I
n
t
ern
a
t
i
o
n
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l
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rn
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l
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d
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o
mp
u
t
er
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n
g
i
n
eeri
n
g
(
I
J
E
C
E
)
V
o
l
.
11
,
N
o
.
1
,
F
e
b
ru
a
ry
2
021
,
p
p
.
863
~
871
I
S
S
N
:
208
8
-
87
08
,
D
O
I
:
10.
115
91
/
i
j
e
c
e
.
v11
i
1
.
pp
86
3
-
8
71
8
63
Jo
u
r
n
al
h
om
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pa
ge
:
h
t
t
p
:
/
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i
j
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c
e
.
i
a
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s
c
o
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e
.
c
o
m
L
o
w
pow
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p
se
ud
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ran
do
m n
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b
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at
or
bas
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s
c
a
t
e c
ha
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m
ap
M
o
ha
m
e
d
Sa
be
r
1
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Ma
r
w
a
M.
E
i
d
2
1
D
e
pa
rt
m
e
n
t
of
Com
m
uni
c
a
t
i
on
s
a
nd Com
pu
t
e
rs
,
F
a
c
u
l
t
y
of
E
ngi
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ri
ng
,
D
e
l
t
a
U
ni
ve
rs
i
t
y
for S
c
i
e
nc
e
a
nd
T
e
c
hno
l
ogy,
E
g
ypt
2
D
e
pa
rt
m
e
nt
of
Com
m
uni
c
a
t
i
on
s
a
nd E
l
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c
t
roni
c
s
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D
e
l
t
a
H
i
gh
e
r I
ns
t
i
t
ut
e
of
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ngi
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e
e
ri
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nd
T
e
c
h
nol
ogy (D
H
IE
T
)
,
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gyp
t
A
rt
i
cl
e
I
n
f
o
A
B
S
T
RA
C
T
Ar
t
i
c
l
e
h
i
s
t
o
r
y
:
R
ecei
v
ed
A
pr
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2
02
0
Re
v
i
s
e
d
J
un
17
,
202
0
A
ccep
t
e
d
J
un
2
8,
2
020
L
em
n
i
s
cat
e
ch
ao
t
i
c
m
ap
(
L
CM
) provi
de
s
a
w
i
d
e
ra
nge
of c
ont
ro
l
pa
ra
m
e
t
e
rs
,
c
a
nc
e
l
i
ng
t
he
ne
e
d for s
e
v
e
r
a
l
rounds
of s
ubs
t
i
t
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i
ons
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a
n
d e
xc
e
l
l
e
n
t
pe
rform
a
n
c
e
i
n
t
he
c
onfus
i
on
pro
c
e
s
s
.
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nfor
t
una
t
e
l
y,
t
h
e
ha
rdw
a
r
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m
ode
l
of
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s
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pl
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l
d pr
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m
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bl
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pa
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ode
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e
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al
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roduc
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ne
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ps
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num
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n
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L
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ode
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t
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ts
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c
rypt
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on s
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y
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d
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p
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nu
m
be
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g
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tor
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ead
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s
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s
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t
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CC B
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l
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n
s
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or
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po
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t
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or
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oh
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a
be
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nt
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m
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t
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ons
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d
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o
m
p
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a
c
ul
t
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n
gi
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l
t
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U
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d
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c
h
n
o
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y
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l
k
a
s
,
D
a
k
a
h
l
i
a
G
o
v
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rn
o
ra
t
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,
E
gy
pt
.
E
m
a
i
l
:
Mo
ha
m
e
d.
s
a
be
r
@
de
l
t
a
uni
v.
e
du
.
e
g
1.
I
N
T
R
O
D
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C
T
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O
N
P
s
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o
c
h
a
o
t
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c
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a
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om
n
u
m
b
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g
en
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at
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s
(P
C
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N
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)
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s
a
v
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l
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t
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o
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pl
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f
P
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s u
si
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g
M
A
TLA
B
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he
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om
m
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a
y t
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P
C
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f
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d
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f
eed
b
ac
k
s
h
i
f
t
r
e
g
i
s
t
e
r
[1
-
3
].
A
n
ot
he
r
t
e
c
hni
que
u
s
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d
a
c
o
u
p
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w
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t
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-
va
r
yi
n
g
de
l
a
y
[
4
]
.
T
h
e r
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r
ch
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r
s
i
n
[
5
]
p
r
o
p
o
s
e
d a
P
R
N
G
ba
s
e
d
on
L
or
e
nz
s
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t
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m
s
w
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t
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PG
A
i
m
p
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t
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a
n
op
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ting
f
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que
n
c
y o
f
7
8.
149
MH
z
.
I
n
[
6
]
,
t
he
a
ut
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or
s
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n
ve
s
t
i
ga
t
e
t
he
f
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xe
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-
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at
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,
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a
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R
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ba
s
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o
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m
a
ps
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pr
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a
r
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w
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F
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m
p
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d
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s
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c
h
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t
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m
a
p
s
pr
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s
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nt
e
d
i
n [
7
].
I
n [
8
]
,
A p
s
e
u
d
o
-
r
a
n
do
m
ge
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r
a
t
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ge
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a
c
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q
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A
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m
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m
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t
a
t
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o
n
.
I
n
[
9
]
,
a
not
h
e
r
i
de
a
us
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d
t
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m
ak
e
P
RN
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p.
A
n
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s
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g
n t
o
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d wi
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h F
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1
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.
In
[
1
1
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,
a
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
11
,
No
.
1
,
F
e
b
r
ua
r
y
2
02
1
:
863
-
8
71
8
64
m
a
p
s
t
h
a
t
h
a
v
e ch
a
o
t
i
c
be
ha
vi
o
r
onl
y f
o
r
s
m
a
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nge
s
of
c
o
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r
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pa
r
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r
s
'
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An
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on
of
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he
or
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gi
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i
m
a
ge
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xe
l
[
1
2
]
.
