
G
a
lo
is
F
ield
s
i
n
CNTF
ET
a
n
d
QCA
Tec
h
n
o
lo
g
i
e
s,
”
in
2
0
1
2
IEE
E
C
o
mp
u
ter
S
o
c
iety
An
n
u
a
l
S
y
mp
o
si
u
m o
n
VL
S
I
,
2
0
1
2
,
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p
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4
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0
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1
1
0
9
/I
S
VLS
I.
2
0
1
2
.
5
7
.
[2
]
T.
P
ru
ss
,
P
.
Ka
ll
a
,
a
n
d
F
.
E
n
e
sc
u
,
“
Eq
u
iv
a
len
c
e
v
e
rifi
c
a
ti
o
n
o
f
l
a
rg
e
G
a
lo
is
field
a
rit
h
m
e
ti
c
c
irc
u
it
s
u
si
n
g
w
o
rd
-
lev
e
l
a
b
stra
c
ti
o
n
v
ia
G
rö
b
n
e
r
b
a
se
s,
”
i
n
Pro
c
e
e
d
in
g
s
o
f
t
h
e
5
1
st
An
n
u
a
l
De
sig
n
A
u
to
m
a
ti
o
n
C
o
n
fer
e
n
c
e
,
2
0
1
4
,
p
p
.
1
-
6
.
[3
]
X.
Li
u
,
Y.
F
a
n
,
a
n
d
H.
Li
u
,
“
G
a
l
o
is
LCD
c
o
d
e
s
o
v
e
r
fi
n
it
e
field
s,
”
Fi
n
it
e
Fi
e
l
d
s
a
n
d
T
h
e
ir
Ap
p
li
c
a
ti
o
n
s
,
v
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l.
4
9
,
p
p
.
2
2
7
–
2
4
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,
2
0
1
8
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d
o
i:
1
0
.
1
0
1
6
/j
.
ffa
.
2
0
1
7
.
1
0
.
0
0
1
.
[4
]
S
.
S
h
i
v
a
sh
a
n
k
a
r,
M
.
Ku
d
a
ri,
a
n
d
P
.
S
.
Hire
m
a
th
,
“
A
G
a
lo
is
field
-
b
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se
d
tex
tu
re
re
p
re
se
n
tatio
n
f
o
r
fa
c
e
re
c
o
g
n
it
io
n
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
A
p
p
li
e
d
En
g
i
n
e
e
rin
g
Res
e
a
rc
h
,
v
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l.
1
3
,
n
o
.
1
8
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p
p
.
1
3
4
6
0
-
1
3
4
6
5
,
2
0
1
8
.
[5
]
S
.
Li
n
,
K.
Ab
d
e
l
-
G
h
a
ffa
r,
J.
Li
,
a
n
d
K
.
Li
u
,
“
Itera
ti
v
e
so
ft
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d
e
c
isio
n
d
e
c
o
d
i
n
g
o
f
re
e
d
-
S
o
lo
m
o
n
c
o
d
e
s
o
f
p
rime
len
g
t
h
s,
”
in
2
0
1
7
IEE
E
I
n
te
rn
a
ti
o
n
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l
S
y
mp
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(IS
I
T
)
,
2
0
1
7
,
p
p
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3
4
1
-
3
4
5
,
d
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0
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0
9
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IT
.
2
0
1
7
.
8
0
0
6
5
4
6
.
[6
]
P
.
Li
u
,
Z
.
P
a
n
,
a
n
d
J.
Lei,
“
P
a
ra
m
e
ter
Id
e
n
ti
fica
ti
o
n
o
f
Re
e
d
-
S
o
l
o
m
o
n
Co
d
e
s
Ba
se
d
o
n
P
ro
b
a
b
i
li
t
y
S
tatisti
c
s
a
n
d
G
a
lo
is
F
ield
F
o
u
rier
T
ra
n
sfo
rm
,
”
IEE
E
Acc
e
ss
,
v
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l
.
