In
d
o
n
e
sian
Jou
r
n
al of
Ele
c
tr
i
c
a
l
En
g
in
e
erin
g
a
n
d
C
om
pu
t
er S
c
ien
ce
Vol.
17, No.
2, F
ebruary 2020,
pp.
929~940
ISSN: 2502-
4752,
DOI
:
10.115
91/ijeecs.
v
17.
i
2
.
pp929-940
9
29
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
je
ec
s.iaesc
o
re
.co
m
D
e
sign of a Matlab toolbox and
GUI for minim
al realizations
K
a
r
i
m Ch
erifi,
Kamel Haric
h
e
Th
e instit
ute
o
f
e
l
ectrical
and
elect
ron
i
c en
g
i
neerin
g,
M
’h
a
m
ed
B
o
u
g
a
ra
U
ni
vers
it
y,
A
lg
eria
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
M
ay
2
6
, 2
019
Re
vise
d Ju
l 2
7
,
201
9
Ac
ce
p
t
ed
Au
g
1
1
,
2
019
M
i
nim
a
l
reali
zati
o
n
f
o
r
l
i
n
ear
s
ys
tems
h
as
b
een
s
t
udied
e
x
t
ensi
vely
i
n
the
literat
u
re.
Techni
ques
proposed
d
iff
e
r
i
n
t
erms
o
f
the
configur
at
io
n
o
f
t
h
e
st
ate
space
f
o
rm,
the
ti
m
e
e
fficiency
o
f
th
e
alg
o
ri
thm
and
t
h
e
re
du
c
t
io
n
o
f
m
e
m
o
ry
s
to
rage.
The
mi
n
i
m
a
l
real
izati
o
n
to
o
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b
o
x
p
r
es
ent
e
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s
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ost
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o
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t
h
e
a
p
p
l
i
c
a
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n
.
T
h
e
g
i
v
en
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y
s
t
e
m
c
a
n
b
e
r
e
p
r
e
s
en
ted by
a
tran
s
f
er f
u
n
c
t
i
on o
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by
raw (f
req
u
en
cy o
r tim
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ain) da
t
a. A
grap
hical
us
e
r
in
terf
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(G
UI)
was
im
p
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e
m
ent
e
d
in
o
rd
er
t
o
eas
e
the
us
e
o
f
t
hi
s
t
o
o
l
b
ox
and
all
o
w to rapi
d
l
y
t
est the
meth
ods an
d
d
is
p
l
ay
t
he
r
es
ults.
K
eyw
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s
:
Co
mp
ut
e
r
-a
i
d
ed
co
n
t
r
ol
Co
nt
rol
en
gi
n
e
e
r
i
ng
M
i
n
i
m
a
l r
ealiz
a
t
i
o
n
S
y
stem
m
odel
l
i
n
g
Co
pyri
gh
t © 2
020 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
Scien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
K
a
r
i
m
C
h
e
r
if
i,
The
inst
i
t
u
t
e
o
f
e
lectric
a
l
a
n
d
e
lec
t
r
o
n
i
c
e
ngi
ne
eri
ng,
M’ham
e
d
Bo
u
g
ar
a U
n
i
v
e
r
s
i
t
y
,
Inde
pe
n
d
e
n
ce
A
ve
nue
,
3500
0
,
Boume
r
dès,
A
lger
i
a
.
Em
ail:
cher
i
f
ik
a
r
imdz
@gma
i
l
.
c
om
1.
I
N
TR
OD
U
C
TI
O
N
M
i
n
i
ma
l
r
eali
z
a
t
i
o
n
an
d
m
ode
l
re
du
ct
io
n
[1,
2]
a
re
w
i
d
e
l
y
use
d
t
o
o
bt
ai
n
m
a
them
at
ical
repr
esenta
t
i
o
n
s
of
s
y
s
t
e
m
s
in
sta
t
e
spac
e for
m
with t
he
s
m
a
lle
s
t p
o
ss
i
b
l
e
n
um
ber
of sta
te
s
[3-7]
.
M
a
n
y
d
efi
n
it
ion
s
h
av
e
b
e
en
g
i
v
en
t
o
re
al
i
z
ati
o
n
s
but
g
en
era
l
ly
sp
eaki
n
g
,
a
r
ea
l
i
z
a
tio
n
i
s
t
h
e
p
r
o
c
e
s
s
of
t
rans
f
o
r
m
in
g
e
x
a
c
t
l
y
a
s
yste
m
from
i
t
s
fre
que
nc
y
ba
se
d
t
r
ans
f
e
r
fu
n
c
tio
n
G(s)
t
o
a
time
b
a
se
d
st
at
e
sp
a
ce
repr
esentation (A, B, C, D)
:
X
AX
B
U
YC
XD
U
(
1
)
Wh
e
r
e
U
i
s
t
h
e
i
np
ut
v
e
c
t
o
r
re
g
r
ou
pin
g
m
i
n
put
s.
Y
i
s
t
h
e
o
u
t
p
u
t
vec
t
or
r
e
g
ro
up
ing
w
i
t
h
p
i
np
uts.
X
is
t
he
s
ta
te
v
e
c
t
or
w
i
t
h
dime
nsi
on
n.
A
i
s
an
n
×
n
s
ta
te
m
at
rix.
B
i
s
a
n
n
×m
i
np
ut
m
a
t
ri
x.
C
i
s
a
p×
n
o
u
t
p
ut
ma
trix.
D
is a p
×m
f
ee
dforw
a
rd m
atrix.
A
m
i
n
i
m
a
l
r
e
a
l
i
z
a
t
i
o
n
i
s
a
r
e
a
l
i
z
a
t
i
o
n
w
i
t
h
a
m
i
n
i
m
a
l
o
r
d
e
r
n
c
alle
d
t
h
e
Mc
Mil
lia
n
de
gree
.
A
ll
min
i
ma
l
re
ali
z
a
t
i
ons
a
re
e
qu
i
v
ale
n
t
[
3
].
I
t
is
w
orth
n
o
tin
g
t
ha
t
a
s
t
at
e
spa
ce
repr
esenta
t
i
o
n
i
s
a
min
i
m
a
l
rea
l
i
z
a
t
i
o
n
of
a
pr
oper
ratio
na
l func
t
i
o
n
G
(s) i
f
an
d
o
nly
if (
A
,
B
)
is
c
ontro
lla
b
l
e
an
d (A
, C)
is
obser
va
b
l
e
[3]
.
Bes
i
de
t
i
m
e
reduc
t
i
o
n
i
n
c
o
n
t
r
o
ller
a
nd
ob
se
r
v
er
d
esi
g
n
s
[
4
,
5
]
,
minim
a
l
r
ealiz
a
t
i
ons
i
n
g
e
ne
ral
ha
v
e
the
a
dva
n
t
a
g
e
of
r
edu
c
i
n
g
th
e
c
o
st
o
f
i
m
p
l
em
enta
ti
on
o
f
t
he
s
ta
te
s
pac
e
e
qua
tio
ns
i
n
t
e
rm
s
of
e
l
e
c
t
ron
i
c
com
p
o
n
e
n
t
s
.