T
h
e
L
CM
who
s
e
c
r
yp
tog
r
a
ph
ic
pr
o
pe
r
t
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e
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ha
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on
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t
r
a
t
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t
o
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v
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n
t
h
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f
us
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on
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oc
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s
s
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l
i
m
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na
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e
d
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or
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l
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o
un
ds
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bs
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i
t
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i
on
s
of
t
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pi
xe
l
s
va
l
u
e
s
a
nd
ha
v
e
a
w
i
de
r
a
n
ge
of
c
ont
r
ol
pa
r
a
m
e
t
e
r
’
s
va
l
ue
s
[
1
3
].
T
he
ba
s
i
c
e
qu
a
t
i
ons
of
L
CM
ar
e
:
(
+
1
)
=
cos
(
2
(
)
)
1
+
s
i
n
2
(
2
(
)
)
(
1)
(
+
1
)
=
2
√
2
s
i
n
2
(
)
cos
(
2
)
(
)
1
+
s
i
n
2
2
(
)
(
2)
W
h
e
r
e
t
h
e
i
n
i
t
i
a
l
c
o
n
d
i
t
i
o
n
s
0
,
0
a
r
e
gi
ve
n
f
r
o
m
t
he
i
nt
e
r
e
va
l
[
−
1
:
+
1
]
a
n
d
0
>
3
fo
r
t
h
e
hyp
e
r
ch
ao
t
i
c
re
g
i
m
e
. I
n
Fi
g
u
r
e
1
,
t
h
e
bi
f
ur
c
a
t
i
on
di
a
g
r
a
m
a
n
d
t
he
L
ya
p
u
no
v
e
x
p
one
nt
s
of
L
CM
ar
e
s
ho
wn
in
F
igu
r
e
1
(
a
)
t
h
at
an
d
F
i
g
u
r
e
1
(
b
)
r
es
p
ect
i
v
el
y
.
(
a)
(
b)
F
i
g
ur
e
1.
A
na
l
ys
i
s
of
t
he
l
e
m
ni
s
c
a
t
e
m
a
p'
s
c
ha
ot
i
c
b
e
ha
v
i
or
,
(
a
)
Bi
f
u
r
c
a
t
i
o
n
d
i
a
g
r
a
m
,
(
b)
L
y
a
p
uno
v
e
x
pon
e
n
ts
T
h
e
e
qu
a
tion
s
of
L
CM
h
av
e
tr
igon
om
e
tr
i
c
f
u
n
c
t
i
o
n
s
(
s
i
n
,
c
o
s
)
,
a
n
d
i
t
can
b
e
i
m
p
l
em
en
t
ed
i
n
a h
ar
d
w
ar
e
m
o
d
el
b
y
d
i
f
f
e
r
en
t
m
et
h
o
d
s
s
u
ch
as
;
loo
k
-
up
t
ab
l
e (
L
U
T
)
b
as
e
d
r
e
ad
-
o
n
l
y
m
e
m
o
ry
(R
O
M
),
CO
RD
I
C
a
l
g
o
r
i
t
h
m
,
T
a
y
l
o
r
’
s
s
e
r
i
e
s
,
a
n
d
l
i
n
e
a
r
s
e
g
m
e
n
t
a
t
i
o
n
[1
4
-
16
].
S
i
nc
e
t
he
t
ot
a
l
p
owe
r
c
o
ns
um
p
t
i
on
of
a
ha
r
d
w
a
r
e
m
ode
l
de
pe
nds
on
t
he
c
o
m
p
o
ne
nt
s
u
s
e
d
i
n
t
h
e
i
m
p
l
e
m
e
n
t
a
t
i
o
n
,
s
o
an
y
r
e
du
c
tion
f
or
t
h
e
s
e
co
m
po
ne
nt
s
r
e
duc
e
s
t
he
o
v
er
al
l
po
we
r
c
o
ns
um
pt
i
on
.
I
n
the
L
C
M
ha
r
d
w
a
r
e
m
o
de
l
,
t
he
c
om
p
one
nt
s
L
U
T
,
R
OM
,
c
o
n
s
u
m
e
m
o
re
p
o
we
r
s
o
,
t
h
e
t
o
t
a
l
p
o
we
r
c
o
ns
um
pt
i
on
r
e
d
uc
t
i
on
a
c
hi
e
ve
d
by
r
e
d
uc
i
n
g t
he
n
um
be
r
o
f
t
h
es
e co
m
p
o
n
en
t
s
i
n
t
h
e
h
ar
d
w
ar
e
m
o
d
e
l
.
T
h
e m
ai
n
i
d
ea o
f
t
h
i
s
p
ap
er
i
s
t
o
p
r
es
en
t
a l
o
w
p
o
w
e
r
i
m
p
l
e
m
e
n
t
a
t
i
o
n
o
f
t
h
e
l
e
m
n
i
s
c
a
t
e
h
a
r
d
w
a
r
e
m
o
d
e
l
.
T
hr
e
e
a
l
t
e
r
na
t
i
ve
s
ha
r
dwa
r
e
m
od
e
l
s
de
s
i
g
ne
d,
e
xpl
a
i
ne
d,
a
nd
i
m
pl
e
m
e
nt
e
d a
c
c
or
di
n
g t
o t
he
m
a
t
he
m
a
t
i
c
a
l
e
qua
t
i
o
ns
of
L
C
M
.
F
u
r
t
h
er
m
o
r
e,
w
e p
r
es
en
t
a
P
RN
G
b
a
s
e
d
on
t
he
be
s
t
l
o
w
p
o
w
e
r F
P
G
A
a
r
c
h
i
t
e
c
t
u
r
e
o
f
t
h
e
L
CM
w
ith MA
T
L
AB
s
i
m
u
l
a
t
i
o
n
s
a
n
d
FP
G
A
s
i
m
u
l
a
t
i
o
n
an
d
i
m
p
l
e
m
e
n
t
a
t
i
o
n
.
T
hi
s
pa
pe
r
o
r
g
an
i
zed
a
s
f
o
l
l
o
w
s
:
S
ect
i
o
n
2
d
es
cr
i
b
es
t
h
e m
at
h
em
at
i
cal
an
al
y
s
i
s
o
f
t
h
r
ee
al
t
er
n
at
i
v
e
m
o
de
l
s
of
L
C
M.