7
,
p
p
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3
3
6
1
9
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9
,
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1
0
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1
1
0
9
/ACCES
S
.
2
0
1
9
.
2
9
0
4
7
1
8
.
[7
]
Q.
Hu
a
n
g
,
L.
Ta
n
g
,
S
.
He
,
Z.
Xi
o
n
g
,
a
n
d
Z.
Wa
n
g
,
“
L
o
w
-
Co
m
p
l
e
x
it
y
E
n
c
o
d
in
g
o
f
Q
u
a
si
-
Cy
c
li
c
Co
d
e
s
Ba
se
d
o
n
G
a
lo
is
F
o
u
rier
Tran
sfo
rm
,
”
IE
E
E
T
ra
n
sa
c
ti
o
n
s
o
n
Co
mm
u
n
ica
ti
o
n
s
,
v
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l.
6
2
,
n
o
.
6
,
p
p
.
1
7
5
7
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7
6
7
,
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n
e
2
0
1
4
,
d
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i:
1
0
.
1
1
0
9
/T
COM
M
.
2
0
1
4
.
2
3
1
6
1
7
4
.
[8
]
G
.
Wu
,
B.
Zh
a
n
g
,
X.
Wen
,
a
n
d
D
.
G
u
o
,
“
Bli
n
d
re
c
o
g
n
it
io
n
o
f
BC
H
c
o
d
e
b
a
se
d
o
n
G
a
lo
is
field
F
o
u
rier
tran
sfo
rm
,
”
in
2
0
1
5
I
n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
W
ire
les
s
Co
mm
u
n
ica
ti
o
n
s
&
S
ig
n
a
l
Pro
c
e
ss
in
g
(W
CS
P)
,
2
0
1
5
,
p
p
.
1
-
4
,
d
o
i:
1
0
.
1
1
0
9
/W
CS
P
.
2
0
1
5
.
7
3
4
1
2
4
3
.
[9
]
A.
Ka
rp
e
n
k
o
a
n
d
N.
T
o
m
o
v
a
,
“
Bo
c
h
v
a
r'
s
th
re
e
-
v
a
l
u
e
d
lo
g
ic
a
n
d
li
tera
l
p
a
ra
lo
g
ics
:
T
h
e
ir
latti
c
e
a
n
d
fu
n
c
ti
o
n
a
l
e
q
u
iv
a
len
c
e
,
”
L
o
g
ic a
n
d
L
o
g
ica
l
Ph
il
o
s
o
p
h
y
,
v
o
l.
2
6
,
n
o
.
2
,
p
p
.
2
0
7
-
2
3
5
,
2
0
1
7
.
[1
0
]
A.
S
c
h
u
m
a
n
n
,
“
Lo
g
ica
l
De
term
in
a
c
y
v
e
rsu
s
Lo
g
ica
l
C
o
n
ti
n
g
e
n
c
y
.
T
h
e
Ca
se
o
f
Łu
k
a
sie
wic
z
’s
Th
re
e
-
v
a
lu
e
d
Lo
g
ic,
”
S
tu
d
i
a
Hu
ma
n
a
,
v
o
l.
8
,
n
o
.
2
,
p
p
.
8
-
1
5
,
De
c
2
0
1
9
.
[1
1
]
N.
F
ra
n
c
e
z
a
n
d
M
.
Ka
m
in
sk
i
,
“
S
tru
c
tu
ra
l
r
u
les
f
o
r
m
u
lt
i
-
v
a
l
u
e
d
l
o
g
ics
,
”
L
o
g
ica
U
n
ive
rs
a
li
s
,
v
o
l.
1
3
,
n
o
.
1
,
p
p
.
6
5
-
7
5
,
2
0
1
9
.
[1
2
]
J.
Lu
k
a
sie
wic
z
,
“
On
th
re
e
-
v
a
lu
e
d
lo
g
ic,”
in
S
e
lec
t
wo
rk
s
,
Am
ste
rd
a
m
:
No
rth
-
Ho
ll
a
n
d
P
u
b
li
s
h
in
g
C
o
m
p
a
n
y
,
1
9
7
0
,
p
p
.