D
i
ffe
re
nt
t
ec
h
n
i
q
ues
e
x
is
t
for
minima
l
r
eal
iza
t
i
on.
E
a
c
h
t
echn
i
que
h
as
i
t
s
a
dva
n
t
a
g
e
s
a
nd
i
t
s
di
sa
d
v
a
n
ta
ges.
S
ome
tec
hni
q
u
es
f
oc
use
d
o
n
ob
ta
in
i
ng
th
e
sta
t
e
s
pac
e
r
e
pre
s
e
n
t
a
t
i
o
n
i
n
a
m
i
n
i
ma
l
t
i
m
e
a
nd
other
focused
on
the
for
m
o
f
t
h
e
m
a
tric
es
o
f
t
h
e
s
t
a
t
e
sp
a
ce
re
present
a
tio
n.
D
epe
n
d
i
n
g
o
n
t
h
e
ap
p
l
i
cati
o
n,
ti
m
e
e
ffic
ie
nc
y
or
c
on
f
i
g
u
ra
t
i
on
of
t
he
r
esu
l
t
i
n
g
m
i
n
im
al
r
e
a
li
z
a
t
i
on
ma
y
be
p
referr
ed.
Th
is
r
e
q
ui
r
e
s
to
h
a
v
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 250
2-
475
2
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
, V
o
l
.
1
7
,
N
o
. 2, F
e
b
ruary
20
20
: 929
-
940
93
0
to
ol
t
ha
t
w
o
u
l
d
a
l
l
o
w
r
e
sea
r
che
r
s
a
n
d
e
n
g
i
ne
ers
t
o
e
as
i
l
y
com
p
u
te
m
i
n
i
m
a
l
r
ealiza
tio
n
.
U
p
to
n
ow
s
uch
a
com
p
le
te t
o
o
l
c
oul
d
not
b
e f
o
un
d
i
n
the
l
i
t
era
t
ure.
Ma
ny
to
ol
b
o
x
e
s
ha
ve
b
ee
n
i
m
plem
en
ted
t
o
h
e
l
p
re
se
arc
h
ers
a
n
d
en
g
i
ne
er
s
i
n
t
he
ir
w
ork
[8-
1
4
]
.
Th
is
M
A
TLA
B
to
o
l
bo
x
for
m
i
nima
l
r
eal
iz
a
t
i
o
n
ca
n
be
c
om
bine
d
t
o
oth
e
r
too
l
s
t
o
d
e
s
ig
n
c
ont
ro
ll
ers
a
nd
obs
erve
rs
i
n
a
n
e
fficie
n
t
w
a
y.
A
l
t
ho
u
g
h
a
to
olb
o
x
f
or
m
i
n
i
m
al
r
e
a
l
i
z
a
t
i
on
w
a
s
pr
esen
ted
i
n
t
he
p
as
t
[1
5
]
,
it
i
s
inc
o
m
p
let
e
a
s
it
prese
n
ts
o
n
l
y
o
n
e
me
tho
d
a
nd
is
n
o
t
u
se
r
frien
d
l
y
as
it
d
o
es
n
o
t
h
a
v
e
a
grap
hic
a
l
u
se
r
int
e
rf
ace
(GUI).
I
n
t
h
i
s
p
a
pe
r,
f
irst,
the i
m
p
l
e
m
ented
mi
n
i
m
a
l
r
ealiza
t
i
on
t
e
chn
iq
u
e
s
are
p
r
e
s
ent
e
d
th
e
o
re
t
i
cal
ly
,
t
h
en
,
the
grap
h
i
ca
l
u
s
er
i
n
t
erfac
e
(
G
U
I
)
is
p
rese
n
t
e
d
a
l
ong
w
i
t
h
i
n
d
i
v
i
dua
l
func
t
i
o
n
s
c
o
rr
espo
nd
ing
t
o
t
he
d
i
ffe
ren
t
minim
a
l
rea
liz
ati
o
n
t
e
c
h
n
i
q
u
es.
F
i
n
a
l
l
y,
t
he
G
U
I
i
s
te
ste
d
u
sin
g
prac
t
i
c
al
a
pp
li
cat
ion
s
a
nd
d
if
fe
ren
t
tech
n
i
q
u
es
a
re
com
par
e
d us
in
g the
min
i
ma
l re
aliz
at
i
on t
o
olbo
x.
I
n
t
he
b
roa
d
s
ense
,
rea
l
iz
a
tio
ns
a
im
t
o
o
b
ta
i
n
s
ys
t
e
ms
i
n
sta
t
e
s
pac
e
r
ep
re
senta
t
i
ons
e
v
e
n
for
r
a
w
in
put-
o
u
t
pu
t
d
a
ta.
O
n
e
of
t
h
e
m
ost
pr
o
m
is
i
n
g
m
e
th
o
d
s
for
da
t
a
f
r
o
m
reque
nc
y
d
o
ma
in
a
nd
t
i
m
e
d
om
ain
,
a
r
e t
h
e
met
h
od
s b
a
se
d
on
Lowe
n
er
fram
e
work [6, 7
]
. These are al
so pr
e
s
e
nted
a
nd im
p
le
ment
ed
i
n this
paper.
Th
e
p
r
e
s
e
n
t
e
d
t
o
ol
box
i
s
v
a
lid
f
o
r
s
ingl
e
inp
u
t
si
ngl
e
ou
tpu
t
(
S
I
S
O
)
s
y
s
t
e
m
s
a
s
w
e
l
l
a
s
m
u
l
t
i
i
n
p
u
t
mult
i o
u
t
p
u
t
(
MIMO
)
syste
m
s.
I
t is a
lso
vali
d for
cont
i
n
uo
us
t
i
m
e
a
nd di
scr
e
te
tim
e
s
y
s
t
em
s.
2.
PROPO
S
E
D
PROCEDURE
S
The
r
e
e
x
i
s
t
m
a
ny
m
inim
al
r
ea
li
z
a
t
i
on
t
e
c
h
niq
u
e
s
[
16-1
8
]
.
I
n
t
h
i
s
pa
pe
r
w
e
d
is
t
i
n
g
u
is
h
t
w
o
ma
in
c
a
t
e
go
ri
e
s
:
re
al
i
zati
o
n
fro
m
a
t
r
a
n
sf
er
f
un
ct
ion
a
n
d
rea
l
i
z
a
t
io
ns
from
da
ta.
I
n
t
hi
s
sect
io
n,
w
e
present
t
h
e
the
o
re
tica
l
b
as
i
s
for
the
m
e
t
h
o
d
s im
p
l
em
ente
d in
t
he
t
oo
lb
o
x
.
I
n
1
9
6
3
,
G
i
l
b
e
r
t
p
r
e
s
e
n
t
e
d
a
m
e
t
h
o
d
b
a
s
e
d
o
n
t
h
e
p
a
r
t
i
a
l
f
r
a
c
t
i
on
o
f
t
h
e
t
r
an
sf
e
r
f
un
ct
io
n
[1
9
]
.