I
n s
e
c
t
i
o
n
3,
F
P
GA
I
m
pl
e
m
e
nt
a
t
i
o
ns
of
t
h
e
t
h
re
e
h
a
rd
w
a
re
m
o
d
e
l
s
o
f L
C
M
a
r
e p
r
e
s
en
t
ed
.
T
h
e
F
P
G
A
h
a
r
d
w
a
r
e
i
m
p
l
e
m
e
n
t
a
t
i
o
n
r
e
s
u
l
t
s
pr
o
vi
de
d
i
n s
e
c
t
i
on
4.
T
he
ha
r
d
w
a
r
e
i
m
pl
e
m
e
nt
a
t
i
on
of
t
he
P
R
N
G
ba
s
e
d
on t
he
l
o
w
e
s
t
po
we
r
c
on
s
um
pt
i
o
n h
a
r
d
w
a
r
e
m
o
de
l
i
s
p
r
es
e
n
t
ed
i
n
s
e
c
t
i
on 5.
S
e
c
t
i
o
n
6
p
r
e
se
n
t
s
N
I
S
T
S
P
800
-
22
r
a
n
d
o
m
i
z
a
t
i
o
n
te
s
ts
f
or
a
pr
opo
s
e
d
P
R
N
G.
S
ect
i
o
n
7
p
r
e
s
en
t
s
a co
m
p
ar
i
s
o
n
b
et
w
een
t
he
p
r
op
os
e
d
m
o
de
l
a
n
d
r
e
c
e
nt
c
o
m
pa
r
a
bl
e
m
od
e
ls
.
F
i
n
a
l
l
y
,
t
h
i
s
c
onc
l
us
i
on
p
r
e
s
e
nt
e
d
i
n
s
e
c
tio
n
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
l
e
c
&
C
om
p
E
n
g
I
S
S
N
:
208
8
-
87
08
L
ow
pow
e
r
ps
e
ud
o
-
r
and
om
nu
m
b
e
r
g
e
n
e
r
a
to
r
b
as
e
d
on…
(
M
oha
m
e
d
Sa
be
r
)
8
65
2.
P
R
O
P
O
SE
D
L
C
M
M
O
D
E
L
S
2.
1.
M
o
d
i
f
i
ed
mo
d
el
T
h
e
f
i
r
s
t
al
t
er
n
at
i
v
e “C
o
n
v
e
n
t
i
o
n
al
” m
o
d
el
a
ch
i
ev
e
d
b
y
u
s
i
n
g
t
h
e b
as
i
c m
at
h
em
at
i
cal
eq
u
at
i
o
n
s
o
f
l
em
n
i
s
cat
e ch
a
o
t
i
c m
ap
,
w
h
i
ch
ar
e
(
1
-
2
).
Th
e s
eco
n
d
al
t
er
n
at
i
v
e “
M
o
d
i
f
i
ed
”
m
a
p u
s
e
s
t
w
o a
b
br
e
vi
a
t
i
o
ns
t
o
(
1
)
a
n
d
(
2
)
u
s
i
n
g
t
h
e
t
r
i
g
o
n
o
m
e
t
r
i
c
i
d
e
n
t
i
t
i
e
s
,
w
h
i
c
h
a
r
e
:
s
i
n
2
(
)
+
cos
2
(
)
=
1
(3
)
2
s
i
n
(
)
cos
(
)
=
s
i
n
(
2
)
(4
)
U
s
ing
(
3)
c
o
nv
e
r
t
s
t
he
de
no
m
i
na
t
or
o
f
(1
)
a
s
f
o
l
l
o
w
s
:
1
+
s
i
n
2
2
(
)
=
2
−
cos
2
2
(
)
(5
)
A
ls
o
,
us
ing
(
4)
c
on
v
e
r
ts
th
e
nu
m
e
r
a
to
r
of
(
2)
a
s
f
o
llow
s
:
2
√
2
s
i
n
2
(
)
cos
(
2
(
)
)
=
√
2
s
i
n
(
2
×
2
(
)
)
(6
)
S
o
,
t
h
e
s
eco
n
d
al
t
er
n
at
i
v
e
“
M
odi
f
i
e
d
”
ha
s
t
h
e
f
ol
l
ow
i
ng
e
q
ua
t
i
on
s
(
+
1
)
=
cos
(
2
(
)
)
2
−
2
(
2
(
)
)
(7
)
(
+
1
)
=
√
2
s
i
n
2
×
2
(
)
1
+
s
i
n
2
2
(
)
(8
)
2
.
2
.
P
r
a
ct
i
ca
l
mo
d
el
T
h
e t
h
i
r
d
al
t
er
n
at
i
v
e “P
r
act
i
cal
” u
s
es
t
h
r
ee
ab
b
r
e
v
i
at
i
o
n
s
t
o
(
1
)
an
d
(
2
)
;
us
i
ng
t
he
t
r
i
go
no
m
e
t
r
i
c
i
d
e
n
t
i
t
i
e
s
i
n
(
3
)
,
(
4
)
,
a
n
d
t
h
e
f
o
l
l
o
w
i
n
g
i
d
e
n
t
i
t
y
:
cos
(
2
)
=
cos
2
(
)
−
s
i
n
2
(
)
=
2
cos
2
(
)
−
1
=
1
−
2
s
i
n
2
(
)
(
9)
s
i
n
2
(
)
=
1
2
−
1
2
cos
(
2
)
(
10
)
In
(3
) c
o
n
v
e
rt
s
(1
) t
o
b
e
(5
),
w
h
i
l
e
(
4
) c
o
n
v
e
rt
s
(
2)
t
o (
6
)
,
a
s
d
one
i
n “
M
odi
f
i
e
d
” m
o
d
el
.
S
u
b
s
t
i
t
u
t
e
w
i
t
h
(
7
)
i
n
(
6
)
l
e
a
d
s
t
o
(
+
1
)
=
√
2
s
i
n
2
×
2
(
)
1
.
5
−
0
.