8
7
–
8
8
.
[1
3
]
I.
E.
S
u
leim
e
n
o
v
,
e
t
a
l
.,
“
Artifi
c
ial
In
telli
g
e
n
c
e
:
wh
a
t
is
it
?
,
”
i
n
Pro
c
e
e
d
in
g
s
o
f
th
e
2
0
2
0
6
t
h
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Co
m
p
u
ter
a
n
d
T
e
c
h
n
o
lo
g
y
Ap
p
li
c
a
t
io
n
s
,
2
0
1
5
,
p
p
.
2
2
-
2
5
.
[1
4
]
I.
E.
S
u
leim
e
n
o
v
,
e
t
a
l
.,
“
Dia
lec
ti
c
a
l
u
n
d
e
rsta
n
d
in
g
o
f
in
f
o
rm
a
ti
o
n
in
t
h
e
c
o
n
tex
t
o
f
th
e
a
rti
fici
a
l
in
telli
g
e
n
c
e
p
ro
b
lem
s,
”
i
n
IOP
C
o
n
fer
e
n
c
e
S
e
rie
s: M
a
ter
ia
ls
S
c
ien
c
e
a
n
d
E
n
g
i
n
e
e
rin
g
,
v
o
l.
6
3
0
,
n
o
.
1
,
2
0
1
9
,
p
p
.
0
1
2
0
0
7
.
[1
5
]
D.
V.
Efan
o
v
,
“
Tern
a
ry
P
a
rit
y
Co
d
e
s:
F
e
a
tu
re
s,
”
2
0
1
9
IEE
E
E
a
st
-
W
e
st
De
sig
n
&
T
e
st
S
y
mp
o
siu
m
(
EW
DTS
)
,
2
0
1
9
,
p
p
.
1
-
5
,
d
o
i:
1
0
.
1
1
0
9
/E
WDT
S
.
2
0
1
9
.
8
8
8
4
4
1
.
[1
6
]
C.
Vu
d
a
d
h
a
,
A.
S
u
ry
a
,
S
.
Ag
r
a
wa
l,
a
n
d
M
.
B.
S
rin
i
v
a
s,
“
S
y
n
th
e
sis
o
f
Ter
n
a
ry
L
o
g
ic
Circu
it
s
Us
in
g
2
:
1
M
u
lt
i
p
lex
e
rs,
”
IE
EE
T
ra
n
s
a
c
ti
o
n
s
o
n
Circ
u
it
s
a
n
d
S
y
ste
ms
I:
Re
g
u
l
a
r
P
a
p
e
rs
,
v
o
l
.
6
5
,
n
o
.
1
2
,
p
p
.
4
3
1
3
-
4
3
2
5
,
De
c
.
2
0
1
8
,
d
o
i
:
1
0
.
1
1
0
9
/T
C
S
I.
2
0
1
8
.
2
8
3
8
2
5
8
.
[1
7
]
M
.
S
h
a
h
a
n
g
ian
,
S
.
A.
Ho
ss
e
in
i
,
a
n
d
S
.
H.
P
.
Ko
m
leh
,
“
De
sig
n
o
f
a
m
u
lt
i
-
d
ig
i
t
b
in
a
ry
-
to
-
tern
a
r
y
c
o
n
v
e
rter
b
a
se
d
o
n
CNTF
ET
s,
”
Circ
u
it
s,
S
y
ste
ms
,
a
n
d
S
ig
n
a
l
Pro
c
e
ss
in
g
,
v
o
l
.
3
8
,
n
o
.
6
,
p
p
.
2
5
4
4
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5
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3
,
2
0
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9
,
d
o
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0
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1
0
0
7
/s
0
0
0
3
4
-
018
-
0
9
7
7
-
3
.
[1
8
]
T.
Li
u
a
n
d
X.