A
ltho
u
gh
t
h
is
m
etho
d
is
i
n
t
er
est
i
n
g
i
n
term
s
of
t
he
r
esu
lti
n
g
c
o
n
f
i
g
u
r
a
t
i
o
n
,
i
t
i
s
n
o
t
g
e
n
e
r
a
l
b
e
c
a
u
s
e
i
t
i
s
n
o
t
app
l
icab
le
t
o
re
peate
d
p
o
l
es.
Thus,
th
i
s
m
eth
o
d
w
ill
n
o
t
b
e
de
t
ai
le
d
he
r
e
.
A
nothe
r
po
pu
l
a
r
m
e
th
od
i
s
t
he
K
a
lm
an
d
e
c
o
mpos
it
ion
m
e
t
h
o
d
.
The
goa
l
of
t
h
i
s
me
tho
d
i
s
to
o
bt
a
in
a
m
i
n
im
al
r
e
a
l
i
z
a
t
i
on
g
i
ve
n
a
no
n-
minim
a
l
re
aliz
ati
o
n.
O
t
h
e
r
m
eth
o
d
s
base
d
o
n
t
he
H
a
n
kel
m
a
trix
w
e
r
e
presen
te
d
in
t
he
f
o
l
low
i
n
g
y
ea
r
s
.
We
prese
n
t
he
re
t
w
o
m
e
t
ho
ds
b
a
s
e
d
o
n
t
h
e
H
a
n
k
e
l
m
atr
i
x:
t
he
S
in
gu
l
a
r
v
a
l
u
e
d
e
c
o
m
p
o
s
i
t
i
o
n
(
S
V
D
)
m
e
t
h
o
d
a
n
d
the r
o
w
sea
r
chi
ng m
e
th
o
d
.
F
i
nall
y,
m
e
t
hods
b
ased
o
n copr
i
m
e
fra
ctions
o
f t
h
e
trans
f
e
r
fun
ctio
n
are
pre
s
e
n
te
d.
C
once
r
n
i
ng
th
e
rea
l
iz
a
tio
ns
f
rom
data,
w
e
p
re
sen
t
t
w
o
m
e
t
h
ods
b
a
s
ed
o
n
t
h
e
L
o
ew
ner
m
a
trix.
One
me
tho
d
i
s
a
r
e
aliz
at
i
on
fro
m
fre
que
ncy
doma
i
n
da
ta
w
hi
le
t
he
o
t
h
e
r
one
i
s
a
r
e
a
l
i
z
at
i
o
n
fr
om
t
im
e
doma
i
n
da
ta.
2.1.
Kalm
an
D
e
c
omp
o
si
t
i
on
Th
e
Ka
l
m
a
n
d
e
c
o
mp
osi
t
i
o
n
me
t
h
od
[2
0
]
i
s
a
n
i
nd
i
r
ec
t
me
t
hod
w
hi
c
h
re
qu
ire
s
t
o
have
f
irst
a
n
o
n
-
mi
n
i
mal
re
a
l
i
zat
ion
to
b
e
ab
le
t
o
co
mpu
t
e
t
h
e
min
i
ma
l
real
i
zati
on.
O
nc
e
a
rea
liz
a
tio
n
is
o
b
t
ai
ne
d,
K
alm
a
n
dec
o
mp
os
i
t
i
o
n is use
d to se
p
a
r
ate
the s
y
stem
in
t
o fo
ur
p
ar
t
s
:
a)
A
c
ont
r
o
lla
ble
and
o
b
se
rva
b
le
p
art
(c-
o
).
b)
A
non-
co
n
t
roll
a
b
l
e
an
d
o
bserva
ble
par
t
(
nc-
o
).
c)
A
c
ont
r
o
lla
ble
and
n
o
n
-o
bserva
ble
par
t
(
c-
no).
d)
A
non-
co
n
t
roll
a
b
l
e
an
d
n
on-
o
b
serva
b
le
par
t
(nc-
no).
K
a
lma
n
d
ec
o
m
pos
i
t
i
on
is
o
b
t
a
i
ne
d
usi
ng
a
si
m
i
l
a
ri
ty
t
r
a
nsform
at
i
o
n.
A
fter
K
a
l
ma
n
de
com
p
o
s
it
io
n,
the o
b
t
ai
ne
d
sy
ste
m
i
s
i
n
t
he f
orm:
14
12
13
24
34
00
0
0
0
00
00
00
ˆˆ
ˆˆ
cn
o
cn
o
co
co
co
n
c
o
nc
no
nc
o
A
AB
AA
A
AB
A
BC
C
C
D
D
A
A
A
(
2
)
S
i
n
c
e
by
d
e
f
i
n
iti
o
n
a
minimal
re
al
i
zati
o
n
is
c
ont
rol
l
a
bl
e
and
o
bserv
a
ble,
o
n
l
y
tha
t
p
art
i
s
k
ep
t.
U
s
ing
t
h
e form
(2), the
m
i
n
im
al r
ealiza
t
i
o
n is
give
n
b
y (3)
:
co
c
o
co
X
AX
B
U
YC
X
D
U
(
3
)
Th
e
ma
in
a
dva
n
t
ag
e
of
t
hi
s
fo
rm
i
s
th
e
a
b
il
i
t
y
t
o
u
se
i
t
wh
en
t
he
g
ive
n
s
ys
tem
is
a
l
r
eady
in
s
ta
te
space
form
bu
t
it
i
s
n
o
t o
f
m
in
ima
l
orde
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
D
e
sig
n
o
f
a Mat
l
ab t
o
olb
o
x
a
nd G
U
I
for m
i
nim
a
l re
al
izat
i
ons (K
ar
i
m
Che
r
ifi)
93
1
2.2.
Han
k
e
l
Mat
ri
x an
d
S
VD
The
H
a
nke
l m
a
tri
x
is de
fi
ned
a
s
:
1
2
2
3
1
12
2
12
1
HH
H
r
HH
H
r
T
Hr
Hr
H
r
Hr
Hr
H
r
(
4
)
wher
e H(i) are Mark
ov
p
a
ram
e
te
rs which
c
a
n
b
e
com
p
u
t
e
d
fr
o
m
t
h
e
tra
nsf
e
r
funct
i
on a
s
:
12
(
)
(
0
)
H
(
1
)
s
(
2
)
.....
Gs
H
H
s
(
5
)
Fo
r
SI
SO
s
y
s
t
e
ms
H
(
i
)
i
s
j
u
s
t
a
s
c
a
l
a
r
.
T
h
eorem
1:
A stric
tly
pr
op
er rat
i
on
a
l
fu
nc
t
i
o
n
G
(
s) has de
g
r
e
e
n if a
nd o
n
l
y
i
f
ran
k
{T
(n,
n
)
}
=ran
k{T
(
n+k,
n+l)} for eve
ry
k
,
l
=
1,2…
…
P
r
oof
o
f t
h
e
o
r
e
m
1: [3].
The
r
e
e
x
is
t
m
a
ny
m
eth
o
d
s
ba
se
d
o
n
t
he
H
an
kel
ma
tri
x
.
We
p
re
se
n
t
h
e
r
e
t
w
o
m
e
t
h
o
d
s
:
o
n
e
b
a
s
e
d
o
n
the S
V
D
a
nd the
othe
r one
o
n
row
se
arc
h
in
g.