5
cos
2
×
2
(
)
(
11
)
S
i
n
c
e
(
)
s
i
n
2
×
2
(
)
=
2
×
2
cos
2
×
2
(
)
(
12
)
Re
w
r
i
t
i
n
g
(
8
)
(
+
1
)
=
√
2
s
i
n
2
×
2
(
)
1
+
s
i
n
2
2
(
)
(
13
)
I
n
d
i
s
c
r
e
t
e
-
t
i
m
e
,
t
h
e
t
i
m
e
d
i
f
f
e
r
e
n
t
i
a
t
i
o
n
i
s
c
a
l
c
u
l
a
t
e
d
u
s
i
n
g
(
)
=
(
)
−
(
−
1
)
(
14
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
11
,
No
.
1
,
F
e
b
r
ua
r
y
2
02
1
:
863
-
8
71
8
66
I
t
m
e
a
n
s
b
y onl
y us
i
n
g
a
one
-
t
i
m
e
d
e
l
a
y
a
n
d
s
u
b
t
r
a
c
t
o
r
;
w
e
c
a
n
o
b
t
a
i
n
a
t
i
m
e
d
i
f
f
e
r
e
n
t
i
a
t
o
r
.
S
o
,
t
h
e
t
h
i
r
d
a
l
t
e
r
n
a
t
i
v
e
“
p
r
ac
t
i
cal
”
ha
r
d
wa
r
e
m
o
de
l
i
m
pl
e
m
e
nt
s
t
he
f
ol
l
ow
i
ng
e
q
ua
t
i
o
ns
:
(
+
1
)
=
cos
2
(
)
2
−
cos
2
2
(
)
(
15
)
(
+
1
)
=
√
2
s
i
n
2
×
2
(
)
1
.
5
−
2
×
d
dx
(
n
)
(
s
i
n
2
×
2
(
)
)
(
16
)
3.
F
P
G
A
I
MP
L
E
ME
N
T
AT
I
O
N
O
F
P
R
O
P
O
S
E
D
L
C
M
T
h
e
h
a
r
d
w
ar
e
m
o
d
el
s
o
f
t
h
e l
em
n
i
s
cat
e a
r
ch
i
t
ect
u
r
es
i
s
d
es
i
g
n
e
d
u
s
i
n
g
X
i
l
i
n
x
s
y
s
t
em
g
en
e
r
at
o
r
(X
S
G
)
[
1
7
-
2
2]
.
I
n
t
hi
s
pa
pe
r
,
w
e
i
m
pl
e
m
e
nt
t
he
s
i
ne
a
n
d
c
o
s
i
ne
f
u
nc
t
i
on
s
us
i
n
g
L
U
T
ba
s
e
d
R
O
M
i
n
t
he
t
h
r
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ab
l
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1
i
n
d
i
cat
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m
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er
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ab
l
e
1
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N
o.
of
L
UT
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n
t
he
t
hr
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ha
r
d
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r
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ode
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ode
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N
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f L
U
Ts
C
onve
nt
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o
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l
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o
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if
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Pr
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T
he
t
hr
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a
l
t
e
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t
i
ve
s
of
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h
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L
C
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ys
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a
r
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m
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l
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us
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n
g t
he
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G
pr
o
gr
a
m
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n t
hi
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t
w
o
f
i
x
ed
-
poi
nt
f
or
m
a
t
s
,
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l
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o t
he
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hr
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r
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hi
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t
ur
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e i
m
p
l
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en
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ed
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n
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e s
am
e
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rd
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p
ar
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an
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4
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.
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he
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S
G
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o
n
ve
nt
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o
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l
ha
r
d
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r
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a
r
c
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e
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t
ur
e
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l
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h de
pe
n
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on
(
1
-
2)
i
s sh
o
w
n
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n
F
i
gu
r
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2
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he
“
M
odi
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e
d”
X
S
G
m
ode
l
,
w
h
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c
h i
m
pl
e
m
e
nt
(
7
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8)
i
s sh
o
w
n
i
n
F
i
g
u
r
e
3
.
T
h
e
“P
r
act
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cal
” X
S
G
m
o
de
l
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h
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ppl
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e
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t
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5
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6)
is
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ho
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n
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igu
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e
4.
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i
gu
r
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2.
X
S
G
m
o
de
l
o
f
“
C
on
ve
nt
i
o
na
l
”
L
C
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
E
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e
c
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om
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E
n
g
I
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S
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8
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87
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L
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ig
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r
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H
A
R
D
W
A
RE
S
I
M
U
L
AT
I
O
N RE
S
UL
T
S
4.
1.
Bi
f
u
r
c
a
t
i
o
n
d
i
a
g
r
a
m
T
ab
l
e 2
s
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m
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ar
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et
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f
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r
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ag
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h
r
ee m
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el
s
g
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er
at
e
d
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y
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he
o
r
e
t
i
c
a
l
s
i
m
ul
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t
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ons
us
i
n
g Ma
t
l
a
b
a
nd bi
f
ur
c
a
t
i
on di
a
g
r
a
m
g
e
ne
r
a
t
e
d
b
y
t
he
ha
r
d
w
a
r
e
m
o
de
l
.
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he
di
f
f
e
r
e
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e
be
t
w
e
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n
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he
t
w
o
t
y
pe
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o
f
s
i
m
ul
a
t
i
on
be
c
a
us
e
of
t
he
f
i
ni
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e
w
or
d l
e
ngt
h
i
n t
he
di
gi
t
a
l
h
a
r
d
w
a
r
e
m
o
d
e
l
s
[2
3
].
4.
2.
I
mp
l
eme
n
t
a
t
i
o
n
res
u
l
t
s
T
h
e
i
m
p
l
e
m
e
n
t
a
t
i
o
n
r
e
s
u
l
t
s
f
o
r
t
h
e
t
h
r
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e
-
ha
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dwa
r
e
L
C
M m
ode
l
s
a
r
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pr
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s
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nt
e
d i
n T
a
bl
e
3.
N
o
t
e
t
h
a
t
t
h
e m
a
x
i
m
u
m
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q
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t
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at
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i
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e
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s
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s
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a
x
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m
u
m
f
r
eq
u
e
n
cy
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s
t
h
e
s
a
m
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
11
,
No
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1
,
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e
b
r
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y
2
02
1
:
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71
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68
T
a
bl
e
2.