C
h
e
n
,
“
De
e
p
Le
a
rn
in
g
-
Ba
se
d
Be
li
e
f
P
ro
p
a
g
a
ti
o
n
Alg
o
rit
h
m
o
v
e
r
No
n
-
Bin
a
ry
F
in
it
e
F
ield
s,
”
in
2
0
2
0
In
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
W
ire
les
s
Co
mm
u
n
ica
ti
o
n
s
a
n
d
S
i
g
n
a
l
Pr
o
c
e
ss
in
g
(W
CS
P)
,
2
0
2
0
,
p
p
.
1
6
4
-
1
6
9
,
d
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i:
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0
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1
1
0
9
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P
4
9
8
8
9
.
2
0
2
0
.
9
2
9
9
8
7
5
.
[1
9
]
H.
Din
g
,
e
t
a
l
.
,
“
Lo
w
Co
m
p
lex
i
ty
Itera
ti
v
e
Re
c
e
iv
e
r
with
Lo
ss
le
ss
In
fo
rm
a
ti
o
n
Tra
n
sfe
r
fo
r
N
o
n
-
Bin
a
ry
LD
P
C
Co
d
e
d
P
DMA
S
y
ste
m
,
”
IEE
E
Ac
c
e
ss
,
v
o
l.
8
,
p
p
.
1
5
0
9
6
4
-
1
5
0
9
7
3
,
2
0
2
0
,
d
o
i:
1
0
.
1
1
0
9
/ACCE
S
S
.
2
0
2
0
.
3
0
1
6
6
9
7
.
[2
0
]
H.
P
.
Th
i
a
n
d
H.
Lee
,
“
Ba
sic
-
S
e
t
Trelli
s
M
i
n
–
M
a
x
De
c
o
d
e
r
Arc
h
i
tec
t
u
re
fo
r
N
o
n
b
in
a
r
y
LDP
C
Co
d
e
s
with
Hi
g
h
-
Ord
e
r
G
a
lo
is
F
ield
s,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Ver
y
L
a
r
g
e
S
c
a
l
e
In
teg
ra
ti
o
n
(
VL
S
I)
S
y
ste
ms
,
v
o
l.
2
6
,
n
o
.
3
,
p
p
.
4
9
6
-
5
0
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,
M
a
rc
h
2
0
1
8
,
d
o
i:
1
0
.
1
1
0
9
/
TVLS
I.
2
0
1
7
.
2
7
7
5
6
4
6
.
[2
1
]
B.
S
c
h
o
tsc
h
,
R.
Lu
p
o
a
ie
,
a
n
d
P
.
Va
ry
,
“
Th
e
p
e
rf
o
rm
a
n
c
e
o
f
lo
w
-
d
e
n
sity
ra
n
d
o
m
li
n
e
a
r
f
o
u
n
tain
c
o
d
e
s
o
v
e
r
h
i
g
h
e
r
o
rd
e
r
G
a
lo
is
field
s
u
n
d
e
r
m
a
x
imu
m
li
k
e
li
h
o
o
d
d
e
c
o
d
i
n
g
,
”
in
2
0
1
1
4
9
th
An
n
u
a
l
A
ll
e
rto
n
Co
n
fer
e
n
c
e
o
n
Co
mm
u
n
ica
ti
o
n
,
C
o
n
tr
o
l,
a
n
d
C
o
mp
u
ti
n
g
(
Al
ler
to
n
)
,
2
0
1
1
,
p
p
.
1
0
0
4
-
1
0
1
1
,
d
o
i:
1
0
.
1
1
0
9
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e
rt
o
n
.
2
0
1
1
.
6
1
2
0
2
7
7
.
[2
2
]
I.
M
o
ld
a
k
h
a
n
,
D.
B.
S
h
a
lt
i
k
o
v
a
,
Z.
M
.
Eg
e
m
b
e
rd
y
e
v
a
,
a
n
d
I.
E.