I
n
the
f
irs
t
m
etho
d, the
si
ngu
l
a
r
value
dec
o
mpos
i
tio
n
o
f
t
he
H
a
nke
l
ma
t
r
i
x
(
4)
i
s
com
pute
d
:
0
00
T
TK
L
(
6
)
By
d
efi
n
it
ion
, K
a
n
d
T
L
are
o
r
t
h
o
gon
al
a
nd
12
d
iag
,
,
,
n
w
h
e
r
e
i
a
r
e
t
h
e
s
q
u
a
r
e
r
o
o
t
s
of
t
he
p
osit
iv
e
eige
n
v
al
ues
o
f
T
TT
.
The r
a
nk of T
can
b
e de
duc
e
d
f
rom
theor
e
m
1.
Let
K
d
e
n
ot
e
t
h
e
f
i
rst
n
co
lumn
s
of
K
a
nd
T
L
d
enot
e
the
first
n
r
o
ws
o
f
T
L
.
T
h
e
n
T
c
a
n
b
e
dec
o
mp
ose
d
a
s:
1/
2
1
/
2
:
O
TT
TK
L
K
L
ΛΛ
Λ
(
7
)
wher
e
1/
2
OK
Λ
a
nd
1/
2
T
L
Λ
.
Is t
h
e c
ont
rol
l
a
bi
li
ty
ma
t
ri
x
a
n
d
is
O
t
he
o
bser
va
b
ili
ty m
atri
x.
The
re
sult
in
g m
i
ni
m
a
l r
ealiz
a
tio
n
i
s
g
ive
n
b
y:
A
OT
(8)
B
F
i
r
s
t
p
colum
n
s
of
(
9
)
C
F
i
r
st
q
c
olum
ns
o
f
O
(
1
0
)
(0
)
DH
(1
1
)
Th
is m
i
n
ima
l
r
ea
li
z
a
t
i
on
is a
l
s
o c
a
lle
d ba
l
a
n
ced rea
l
i
z
a
t
i
on
be
ca
use
t
h
e
con
t
ro
ll
ab
il
i
t
y
m
a
t
r
ix
and
t
h
e
ob
serv
abil
it
y
ma
t
r
ix
O
sa
tisfy:
''
OO
(
1
2
)
A
m
odifie
d
ver
si
on
of th
i
s
m
e
th
o
d
i
s use
d
in
mode
l
red
u
c
t
i
o
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 250
2-
475
2
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
, V
o
l
.
1
7
,
N
o
. 2, F
e
b
ruary
20
20
: 929
-
940
93
2
2.3.
Han
k
e
l
Mat
ri
x an
d
R
o
w
S
e
arc
h
in
g
Th
is
m
eth
od
c
ons
is
t
s
o
f
sea
r
chi
n
g
for
l
i
n
e
arly
d
e
p
en
de
n
t
r
ow
s
(
c
o
lu
mn
s)
i
n
th
e
Han
k
e
l
ma
t
r
ix
.
Be
ca
use
of
t
he
s
truc
t
u
re
o
f
t
h
e
H
a
nke
l
ma
t
r
ix
a
nd
t
he
ore
m
1
,
i
f
one
r
ow
i
n
a
b
l
oc
k
r
o
w
i
s
l
i
n
ea
rl
y
depe
nde
n
t
on i
t
s pre
v
i
o
u
s
r
ow
s, the
n
it
i
s
als
o
li
n
ear
ly
d
e
p
en
de
nt
o
n t
h
e
s
u
b
s
e
qu
en
t
r
o
w
s
i
n
t
h
e
s
a
me
b
l
o
ck
r
o
w
.
Let
i
be
t
he
n
u
m
be
r
of
line
a
rly
i
n
depe
nde
n
t
r
ow
s
i
n
a
b
l
o
ck
r
ow
i
w
h
e
re
i
=1,
2…,
a.
E
ach
prima
r
y
l
i
ne
ar
ly
d
e
p
e
nde
n
t
r
o
w
i
n
a
gi
ve
n
b
l
oc
k
row
w
i
l
l
b
e
w
r
i
tte
n
as
a
l
i
n
ea
r
com
b
i
n
a
tio
n
o
f
i
ts
p
re
vio
u
s
bl
oc
k
r
o
w
s
.
A
pr
i
m
ar
y
l
i
n
ear
ly
d
e
p
e
n
d
e
n
t
r
o
w
i
s
t
h
e firs
t
l
i
nea
r
l
y
de
pe
nd
e
n
t
r
o
w
i
n
a
g
i
v
en
b
loc
k
r
ow
.
A
t
t
he
end,
t
he
outc
o
m
e
o
f
the
r
o
w
sea
r
ch
in
g
a
l
g
o
ri
thm
w
i
l
l
b
e
t
h
e
c
o
e
f
f
i
c
i
e
nt
s
co
rre
s
po
ndi
n
g
t
o
th
e
q
p
r
i
m
a
r
y
line
a
rl
y de
pen
d
en
t r
o
w
s
:
11
1
1
1
1
2
2
1
2
1
1
22
22
2
11
1
2
2
2
11
0
0
00
0
0
00
1
0
1
1
0
0
0
0
0
10
1
0
0
1
1
0
qq
q
q
q
q
q
q
q
q
ka
a
ka
a
a
a
ka
a
a
a
a
a
(
1
3
)
Su
c
h
t
h
a
t
0
i
kT
.
A
m
i
nim
a
l r
eal
iza
t
i
on
is gi
v
e
n
by:
1
11
1
2
21
22
2
12
0
0
0
0
0
0
qq
q
q
q
q
h
Ab
h
AA
b
AB
D
AA
A
b
h
(
1
4
)
0
1
0
0
0
0
0
0
0
0
0
0
,
00
1
0
00
12
12
ij
ij
ij
ij
ij
i
ij
i
j
ij
j
for
i
j
A
for
i
j
A
aa
a
aa
a
(
1
5
)
1
1
1
1
2
i
i
i
ii
h
h
b
h
(
1
6
)
F
o
r all
i.
The
m
a
trix C i
s c
o
mpu
t
ed
a
s:
12
10
0
0
0
0
0
0
0
00
0
1
0
0
0
0
0
00
0
0
0
0
1
0
0
q
Cq
(
1
7
)
for i=1, 2…,
q,
and
if
0
i
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
D
e
sig
n
o
f
a Mat
l
ab t
o
olb
o
x
a
nd G
U
I
for m
i
nim
a
l re
al
izat
i
ons (K
ar
i
m
Che
r
ifi)
93
3
If
0
i
f
or
s
ome
i
t
h
e
n
t
he
i
t
h
r
ow
i
n
t
h
e
(i-
1
)
fi
r
s
t
bl
oc
k
c
o
l
u
mns
w
il
l
be
c
on
st
itu
t
e
d
fro
m
ij
av
w
here
j is
t
h
e
num
ber
of t
he
bl
o
c
k
c
olum
n
a
nd
1
,
2
,
j
v
.
2.4.