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om
p
a
r
i
s
o
n
be
t
we
e
n
B
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f
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r
c
a
t
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on
di
a
gr
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m
s
ge
ne
r
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t
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d
by
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t
l
a
b
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s
,
a
n
d
by
h
ar
d
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m
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el
s
M
ode
l
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h
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r
etical S
im
u
la
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atlab
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o
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e)
Har
d
war
e M
o
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el S
im
u
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VHD
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co
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onve
nt
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o
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l
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d
if
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Pr
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a
b
l
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3
.
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a
r
d
w
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r
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i
m
p
l
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m
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t
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n
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s
u
l
t
s
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f
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CM
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ode
l
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eg
is
ter
s
LU
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Fr
eq
u
en
cy
(MH
z
)
Po
wer
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Po
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ed
u
ctio
n
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atio
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om
pa
r
e
d t
o C
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l
1247
7614
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592
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---
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o
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if
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1024
5806
300
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%
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actical
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34.
6
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5.
FPGA
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M
PL
E
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T
A
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ION
OF
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L
CM
R
N
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n
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h
a
r
d
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re
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o
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n
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m
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a
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l
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d
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ng
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ol
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t
s
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nd
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m
ul
t
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pl
e
xe
r
t
o t
he
out
put
s
o
f
t
he
“
P
r
a
c
t
i
c
a
l
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o
de
l
(
x,
y)
a
s
s
h
o
w
n
i
n
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i
g
ur
e
5.
T
he
t
h
r
e
s
hol
d i
s
a
“
R
e
l
a
t
i
ona
l
”
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oc
k
c
o
m
pa
r
e
s
t
he
i
n
put
t
o a
t
hr
e
s
hol
d
va
l
u
e
w
hi
c
h i
s
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i
f
t
he
i
n
put
i
s
a
f
r
a
c
t
i
o
n
h
i
g
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e
r
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n
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n
t
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p
ut
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l
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t
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s
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r
wi
s
e
t
he
o
ut
p
ut
wi
l
l
be
“
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i
g
ur
e
6
s
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ows
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s
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ul
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on
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or
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r
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n
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o
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p
ut
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s
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m
b
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r
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r
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c
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g t
o t
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s
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l
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h
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t
w
e
e
n
t
he
i
n
put
s
“
d
0”
a
n
d
“
d1”
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
l
e
c
&
C
om
p
E
n
g
I
S
S
N
:
208
8
-
87
08
L
ow
pow
e
r
ps
e
ud
o
-
r
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m
b
e
r
g
e
n
e
r
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to
r
b
as
e
d
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(
M
oha
m
e
d
Sa
be
r
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8
69
F
i
gu
r
e
5.
X
S
G
m
o
de
l
o
f
r
a
n
d
o
m
n
um
be
r
ge
n
e
r
a
t
or
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r
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a
r
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m
o
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l
ba
s
e
d
on
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-
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r
e
6.
T
he
out
put
r
a
nd
om
nu
m
be
r
ge
ne
r
a
t
or
“
RN
G
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6.
N
I
S
T
S
P
800
-
2
0
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AN
DO
MI
Z
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T
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O
N
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E
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T
S
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g
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nc
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y
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t
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on s
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m
s
h
oul
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bl
e
t
o
a
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g
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pl
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ne
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m
a
ge
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t
o
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n
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om
l
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e
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o
de
d
i
m
a
ge
s
.
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t
i
s
,
t
he
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e
f
o
r
e
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t
a
l
t
o
t
e
s
t
t
he
r
a
n
do
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i
z
a
t
i
on
of
t
he
e
nc
r
y
pt
e
d
i
m
a
ge
s
obt
a
i
ne
d
b
y t
he
p
r
o
p
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e
d
i
m
a
ge
e
nc
r
ypt
i
o
n
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l
g
o
r
i
t
h
m
[
2
4
]
.
T
h
e
r
e
s
u
l
t
s
g
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v
e
n
i
n
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a
b
l
e
4
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n
d
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c
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t
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t
h
a
t
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i
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t
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a
b
le
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S
P
800
-
22
r
a
nd
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a
n
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s
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e
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onge
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at
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5495
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al s
tatis
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m
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lex
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Pas
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7215
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ial t
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8164
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m
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m
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r
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ar
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t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
11
,
No
.
1
,
F
e
b
r
ua
r
y
2
02
1
:
863
-
8
71
8
70
7.
C
O
MP
A
RI
S
O
NS
I
n
t
hi
s
s
e
c
t
i
o
n,
t
he
p
r
o
p
os
e
d
e
nc
r
y
pt
i
on
s
ys
t
e
m
c
o
m
pa
r
e
d
t
o
r
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c
e
nt
c
ha
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i
c
s
ys
t
e
m
s
.
T
a
bl
e
5
pr
e
s
e
nt
s
t
h
e s
ec
u
r
i
t
y
t
e
s
t
r
es
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l
t
s
i
n
t
h
e cas
e
o
f
u
s
i
n
g
t
h
e L
e
n
a i
m
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e.
A
s
i
n
d
i
c
a
t
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d
i
n
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a
b
l
e
5
,
t
h
e
r
e
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u
l
t
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o
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r
en
cr
y
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t
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o
n
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y
s
t
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R
EF
ER
E
N
C
ES
[1]
L
. K
o
n
c
ar
ev
an
d
S
. L
i
an
,
"
Cha
os
-
Ba
s
e
d Cry
pt
og
ra
phy,
"
Spr
i
nge
r
,
2011.
[2]
F
.
A
rna
ul
t
a
nd
T
.
P
.
B
e
rge
r
,
"
D
e
s
i
gn a
nd
prope
rt
i
e
s
of
a
ne
w
p
s
e
udora
ndom
g
e
ne
ra
t
or
ba
s
e
d
on
a
fi
l
t
e
r
e
d F
CS
R
a
ut
om
a
t
on,
"
IE
E
E
T
r
ans
ac
t
i
on o
n Com
put
e
r
s
,
vo
l
.
54
,
pp
.
1374
–
1
383,
2005
.
[3]
S
.