S
u
leim
e
n
o
v
,
“
Ap
p
li
c
a
ti
o
n
o
f
te
rn
a
ry
l
o
g
ic
fo
r
d
ig
it
a
l
sig
n
a
l
p
ro
c
e
ss
in
g
,
”
i
n
IO
P
Co
n
fer
e
n
c
e
S
e
rie
s:
M
a
ter
ia
ls
S
c
ien
c
e
a
n
d
En
g
in
e
e
rin
g
,
IOP
P
u
b
li
s
h
in
g
,
2
0
2
0
,
v
o
l.
9
4
6
,
n
o
.
1
,
p
p
.
0
1
2
0
0
2
.
[2
3
]
J
.
S
o
n
g
,
Y
.
Y
a
n
g
,
Y
.
Z
h
u
,
a
n
d
Z
.
J
i
n
,
“
A
h
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g
h
p
r
e
c
i
s
i
o
n
t
r
a
c
k
i
n
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s
y
s
t
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se
d
o
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a
h
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r
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d
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t
r
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t
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y
d
e
s
i
g
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e
d
f
o
r
c
o
n
c
e
n
t
r
a
t
e
s
u
n
l
i
g
h
t
t
r
a
n
s
m
i
s
s
io
n
v
i
a
f
i
b
e
r
s
,
”
R
e
n
e
w
a
b
l
e
e
n
e
r
g
y
,
v
o
l
.
5
8
,
p
p
.
1
2
-
1
9
,
S
e
p
t
.
2
0
1
3
,
d
o
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:
1
0
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1
0
1
6
/
j
.
r
e
n
e
n
e
.
2
0
1
3
.
0
1
.
0
2
2
.
[2
4
]
A.
Ro
th
,
A.
G
e
o
rg
iev
,
a
n
d
H.
Bo
u
d
in
o
v
,
“
De
sig
n
a
n
d
c
o
n
str
u
c
ti
o
n
o
f
a
sy
ste
m
fo
r
su
n
-
trac
k
i
n
g
,
”
Ren
e
w
a
b
le
e
n
e
rg
y
,
v
o
l.
2
9
,
n
o
.
3
,
p
p
.
3
9
3
-
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0
2
,
2
0
0
4
,
d
o
i:
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0
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1
0
1
6
/
S
0
9
6
0
-
1
4
8
1
(0
3
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0
1
9
6
-
4
.
[2
5
]
W.
Ke
ste
r,
An
a
lo
g
-
d
i
g
it
a
l
c
o
n
v
e
rs
io
n
,
A
n
a
lo
g
De
v
ice
s,
2
0
0
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t
20
21
:
871
-
87
8
878
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
Ina
b
a
t
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ld
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k
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P
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t
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ty
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r
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9
,
sh
e
wo
r
k
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d
a
t
Ka
R
-
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LL
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(a
m
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ra
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ra
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ra
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)
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o
f
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ra
d
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two
rk
m
o
n
it
o
rin
g
a
n
d
c
o
n
tro
l
d
e
p
a
rtme
n
t
.
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t
h
e
m
o
m
e
n
t
sh
e
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n
g
a
g
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d
in
re
se
a
rc
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in
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e
field
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g
,
e
lec
tr
o
n
ics
,
a
n
d
tele
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o
m
m
u
n
ica
ti
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s
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n
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c
c
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a
n
c
e
with
th
e
to
p
ic
o
f
h
e
r
P
h
D
th
e
sis
“
De
v
e
lo
p
m
e
n
t
o
f
n
e
w ap
p
ro
a
c
h
e
s
to
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tal
sig
n
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l
p
r
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e
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in
g
b
a
se
d
o
n
tern
a
ry
lo
g
ic”
.
Din
a
r
a
K
.