C
o
p
r
ime
Frac
t
i
on
s
G
i
ve
n
a
copri
m
e right
f
ra
ct
ion
G
(
s):
1
RR
Gs
N
s
D
s
(
1
8
)
I
f
the
f
ra
ct
io
n i
s
col
um
n re
duc
ed
t
he
n D
(
s)
and
N
(s)
ca
n be w
ri
tte
n a
s
:
hc
lc
D
sD
H
s
D
L
s
(
1
9
)
lc
N
sN
L
s
(
2
0
)
wher
e
11
1
1
1
0
0
()
()
01
0
uu
up
up
s
ss
Hs
L
s
s
s
s
(
2
1
)
hc
D
,
lc
D
and
lc
N
ar
e
c
onsta
nt
m
a
t
rices.
i
Is the
c
ol
umn
de
gre
e
of D
(
s) for
i=
1
,
2.
.., p.
I
t
w
as
p
roven
[21] t
hat
if a
sys
t
e
m
is
c
on
tro
l
lab
l
e a
n
d ob
ser
v
a
b
l
e t
h
en
:
1
1
()(
)
nr
h
r
IA
B
L
s
D
(
2
2
)
1
rh
c
BD
(2
3
)
A
nd
b
y
def
ini
t
i
on:
1
1
()
(
)
RR
n
Gs
C
I
A
B
N
s
D
s
(
2
4
)
Re
plac
ing
(
2
2
)
and
(23)
r
esults i
n:
R
rh
r
Ds
D
(
2
5
)
()
R
N
sC
L
s
(
2
6
)
W
h
ere:
()
()
rr
Hs
A
L
s
(
2
7
)
Re
plac
ing
(2
4)
i
n
(25):
()
(
)
Rh
c
h
c
r
Ds
D
H
s
D
A
L
s
(
2
8
)
Th
is r
esul
t
s
i
n:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
250
2-
4
7
5
2
I
ndone
s
i
a
n
J
E
le
c
En
g
&
C
o
m
p
S
ci,
V
ol.
1
7
,
N
o
.
2,
F
ebr
u
ar
y
2020
:
929
-
9
4
0
93
4
11
,
,
rh
c
l
c
r
h
c
l
c
AD
D
B
D
C
N
(
29)
r
A
an
d
r
B
ar
e
the
no
n
t
r
i
via
l
r
ow
s
of
A
a
nd
B.
The
resul
t
i
n
g
m
inim
a
l
re
a
liz
ati
o
n is i
n c
o
n
t
r
o
lle
r c
a
non
ica
l
f
o
rm:
a.
A
is
i
n
gene
r
a
l
con
t
r
o
l
l
e
r
c
ano
n
ica
l
f
or
m
w
h
e
r
e
b.
B is i
n
gener
a
l con
t
ro
l
l
er
c
a
n
o
n
ic
a
l
for
m wher
e
c.
CN
l
c
The
c
o
n
t
r
o
l
l
er
c
a
n
o
n
i
c
a
l
f
or
m
w
a
s
obta
i
n
e
d
fr
om
a
r
i
g
ht
c
o
p
r
i
me
fract
ion
.
T
his
is
p
articularly
i
n
t
e
rest
in
g
f
o
r
co
nt
r
o
l
l
e
r
d
e
si
gn
u
sing
pol
e
p
l
a
c
e
m
e
n
t
[
2
2
]
.
If
a
l
ef
t
c
opr
im
e
fr
a
c
tio
n
i
s
u
se
d,
t
he
r
e
s
ult
is
a
m
i
n
ima
l
r
ealiza
t
i
o
n
in
obs
er
ve
r
ca
n
o
n
i
c
a
l
f
or
m
.
B
ot
h
m
e
t
h
o
ds
w
e
r
e
i
m
plem
ente
d
i
n
t
he
m
in
i
m
al
r
ealiza
t
i
o
n
to
o
l
bo
x.
2.
5.
Rea
liza
t
io
n f
r
o
m
Frequency
Do
ma
in
Da
t
a
:
The
fir
s
t
r
e
su
l
t
s
f
o
r
r
e
a
liza
tions
b
a
s
ed
o
n
fr
e
que
nc
y
do
ma
in
d
a
t
a
u
si
n
g
t
he
L
oew
n
er
m
atr
i
x
w
e
r
e
pr
esen
ted
i
n
[
6
]
.
I
n
t
h
i
s
su
bse
c
tio
n
w
e
p
r
e
sent
t
he
m
a
i
n
r
e
s
u
l
t
s
a
nd
a
br
i
e
f
exp
l
a
n
a
t
i
on
of
t
he
p
r
o
ce
dur
e
use
d
to
c
on
trc
u
t
the
n
u
me
rica
l
m
i
nima
l
rea
liz
a
tion.
T
he
r
es
ul
ti
ng
s
y
stem
i
s
a
desc
r
i
p
t
or
s
yste
m
or
a
ls
o
kn
ow
n
a
s
di
ff
er
e
n
tia
l
alg
e
br
a
i
c
e
q
uat
i
on
s
(
D
A
E
).
I
t
has
the
for
m
:
Ex
Ax
B
u
yC
x
D
u
If
E
i
s
i
nver
t
i
b
le,
t
h
e
sta
n
da
rd
s
tate
s
pace
f
or
m
can
b
e
e
a
si
ly
r
e
c
o
v
e
r
e
d
.
I
f
E
i
s
s
i
n
g
u
l
a
r
s
o
m
e
tec
h
n
i
q
u
e
s
e
x
i
st
t
o
tra
n
sf
orm
it
t
o
a
s
ta
nda
r
d
s
ta
te
s
pa
ce
p
r
ov
ide
d
t
ha
t
so
m
e
c
ondi
ti
o
n
s
a
r
e
m
e
t.
M
or
e
de
t
a
ils
c
a
n
be
f
ou
nd
in
[
2
3
-
2
6]
.
G
i
ve
n
r
i
gh
t
fr
e
q
uenc
y
da
ta
:
(
;
r
;
),
1
,
.
..,
ii
i
wi
k
a
n
d
l
ef
t
fr
eq
uenc
y
da
ta
(
;
*
;
v
*
)
,
j
1
,
...,
q
.
jj
j
.