A
l
om
a
r
,
"
M
e
t
hod of de
s
i
gn
i
ng
ge
ne
r
a
t
ors
of ps
e
udora
ndom
s
e
q
ue
nc
e
s
for
i
nfor
m
a
t
i
on
prot
e
c
t
i
o
n ba
s
e
d on
s
hi
ft
re
gi
s
t
e
r
w
i
t
h
non
-
l
i
ne
a
r
f
e
e
dba
c
k func
t
i
on
,
"
J
our
n
al
of
In
f
or
m
at
i
o
n s
e
c
ur
i
t
y
,
vol
.
5
,
pp
.
218
-
227
,
2
014.
[4]
X
.
L
v
,
X
i
a
ofe
ng
L
i
a
o,
a
nd
Bo Y
a
ng
.
,
"
A
nov
e
l
ps
e
udo
-
ra
ndom
num
be
r g
e
ne
r
a
t
or from
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m
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p
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t
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c
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t
h
time
-
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ryi
ng
de
l
a
y,
"
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i
ne
ar
D
y
nam
i
c
s
,
v
ol
.
9
4,
pp
324
-
341,
2
018.
[5]
Re
z
k,
e
t
a
l
.
,
"
R
e
c
onfi
gur
a
bl
e
c
ha
ot
i
c
ps
e
udo r
a
ndom
num
b
e
r
ge
ne
ra
t
or ba
s
e
d
on F
P
G
A
,
"
A
E
U
-
Int
e
r
nat
i
ona
l
J
our
nal
of
E
l
e
c
t
r
oni
c
s
and Com
m
uni
c
at
i
ons
,
vol
.
98
,
pp
.
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-
18
0,
2019
.
[6]
E
l
m
a
n
fa
l
o
t
y a
n
d A
bou
-
Ba
kr,
"
Ra
ndom
prop
e
r
t
y e
nh
a
nc
e
m
e
nt
of a
1D
c
ha
o
t
i
c
P
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w
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t
h
fi
ni
t
e
pr
e
c
i
s
i
o
n
imp
le
me
n
t
a
t
io
n
,
"
Chaos
Sol
i
t
ons
&
F
r
ac
t
a
l
s,
vol
.
144,
pp.
118
-
13
4,
2019
.
[7]
L
. G
er
ar
d
o
,
e
t
a
l
.,
"
H
a
rdw
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r
e
i
m
pl
e
m
e
nt
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t
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on
of ps
e
udo
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ra
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m
num
be
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n
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s
e
d
on
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o
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i
c
m
a
ps
,
"
Nonl
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ne
ar
D
y
na
m
i
c
s
,
vol
.
90
,
pp
.
1661
-
1670
,
20
17.
[8]
H
i
da
ya
t
a
n M
us
t
a
fa
,
"
F
P
G
A
Im
pl
e
m
e
nt
a
t
i
ons
of
Cha
ot
i
c
Q
ua
dra
t
i
c
M
a
p
f
or Cryp
t
ogra
phi
c
A
ppl
i
c
a
t
i
ons
,
"
T
u
rk
i
sh
J
our
nal
of
Sc
i
e
n
c
e
&
T
e
c
hnol
og
y
,
vo
l
.
12,
no.
2,
pp.
113
-
119
,
20
17.
[9]
T
u
n
cer
,
"
T
h
e i
m
p
l
em
en
t
at
i
o
n
o
f
ch
ao
s
-
ba
s
e
d
P
U
F
de
s
i
gns
i
n F
i
e
l
d
progra
m
m
a
bl
e
g
a
t
e
a
rra
y,
"
Non
l
i
ne
a
r
Dy
n
a
mi
c
s,
v
ol
.
8
6,
pp
.
975
-
986
,
2016.
[10]
G
ar
ci
a
,
e
t a
l
.
,
"
C
ha
os
-
ba
s
e
d bi
t
w
i
s
e
dyna
m
i
c
a
l
ps
e
udor
a
ndom
nu
m
be
r ge
n
e
ra
t
or
on F
P
G
A
,
"
IE
E
E
T
r
ans
ac
t
i
ons
on
Ins
t
r
um
e
nt
at
i
on and
Me
as
ur
e
m
e
nt
,
vo
l
.
68,
pp.
2
91
-
293,
2019
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
l
e
c
&
C
om
p
E
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g
I
S
S
N
:
208
8
-
87
08
L
ow
pow
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ps
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o
-
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and
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nu
m
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r
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e
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a
to
r
b
as
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d
on…
(
M
oha
m
e
d
Sa
be
r
)
8
71
[11]
A
. T
h
an
e
a
nd
R
.
Cha
udh
a
ri
,
"
H
a
rdw
a
re
D
e
s
i
gn
a
nd Im
p
l
e
m
e
nt
a
t
i
on of
P
s
e
udora
ndom
N
um
be
r
G
e
ne
ra
t
or
Usi
n
g
Pi
e
c
ew
i
s
e
L
i
n
ea
r
C
h
ao
t
i
c M
ap
,
"
Int
e
r
nat
i
onal
Conf
e
r
e
nc
e
on
A
dv
anc
e
s
i
n C
om
put
i
ng,
Com
m
uni
c
at
i
ons
an
d
Inf
or
m
at
i
c
s
(ICA
CCI),
pp
.
456
-
4
59,
2018
.
[12]
R.
Bori
g
a
,
e
t
a
l
.
,
"
A
N
e
w
F
a
s
t
Im
a
ge
E
nc
rypt
i
on S
c
he
m
e
Ba
s
e
d on Cha
o
t
i
c
M
a
ps
,
"
Int
e
r
nat
i
onal
J
our
nal
of
Co
m
p
u
t
er
s
ci
en
c
e,
vo
l
.
41,
pp.
24
9
-
258,
2014
.
[13]
A
.
D
ă
s
c
ă
l
e
s
c
u
a
nd
R.
Bori
ga
,
"
A
nove
l
ps
e
udo
-
ra
ndom
bi
t
ge
n
e
ra
t
or ba
s
e
d
on a
ne
w
c
oupl
e
of
c
ha
ot
i
c
s
ys
t
e
m
s
,
"
A
n
n
a
l
s o
f
Ov
i
d
i
u
s Un
i
v
e
rsi
t
y
-
E
c
onom
i
c
s
Sc
i
e
nc
e
s
Se
r
i
e
s
,
vol
.