Ma
tr
a
ss
u
lo
v
a
is
a
P
h
D
stu
d
e
n
t
at
t
h
e
Alm
a
ty
Un
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e
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y
o
f
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r
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g
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g
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n
d
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o
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m
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n
2
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sh
e
re
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e
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d
a
b
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s d
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re
e
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n
d
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0
1
7
a
m
a
ste
r'
s d
e
g
re
e
in
"
Ra
d
io
e
n
g
in
e
e
ri
n
g
,
e
lec
tro
n
ics
a
n
d
tele
c
o
m
m
u
n
ica
ti
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n
s"
a
t
th
e
A
lma
ty
Un
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e
rsity
o
f
P
o
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r
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g
i
n
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Tele
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o
m
m
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s.
S
h
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wo
rk
s
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m
m
u
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s
c
o
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p
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n
y
Kc
e
ll
JCS,
a
s
a
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sp
e
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field
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tern
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t.
Ac
ti
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ly
s
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o
m
m
u
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ti
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n
s
,
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e
two
rk
s,
a
rti
ficia
l
in
telli
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e
n
c
e
,
n
e
u
ra
l
n
e
two
r
k
s,
sig
n
a
l
p
r
o
c
e
ss
in
g
.
Din
a
B.
S
h
a
lty
k
o
v
a
is
a
lea
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g
re
se
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h
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r
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t
th
e
Na
ti
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n
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l
En
g
i
n
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e
rin
g
Ac
a
d
e
m
y
o
f
th
e
Re
p
u
b
li
c
o
f
Ka
z
a
k
h
sta
n
.
S
h
e
g
ra
d
u
a
ted
fr
o
m
th
e
Ka
z
a
k
h
S
tate
Un
iv
e
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y
n
a
m
e
d
a
fter
S
.
M
.
Kiro
v
(Alm
a
-
Ata
)
i
n
1
9
8
7
,
F
a
c
u
lt
y
o
f
Ch
e
m
istry
,
De
p
a
rtme
n
t
o
f
C
h
e
m
istry
o
f
Hig
h
-
m
o
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u
la
r
Co
m
p
o
u
n
d
s.
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h
e
d
e
fe
n
d
e
d
h
e
r
th
e
sis
fo
r
th
e
d
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g
re
e
o
f
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a
n
d
id
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h
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c
e
s
in
1
9
9
6
a
t
th
e
sa
m
e
fa
c
u
lt
y
.
At
th
e
p
re
se
n
t
ti
m
e
,
h
e
is ac
ti
v
e
ly
d
e
v
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lo
p
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n
g
i
n
terd
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ip
li
n
a
ry
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o
o
p
e
ra
ti
o
n
,
p
e
rfo
rm
in
g
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rk
a
t
t
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in
ters
e
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ti
o
n
o
f
p
o
ly
m
e
r
c
h
e
m
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,
a
rti
fi
c
ial
in
tell
ig
e
n
c
e
,
a
n
d
o
t
h
e
r
a
re
a
s
o
f
in
fo
rm
a
ti
o
n
t
h
e
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ry
.
S
h
e
is
o
n
e
o
f
th
e
in
it
iat
o
rs
o
f
wo
r
k
in
th
e
fiel
d
o
f
m
o
lec
u
lar
in
fo
rm
a
ti
c
s in
Ka
z
a
k
h
sta
n
.
Ibra
g
im
E.
S
u
leim
e
n
o
v
is
a
p
r
o
fe
ss
o
r
at
th
e
Cr
ime
a
n
F
e
d
e
ra
l
Un
iv
e
rsity
n
a
m
e
d
a
fter
V.I
.
Ve
rn
a
d
sk
y
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n
ti
l
2
0
2
0
-
p
ro
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ss
o
r
o
f
th
e
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a
ty
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i
v
e
rsity
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f
En
e
rg
y
a
n
d
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o
m
m
u
n
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ti
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n
s)
.
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ra
d
u
a
ted
fro
m
th
e
P
h
y
sic
s
De
p
a
rtme
n
t
o
f
th
e
Le
n
in
g
ra
d
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n
iv
e
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n
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m
e
d
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lev
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l
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o
p
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in
terp
re
tatio
n
.
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