Th
e
g
o
a
l
i
s
to f
i
nd
a
t
ran
s
f
e
r
f
u
n
c
t
i
on
H
(s)
t
h
at
i
nt
erpo
l
a
t
e
s
thi
s
data
suc
h
tha
t:
(
)
,
*
(
)
*
ii
i
j
j
j
Hr
w
H
v
(
30)
The
n
one
c
an
r
egr
o
up
the
da
ta
i
n
m
a
tr
ice
s
s
uch
tha
t
f
or
r
ig
ht
d
at
a:
1
12
12
,
kk
k
mk
k
pk
k
Rr
r
r
Ww
w
w
(
31)
an
d
fo
r
l
e
ft d
ata:
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
D
e
sig
n
o
f
a Mat
l
ab t
o
olb
o
x
a
nd G
U
I
for m
i
nim
a
l re
al
izat
i
ons (K
ar
i
m
Che
r
ifi)
93
5
11
1
*v
*
,
L
,
*v
*
qq
q
p
qm
qq
q
l
MV
l
(
3
2
)
The
n
fr
o
m
t
h
is
da
t
a,
one
can
c
on
trcu
t t
h
e
w
e
ll k
n
o
w
n
L
oe
w
n
er
m
a
trix
qk
L
a
s
f
o
l
l
o
w
:
11
11
1
1
11
1
11
1
L
kk
k
qq
q
k
q
k
qq
k
vr
l
w
vr
l
w
vr
l
w
vr
l
w
(
3
3
)
Th
is L
m
a
t
rix sati
sfies t
h
e
Syl
v
es
ter
equa
ti
o
n
:
LM
L
V
R
L
W
(
3
4
)
The
n
one
a
ls
o nee
d
s to c
o
n
tru
c
t the
shi
f
t
e
d
L
o
ew
ne
r m
a
trix
qk
s
L
s
uch t
h
at
:
11
1
11
1
1
1
1
11
1
11
1
1
L
kk
k
k
s
qq
q
q
q
k
q
k
k
qq
k
vr
l
w
vr
l
w
v
r
lw
v
r
lw
(
3
5
)
This
s
L
m
atrix sat
i
sfies
the S
y
l
v
es
ter equati
on:
ss
L
ML
MVR
L
W
(
3
6
)
The
n
one
c
a
n
c
on
truc
t
a r
e
a
l
iz
a
tio
n:
,
,
,
,
0
s
E
L
A
L
BVC
WD
(
3
7
)
I
f
t
he
num
eric
a
l
m
in
i
m
al
r
ea
li
z
a
tio
n
i
s
t
o
be
c
ompu
te
d
an
d t
h
e
nu
me
ri
ca
l
rank
L
k
,
c
o
mp
u
t
e
t
h
e
rank
reve
al
i
ng
S
V
D
:
**
kk
k
LY
X
Y
X
(
3
8
)
Th
e
n
t
h
e
mi
n
imal
rea
l
i
za
ti
on i
s
g
iv
e
n
by:
*
,
*
,
*
,
,
0
kk
k
s
k
k
k
E
Y
LX
A
Y
L
X
B
Y
V
C
W
X
D
(
3
9
)
The
re
su
lt
in
g
sys
t
em
m
ay
b
e
c
o
mp
lex.
A
p
roce
dure
w
a
s
de
vel
o
ped
t
o
r
ec
over
the
u
n
d
er
lyi
n
g
r
eal
syste
m
.
This proc
e
d
u
re
and
t
h
e
proof
s for
the
r
e
sult
s
g
i
ve
n a
b
o
ve
ca
n
be
fo
un
d i
n
[
2
7
].
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 250
2-
475
2
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
, V
o
l
.
1
7
,
N
o
. 2, F
e
b
ruary
20
20
: 929
-
940
93
6
2.6.
R
e
al
izat
ion
from T
ime
D
o
m
a
in
D
ata:
The
g
o
al
i
n
thi
s
pr
o
ced
ur
e is to
i
n
ter
p
ola
t
e
t
h
e
t
i
m
e
doma
i
n
i
n
p
u
t-
ou
t
p
u
t
da
t
a
by a
desc
ri
pt
or
s
yst
e
m:
Ex
Ax
Bu
y
Cx
D
u
(
4
0
)
T
o
a
c
h
i
e
v
e
t
h
i
s
o
b
j
e
c
t
i
v
e
,
a
m
o
d
i
f
i
e
d
L
o
e
w
n
e
r
c
a
n
b
e
u
s
e
d
[
7
]
.
This
a
lg
ori
t
h
m
cons
tr
ucts
a
m
od
e
l
for
a
n
LTI
s
y
s
tem
d
i
rec
tly
f
r
o
m
a
sing
le
tim
e
d
o
m
a
in
i
n
p
u
t/o
u
t
p
ut
s
na
psh
o
t
w
i
t
hou
t
pri
o
r
know
le
dge
o
f
fre
que
nc
y
resp
ons
e
da
ta.
O
f
c
ourse,
the
mo
r
e
k
now
le
d
g
e
a
b
o
u
t
t
h
e
char
a
c
ter
i
s
t
ics
o
f
t
he
s
yste
m,
t
he
m
o
r
e
ac
cura
t
e
t
he
m
ode
l
w
ill
be.
Th
e i
npu
t
u
and
th
e
o
u
t
p
ut
y
o
f
t
h
e sy
st
em a
re
m
e
a
su
re
d
wi
t
h
re
sp
ec
t
to
time
an
d
rec
o
rded
a
s v
e
cto
r
s
u
a
n
d
y
w
i
t
h
l
e
ngt
h
K
w
h
ic
h
corre
spo
n
d
s
to
t
he
n
um
ber
o
f
s
am
ple
s
t
a
ke
n
.
K
m
i
n
i
s
s
e
l
ec
te
d
a
s
a
qua
rte
r
o
f
K
su
ch
t
h
a
t
to
e
nsu
r
e
th
at
t
h
e
o
u
t
pu
t
s
h
av
e
ente
re
d
a
st
e
a
dy
s
t
a
t
e
after
km
i
n
. n is
a
n i
n
t
e
ger
corr
espo
n
d
in
g
to
t
he
dime
n
s
i
o
n of t
he
m
ode
l
.
The
c
h
o
i
ce
o
f
the
i
n
put
u
,
th
e
i
n
t
e
rp
o
l
a
tio
n
po
i
n
ts
a
nd
the
num
be
r
of
s
a
m
ples
K
c
a
n
b
e
c
h
a
nge
d
to
b
e
st
c
o
rre
sp
ond
t
o
t
h
e
sy
st
e
m
a
t
h
a
nd
i
n
c
l
u
di
ng
w
hi
c
h
ran
ge
o
f
f
r
e
q
u
e
n
c
i
e
s
i
s
o
f
i
m
po
rt
an
ce
.
Sp
ec
i
f
i
c
all
y
,
the
range
of t
h
e p
o
ssi
bl
e
i
n
terp
ola
t
i
o
n fr
eque
nc
i
e
s
tha
t
c
an be
cho
s
e
n is
:
22
(
1
)
,
K
KK
(
4
1
)
The
r
ef
ore,
incre
asi
ng t
h
e
n
u
mber
of sam
p
les K
, incr
ease
s
t
h
e
r
a
nge
o
f po
ss
ib
l
e
freq
u
en
c
i
e
s
.
W
e
u
s
e
d
a
m
o
d
i
f
i
e
d
v
e
r
s
i
o
n
o
f
t
h
a
t
a
l
g
o
r
i
t
h
m
i
n
o
u
r
i
m
p
l
e
m
e
n
t
a
t
ion
t
o
m
e
e
t
o
u
r
re
qu
irem
ents.
F
o
r
m
o
re
d
etai
ls o
n the
al
g
o
ri
thm
i
t
sel
f
a
n
d
i
ts pro
of, ple
ase
refer
t
o
[
7].
3.
RESEARCH
M
ETH
O
D
Th
ere
exi
s
t
di
ff
ere
n
t
alg
o
r
i
t
hms
ea
c
h
w
i
t
h
it
s
adv
a
n
t
ag
e
s
a
n
d
d
r
a
w
b
ac
k
s
.