11,
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553
-
558,
20
11.
[14]
P
.
K
um
a
r,
"
F
P
G
A
Im
pl
e
m
e
nt
a
t
i
on o
f t
h
e
T
ri
gonom
e
t
ri
c
F
unc
t
i
on
s
U
s
i
ng
t
he
CO
RD
IC A
l
gori
t
hm
,
"
5t
h
Int
e
r
nat
i
onal
Co
nf
e
r
e
nc
e
on
A
dv
anc
e
d Com
put
i
n
g &
Com
m
uni
c
a
t
i
on S
y
s
t
e
m
s
(IC
A
CCS),
pp
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894
-
900,
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[15]
S
.
N
an
d
i
, et
a
l
.
,
"
F
i
x
e
d poi
n
t
i
m
pl
e
m
e
nt
a
t
i
o
n of t
ri
gonom
e
t
ri
c
fun
c
t
i
on
u
s
i
ng T
a
yl
or's
s
e
ri
e
s
a
nd
e
rror
ch
ar
a
ct
er
i
z
at
i
o
n
,"
Int
e
r
nat
i
ona
l
Conf
e
r
e
n
c
e
o
n A
dv
an
c
e
s
i
n
Com
put
i
ng,
C
om
m
uni
c
at
i
ons
and Inf
or
m
at
i
c
s
(ICA
CCI),
p
p.
44
2
-
446,
2016
.
[16]
M
. S
ab
er
,
et
a
l
.
,
"
Q
ua
dra
t
ure
d
i
re
c
t
di
g
i
t
a
l
fre
qu
e
nc
y s
ynt
he
s
i
z
e
r
us
i
ng F
P
G
A
,
"
I
E
E
E
In
t
e
r
nat
i
on
al
Conf
e
r
e
n
c
e
o
n
Com
put
e
r
E
ngi
n
e
e
r
i
ng and
Sy
s
t
e
m
s
,
pp.
14
-
18
,
2
006.
[17]
X
i
l
i
nx,
V
i
va
do
"
D
e
s
i
gn
S
ui
t
e
U
s
e
r G
ui
de
:
M
ode
l
-
Ba
s
e
d
D
S
P
D
e
s
i
gn us
i
ng
S
ys
t
e
m
G
e
ne
r
a
t
or,
"
U
G
897,
v
2016
.
1
e
d
.
,
X
ilin
x
,
2018
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R
. P
al
an
i
s
a
m
y
,
et
al
.,
"
S
w
i
t
c
hi
n
g pul
s
e
ge
n
e
ra
t
or ge
n
e
ra
t
i
on fo
r D
C
-
D
C boos
t
c
onve
rt
e
r us
i
ng
us
i
ng xi
l
i
nx
-
I
S
E
wi
t
h
F
P
GA p
r
o
c
e
sso
r
,
"
Int
e
r
nat
i
onal
J
our
nal
o
d E
l
e
c
t
r
i
c
a
l
and
Com
put
e
r
E
ngi
ne
e
r
i
ng (IJ
E
CE
)
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A
.
S
t
a
c
ul
,
"
F
i
l
t
e
ri
ng a
nd
a
c
qui
s
i
t
i
on of s
e
ri
a
l
da
t
a
fra
m
e
s
us
i
ng x
i
l
i
nx s
ys
t
e
m
ge
n
e
ra
t
or
,
"
Int
e
r
nat
i
onal
J
our
nal
of
R
e
c
on
f
i
gur
abl
e
and E
m
be
dde
d
s
y
s
t
e
m
s
(IJ
R
E
S),
vol
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,
pp
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11
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2020.
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L
.
Z
ha
ng
,
"
F
i
xe
d poi
nt
F
P
G
A
M
ode
l
ba
s
e
d
de
s
i
gn a
nd op
t
i
m
i
z
a
t
i
on
for H
e
non
M
a
p c
ha
o
t
i
c
ge
n
e
ra
t
or
,
"
I
E
E
E 8
t
h
L
at
i
n A
m
e
r
i
c
an
Sy
m
pos
i
um
on C
i
r
c
ui
t
&
s
y
s
t
e
m
s
,
pp.
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-
4,
2017.
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K
a
ra
ka
ya
,
e
t
a
l
.
,
"
Re
a
l
i
z
a
t
i
ons
o
f D
e
l
a
ye
d
Ce
l
l
ul
a
r N
e
ur
a
l
N
e
t
w
ork M
ode
l
on
F
P
G
A
,
"
2018 E
l
e
c
t
r
i
c
E
l
e
c
t
r
oni
c
s
,
Com
put
e
r
Sc
i
e
n
c
e
,
B
i
om
e
di
c
a
l
E
ngi
ne
e
r
i
ng'
s
'
M
e
e
t
i
ng
(E
B
B
T
),
20
18.
[22]
M
o
h
am
ed
S
ab
er
an
d
E
s
am
A
.
H
ag
r
as
,
"
P
ar
al
l
e
l
m
u
l
t
i
-
l
ay
er
s
el
ect
o
r
S
-
BO
X
ba
s
e
d on
l
or
e
nz
c
hot
i
c
s
ys
t
e
m
w
i
t
h
F
P
G
A
imp
le
m
e
n
ta
tio
n
,
"
Indone
s
i
an J
our
nal
of
E
l
e
c
t
r
i
c
al
E
ngi
ne
e
r
i
ng
and
Co
m
put
e
r
Sc
i
e
n
c
e
,
vol
.
19,
n
o
. 2
,
pp.
784
-
792
,
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20.
[23]
D
.
M
en
ar
d
, et
a
l
.
, "
A
n
al
y
s
i
s
of
F
i
ni
t
e
W
ord
-
L
e
ngt
h E
ffe
c
t
s
i
n F
i
xe
d
-
P
o
in
t S
y
s
te
ms
,
"
Spr
i
nge
r
Cham
,
2019
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[24]
A
Rukhi
n
,
et
a
l
.
,
"
A
S
t
a
t
i
s
t
i
c
a
l
T
e
s
t
S
ui
t
e
for r
a
ndom
a
nd P
s
e
d
uo
-
ra
ndom
N
um
be
r G
e
ne
r
a
t
or
f
or Crypt
ogra
phi
c
A
ppl
i
c
a
t
i
ons
,
"
B
ooz
-
al
l
e
n and
ha
m
i
l
t
on i
n
c
m
c
l
e
a
n v
a,
2010.
[25]
Z
.
H
u
a
, et
a
l
.
,
''
Cos
i
ne
-
t
ra
ns
for
m
-
ba
s
e
d
c
ha
ot
i
c
s
ys
t
e
m
for
i
m
a
ge
e
nc
rypt
i
on,
"
Inf
or
m
at
i
on S
c
i
e
nc
e
s
,
vol
.
480
,
pp.
403
-
419
,
20
19.
[26]
Z
. T
an
g
, et
a
l
.
,
''Im
a
ge
E
nc
rypt
i
on w
i
t
h D
oubl
e
S
pi
ra
l
S
c
a
ns
a
nd Cha
ot
i
c
M
a
p
s
,
''
Se
c
ur
i
t
y
and
Com
m
uni
c
at
i
on
Ne
t
wor
k
s
,
vo
l
.
2
019,
p
p.
1
-
15
,
2
019.
[27]
Z
.
D
e
ng
a
nd S
.
Z
hong,
''A
di
gi
t
a
l
i
m
a
g
e
e
nc
rypt
i
o
n a
l
gori
t
hm
ba
s
e
d on c
ha
ot
i
c
m
a
ppi
ng,
''
J
our
nal
of
A
l
gor
i
t
hm
s
&
Com
put
at
i
onal
T
e
c
hnol
og
y
,
vol
.
13,
pp
1
–
11,
201
9.
[28]
M
.S
. A
zz
az,
e
t
a
l
.
, "
A
n
ew
au
t
o
-
s
w
itc
h
e
d
c
h
a
o
tic
s
y
s
te
m a
n
d
its
F
P
G
A
imp
le
me
n
t
a
tio
n
,
"
Co
m
m
uni
c
at
i
ons
i
n
Nonl
i
ne
ar
S
c
i
e
n
c
e
&
Num
e
r
i
c
al
Si
m
ul
at
i
on
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04,
2013
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[29]
S
.
S
a
doudi
,
e
t
a
l
.,
"
A
n
FPG
A
R
e
a
l
-
t
i
m
e
I
m
pl
e
m
e
nt
a
t
i
on
of
t
h
e
Che
n
‟
s
Ch
a
ot
i
c
S
ys
t
e
m
fo
r
S
e
c
uri
ng
Cha
o
t
i
c
Com
m
uni
c
a
t
i
on
s
,
"
Int
e
r
nat
i
o
nal
J
our
nal
o
f
Non
l
i
ne
ar
Sc
i
en
c
e,
v
ol
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L
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G
er
ar
d
o
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a
l
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,
"
H
a
rdw
a
re
Im
pl
e
m
e
nt
a
t
i
on
of P
s
e
udo
-
ra
n
dom
num
be
r
ge
ne
ra
t
or b
a
s
e
d o
n c
ha
ot
i
c
m
a
ps
,
"
Nonl
i
ne
ar
D
y
na
m
i
c
s
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7.
B
I
O
G
R
A
P
H
IE
S
O
F
A
U
T
H
O
R
S
M
o
ha
m
e
d Sa
be
r
,
h
e
r
ec
ei
v
ed
P
h
.D
.
D
e
gre
e
In Inform
a
t
i
c
s
a
nd Com
m
uni
c
a
t
i
ons
,
K
yus
hu
U
ni
ve
rs
i
t
y,
J
a
p
a
n,
2012.
H
e
w
or
ks
a
s
a
n
a
s
s
i
s
t
a
n
t
profe
s
s
or a
t
D
e
l
t
a
uni
ve
rs
i
t
y f
or s
c
i
e
nc
e
a
n
d
T
e
c
hno
l
ogy,
M
a
ns
oura
,
E
gypt
.
H
i
s
re
s
e
a
rc
h
i
nt
e
re
s
t
s
a
r
e
:
D
i
gi
t
a
l
s
i
gna
l
proc
e
s
s
i
ng,
D
e
s
i
gn
a
nd
imp
le
me
n
t
d
ig
it
a
l c
o
mmu
n
i
c
a
tio
n
s
y
s
te
ms
o
n
F
P
G
A
a
n
d
D
S
P
c
ir
c
u
its
,
S
y
n
c
h
r
o
n
iz
a
t
io
n
in
d
ig
ita
l
re
c
e
i
ve
rs
.
Ma
rw
a
M.
Ei
d
re
c
e
i
ve
d
t
h
e
P
h.
D
.
d
e
gre
e
i
n
E
l
e
c
t
roni
c
s
a
nd Co
m
m
uni
c
a
t
i
o
ns
E
ngi
ne
e
r
i
ng
from
t
he
F
a
c
ul
t
y
of
E
ngi
ne
e
ri
ng
-
M
a
ns
oura
U
ni
ve
rs
i
t
y
-
E
gypt
by
20
15.
S
he
wo
r
k
e
d
a
s a
n
a
ssi
st
a
n
t
profe
s
s
or a
t
D
e
l
t
a
H
i
gh
e
r
Ins
t
i
t
ut
e
for
E
ngi
ne
e
ri
ng
&
T
e
c
hnol
ogy s
i
n
c
e
2011 t
i
l
l
now
.
H
e
r c
urr
e
nt
re
s
e
a
rc
h
i
n
t
e
r
e
s
t
s
a
re
i
n
i
m
a
ge
pr
oc
e
s
s
i
ng,
e
nc
ry
pt
i
on,
w
i
re
l
e
s
s
c
om
m
uni
c
a
t
i
on
s
ys
t
e
m
s
,
a
nd
F
i
e
l
d P
rogra
m
m
a
bl
e
G
a
t
e
A
rra
y
(F
P
G
A
)
a
ppl
i
c
a
tio
n
s
.
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