The
be
st
m
et
ho
d
depe
n
d
s
on
e
a
c
h
s
pec
i
f
i
c
a
p
p
lic
at
io
n.
T
h
i
s
req
u
ires
h
avi
n
g
a
to
ol
t
o
be
a
b
l
e
t
o
c
o
m
p
a
r
e
b
e
t
w
e
e
n
t
h
e
d
i
f
f
e
r
e
n
t
m
e
t
h
o
d
s
and
c
h
oose the
m
o
st
a
ppr
o
p
ri
ate
m
e
t
h
o
d
f
or
t
ha
t
s
p
e
c
i
f
ic
a
p
p
l
i
c
a
t
io
n
.
T
his
t
o
o
l
(
or
c
om
mon
l
y
cal
le
d
too
l
b
o
x
)
is
t
he
m
i
n
i
m
al
r
e
a
li
z
a
t
i
o
n
t
o
ol
b
ox
im
p
l
e
m
e
n
te
d
i
n
M
A
T
LA
B
an
d
pr
e
s
en
t
e
d
i
n
t
hi
s
pa
p
e
r.
M
ATLAB
wa
s
cho
s
en
b
eca
us
e
i
t
i
s
use
d
b
y
a
l
o
t
o
f
r
es
e
a
rc
hers
a
n
d
e
ngi
ne
ers
[
2
8
,
29].
A
l
l
th
e
m
e
tho
d
s
pre
s
e
n
te
d
i
n
S
e
ctio
n
2
w
e
r
e
i
m
p
lem
e
n
t
e
d
i
n
func
tio
ns
:
G
i
lber
t
Me
t
h
o
d
,
K
a
lm
an
d
ec
om
pos
it
io
n,
H
ank
e
l
an
d
S
V
D
,
H
anke
l
and
row
sear
chi
n
g,
L
eft
co
p
r
im
e
fra
c
tio
n
(
L
CF
),
R
i
g
ht
c
opr
im
e
f
ra
ctio
n
(RCF
),
I
nt
e
rfe
rq
(
from
f
reque
nc
y
domain
data)
, Inter
time
(from
time dom
ain data).
Al
l
t
h
e
p
r
og
ra
m
m
ed
f
un
c
t
i
o
ns
a
re
g
roup
e
d
i
n
a
too
l
bo
x
fo
r
m
i
n
i
m
al
r
ea
l
i
z
a
tio
n.
T
his
to
ol
bo
x
c
a
n
b
e
ea
si
ly use
d
us
ing
the
gra
p
h
i
c
a
l use
r
in
t
erfac
e
(G
U
I)
sho
w
n
in F
i
gur
e 1.
The
G
U
I
i
s
di
vi
de
d
i
n
t
o
t
w
o
m
a
i
n
sec
tio
ns
:
T
h
e
firs
t
o
n
e
o
n
t
he
t
op
l
e
f
t
is
t
he
“
in
t
e
rp
ola
t
ion
a
n
d
minim
a
l
r
eal
iz
a
t
i
o
n”
s
ec
tio
n
w
h
ere
on
e
can
o
b
t
a
i
n
a
m
i
ni
m
a
l
re
a
l
i
z
a
t
i
o
n
fr
om
f
r
e
que
nc
y
or
t
im
e
d
o
m
a
i
n
d
ata
by
pressi
n
g
t
h
e
a
ppro
p
ria
t
e
bu
t
t
o
n
.
In
t
he
s
ec
o
nd
sec
t
io
n
,
one
c
a
n
com
p
u
t
e
a
m
i
n
i
m
a
l
re
alza
it
i
on
from
a
trans
f
e
r
f
u
n
c
t
i
on
(
T
F
)
.
S
i
x
b
u
tt
on
s
corre
sp
o
n
d
i
n
g
t
o
s
i
x
m
i
nim
a
l
re
aliz
ati
o
n
me
t
h
o
d
s
are
a
v
ai
lab
l
e.
C
ho
os
in
g
a
spec
ific
m
et
ho
d
w
i
ll
dis
p
la
y
the
res
u
l
t
o
f
t
h
a
t
m
eth
o
d
d
i
r
ec
t
l
y
on
the
sam
e
v
iew
(
F
ig
ure
1).
C
h
o
o
s
i
ng
ano
t
her
m
e
th
o
d
w
i
ll
dis
p
la
y
the
r
e
su
l
t
s
of
t
hat
m
e
tho
d
d
i
s
car
di
ng
t
he
p
re
vious
r
e
s
u
l
t
s
.
F
i
na
lly
o
n
th
e
top
rig
h
t,
i
n
t
h
e
o
p
t
i
o
n
s
s
e
c
t
i
o
n,
one
c
a
n
l
oad
data
,
sa
ve
t
he
r
e
s
u
lts
t
o
a
m
a
t
l
a
b
f
i
l
e
or
c
om
pa
re
t
he
d
iffe
ren
t
minim
a
l
r
ealiz
a
t
i
o
n
me
t
h
od
s
avai
lab
l
e
w
i
th
a
b
o
d
e
p
l
o
t
.
U
nde
r
t
he
se
s
e
c
t
i
o
n
s,
w
e
ha
ve
f
i
v
e
te
x
t
f
i
e
lds
di
sp
la
yi
n
g
t
he
m
a
t
rices
o
f
t
h
e
m
i
n
i
m
a
l
re
a
l
iz
a
t
ion.
I
n
the
nex
t
s
ec
ti
on
,
th
e
GUI
i
s
u
s
ed
t
o
co
mp
ut
e
th
e
m
i
nim
a
l re
aliz
ati
o
n of pra
c
t
i
c
al pr
oble
m
s.
4.
RESULT
S
A
N
D
DISCU
SSIO
N
I
n
o
rde
r
t
o
te
st
t
he
m
e
t
h
o
d
s
f
or
t
he
m
i
n
im
al
r
ea
l
i
z
a
tio
n
from
a
t
ransf
e
r
f
u
n
c
t
i
on
,
a
d
i
st
il
l
a
ti
on
col
u
m
n
s
ys
t
e
m
is
u
sed [
30].
The
m
a
t
r
i
x
t
rans
fe
r func
t
i
o
n
i
s
as
follow:
32
32
32
32
2.
581
6
.7
46
5.
949
2
6
.
64
4
5
4.
087
4
5
2.
622
5
4
.9
59.
48
4
4
5
4
5
ss
s
s
ssss
Gs
s
s
s
ssss
s
(
4
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
ndone
s
i
a
n
J
E
le
c
En
g
&
C
o
m
p
S
ci
I
S
S
N
:
2502-
47
52
Desig
n
o
f
a Matl
ab to
ol
b
o
x a
n
d GUI for mini
m
a
l
re
al
i
z
at
i
ons (K
arim C
h
e
r
ifi)
93
7
En
ter
i
n
g
t
h
i
s
ma
t
r
i
x
t
r
a
n
s
fer
func
t
i
o
n
i
n
t
o
t
h
e
G
U
I
a
nd
c
hoos
i
n
g
fo
r
examp
l
e
left
c
o
p
rime
fract
ion
r
e
sults
i
n
t
h
e
m
i
nima
l
st
a
t
e spa
ce
r
e
ali
z
a
t
io
n sh
ow
n i
n
F
i
g
u
r
e
1.
T
hi
s
ca
n
be
d
o
n
e
f
o
r
all
the
ot
he
r
m
e
thod
s
b
y
se
l
e
c
t
i
ng
the
a
ppr
opr
ia
te
b
u
t
t
on.
Usi
n
g
t
h
e
bu
tto
n
“
M
e
t
h
o
d
s
’
co
mp
ari
s
o
n
”
,
th
e
me
t
hod
s
can
b
e
co
mp
ar
ed
i
n
ter
m
s
of
t
h
e
ir
B
ode
p
l
o
t
wh
ere
t
h
e
t
r
ansf
er
f
u
n
c
ti
on
i
s
pl
ott
e
d
in
d
ot
s
a
n
d
th
e
ot
h
e
r
me
t
h
od
s
as
c
on
t
i
n
uou
s
l
i
n
e
.
F
o
r
t
h
e
e
x
a
m
pl
e
u
s
e
d
,
the
r
e
su
lt
i
ng
Bode
p
l
o
t
i
s
s
ho
w
n
i
n
F
i
g
u
r
e
2
.
F
i
gur
e
1.
M
i
n
i
m
a
l
r
e
a
lizat
io
n
of
a
d
ist
i
lla
ti
o
n
c
ol
umn
usi
n
g
th
e p
r
es
e
n
t
e
d GU
I
F
i
gur
e
2.
B
o
d
e
pl
o
t
c
ompa
r
i
s
on
o
f
t
he
T
F
(
dot
te
d
blue
)
a
n
d
stat
e
s
p
ac
e fo
rm (l
i
n
e
red
)
The
prev
i
ous
e
xam
p
le
a
llow
e
d
us
t
o
tes
t
t
he
c
a
p
a
b
i
l
ities
o
f
t
h
e
G
UI.
Af
ter
f
e
w
click
s
,
a
min
i
mal
r
ealiza
t
i
o
n c
a
n
b
e ob
ta
ine
d
u
s
i
ng
the
c
h
o
se
n
m
i
n
i
m
a
l rea
liz
a
tio
n me
tho
d
.
Th
is a
l
s
o
perm
itte
d
to
de
t
er
mi
ne
t
he
Mc
Mi
l
l
ia
n
de
g
r
ee
.
Sinc
e
the
siz
e
o
f
th
e
ma
t
r
ix
A
i
s
c
l
ea
rl
y
4
t
he
n
the
Mc
M
ill
ian
de
gr
ee
is
4
.
A
l
so,
bas
e
d
o
n
t
h
e
co
mp
ari
s
on
o
f
t
h
e
me
thod
s,
t
h
e
B
od
e
p
l
ot
o
f
th
e
o
r
i
g
in
al
s
y
s
t
em
p
er
fec
t
l
y
s
u
p
er
po
se
s
with
t
he
r
e
s
u
lti
ng
m
e
tho
d
s.
T
his
pr
o
v
es
t
ha
t
the
s
e
m
i
nima
l
r
e
ali
z
a
t
i
ons
a
r
e
i
n
d
ee
d
ex
a
ct.
Since
the
a
l
g
o
r
i
t
hm
s
ha
ve
s
i
m
il
a
r
tim
e
co
m
p
lex
i
tie
s
be
twe
e
n
ran
gi
n
g
b
etw
e
e
n
3
n
and
4
n
,
the
e
n
g
i
ne
er
o
r
the
r
e
sea
r
che
r
w
il
l
gen
e
rall
y
cho
o
se
t
he
m
eth
o
d
b
ase
d
o
n
th
e
usef
u
l
ne
ss
o
f
the
c
o
n
f
ig
ur
a
t
i
o
n
of
t
he
s
ta
te
s
pa
c
e
r
epr
e
sentat
ion.
I
n
o
r
d
e
r
t
o
te
s
t
t
he
L
oe
w
n
er
m
eth
o
d
g
i
ven
fr
e
q
uenc
y
d
o
m
a
i
n
da
ta
,
we
u
se
t
he
b
e
a
m
exam
p
l
e
of
or
d
e
r
3
4
8
f
r
o
m
[
31]
.
T
he
L
oe
w
n
er
m
eth
o
d
a
l
l
o
w
s
t
o
c
hoos
e
t
h
e
n
u
m
er
ica
l
m
i
n
i
a
l
or
de
r
base
d
on
t
he
d
e
cay
o
f
si
ng
u
l
a
r
v
al
ues
.
I
n
or
der
to
c
a
p
tur
e
t
he
b
eha
v
i
o
ur
o
f
t
h
e
sy
ste
m
,
t
he
o
r
d
er
i
s
chose
n
t
o
b
e
14.
T
he
r
esul
t
s
a
r
e
show
n
i
n
F
i
gur
e
3.
T
he
o
r
i
g
i
n
a
l
and
r
e
su
lti
n
g
b
o
d
e
p
l
o
t
s
ar
e
de
p
i
c
t
ed
in
Figu
re
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 250
2-
475
2
Ind
ones
i
a
n
J
E
lec
En
g &
Co
m
p
S
c
i
, V
o
l
.
1
7
,
N
o
. 2, F
e
b
ruary
20
20
: 929
-
940
93
8
F
i
nal
l
y
i
n
o
rde
r
t
o
te
st
t
he
t
i
m
e
dom
a
i
n
L
o
e
w
ner
m
e
th
od,
w
e
co
n
s
i
der
P
e
nzl
'
s
t
i
m
e
-c
o
n
t
i
n
uo
us
LTI
syste
m
i
n
t
r
o
duc
ed
i
n
[32]
,
w
h
ich
i
s
i
nve
sti
g
a
t
e
d
i
n
the
c
o
n
t
e
x
t
o
f
the
L
o
e
w
ner
a
pproac
h
.
T
h
e
d
a
ta
g
ive
n
i
s
in
form
o
f
i
n
pu
t
-
ou
tpu
t
t
i
m
e
d
o
m
ain
data.
U
s
ing
t
h
e
t
h
e
bu
t
t
o
n
“
ti
m
e
d
om
ain
in
ter
p
ol
a
t
i
on”.
We
o
b
t
a
i
n
the
sy
st
em
s
ho
wn
i
n
Figu
re
4
.
A
c
o
m
p
a
r
i
s
o
n
b
e
t
w
ee
n
t
h
e
bode
p
lot
s
o
f
the
ori
g
i
n
a
l
s
y
s
te
m
and
the
i
n
t
e
rpo
l
ate
d
syste
m
i
n
desc
r
i
p
t
or
f
orm
a
r
e
show
n in F
igur
e 5.
F
i
gure
3.
R
e
s
ul
t of t
he
i
nter
pola
t
i
on o
f
t
he
b
e
a
m
e
x
am
pl
e
a
s
s
h
ow
n i
n
t
he
G
U
I
F
i
gure
4. Resu
l
t of
t
he P
enz
l
e
xam
p
le’s
i
n
t
e
r
po
l
a
tio
n
as sho
w
n
i
n
t
h
e
GUI
Evaluation Warning : The document was created with Spire.PDF for Python.