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,
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Ad
ap
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tech
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1
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3
]
.
So
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s
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[
4
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5
]
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[
6
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,
a
n
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s
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[
7
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8
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,
h
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b
y
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[
9
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1
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1
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.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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T
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KOM
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KA
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elec
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p
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l Co
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,
Vo
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18
,
No
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6
,
Dec
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r
2
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0
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3
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7
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79
3074
T
h
e
r
ec
u
r
s
iv
e
i
n
v
er
s
e
(
R
I
)
a
lg
o
r
ith
m
[
1
5
]
h
as
b
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n
p
r
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p
o
s
ed
to
o
v
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r
co
m
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s
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m
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s
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t
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as
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ee
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s
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alg
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m
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o
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m
s
s
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n
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ican
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b
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n
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s
s
m
ea
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s
q
u
ar
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o
r
(
MSE
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[
1
6
]
,
in
v
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io
u
s
s
ettin
g
s
,
with
less
co
m
p
u
tatio
n
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d
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u
p
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ate
eq
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n
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f
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R
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a
lg
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[
1
7
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n
d
-
o
r
d
er
esti
m
atio
n
o
f
t
h
e
co
r
r
elatio
n
s
.
I
n
t
h
i
s
p
a
p
e
r
,
w
e
p
r
o
p
o
s
e
t
h
e
u
s
e
o
f
d
i
s
c
r
e
t
e
w
a
v
e
l
e
t
t
r
a
n
s
f
o
r
m
(
D
W
T
)
t
o
i
m
p
r
o
v
e
t
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
t
h
e
s
e
c
o
n
d
-
o
r
d
e
r
R
I
a
l
g
o
r
i
t
h
m
.
T
h
is
d
o
m
ain
-
b
ased
tr
an
s
f
o
r
m
a
tio
n
g
u
r
en
tees
th
e
r
e
d
u
ctio
n
o
f
th
e
s
elf
-
co
r
r
elatio
n
o
f
th
e
in
p
u
t
s
ig
n
al
th
at,
in
tu
r
n
,
h
elp
s
to
o
v
er
co
m
es
th
e
lo
w
co
n
v
er
g
e
n
ce
r
ate
o
f
th
e
s
ec
o
n
d
-
or
d
er
R
I
alg
o
r
ith
m
.
Hen
ce
,
we
u
s
e
th
e
ad
v
an
ta
g
es
o
f
th
e
R
I
alg
o
r
ith
m
co
m
p
a
r
ed
to
th
e
R
L
S
alg
o
r
ith
m
an
d
b
y
th
e
v
ir
tu
e
o
f
DW
T
,
th
e
co
n
v
er
g
en
ce
r
ate
is
in
cr
ea
s
ed
.
T
h
e
r
est
o
f
th
e
p
ap
er
ca
n
b
e
d
escr
ied
as
f
o
llo
ws:
i
n
s
ec
tio
n
2
,
DW
T
i
s
r
ev
iewe
d
.
I
n
s
ec
tio
n
3
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
in
tr
o
d
u
ce
d
.
I
n
s
ec
tio
n
4
,
s
im
u
latio
n
r
esu
lts
th
at
co
m
p
ar
e
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
t
o
th
o
s
e
o
f
th
e
R
I
,
s
ec
o
n
d
-
o
r
d
er
R
I
an
d
R
L
S
alg
o
r
ith
m
s
in
d
if
f
e
r
en
t
Gau
s
s
ian
an
d
im
p
u
ls
iv
e
n
o
is
e
en
v
ir
o
n
m
en
ts
in
a
n
o
is
e
ca
n
ce
llatio
n
s
ettin
g
ar
e
p
r
esen
ted
.
F
in
ally
,
co
n
clu
s
io
n
s
ar
e
d
r
awn
i
n
s
ec
tio
n
5
.
2.
DIS
CR
E
T
E
WA
VE
L
E
T
T
R
ANSF
O
RM
(
DW
T
)
Mu
lti
-
r
eso
lu
ti
o
n
d
ec
o
m
p
o
s
iti
o
n
th
eo
r
y
th
at
was
d
e
v
elo
p
e
d
b
y
Ma
llat
[
1
8
]
,
g
iv
es
s
ca
le
-
in
v
ar
ian
t
in
ter
p
r
etatio
n
o
f
s
ig
n
als
an
d
im
ag
es.
W
av
elet
tr
an
s
f
o
r
m
is
co
n
s
id
er
ed
to
b
e
a
p
o
wer
f
u
l
ap
p
r
o
ac
h
o
f
m
u
lti
-
r
eso
lu
tio
n
a
n
aly
s
is
to
an
aly
s
e
s
ig
n
als th
at
p
o
s
s
ess
b
o
th
lo
w
an
d
h
ig
h
-
f
r
eq
u
en
c
y
co
m
p
o
n
en
ts
.
I
t
h
as b
ee
n
d
ev
elo
p
e
d
to
s
o
lv
e
th
e
tim
e
-
f
r
eq
u
en
c
y
r
eso
lu
tio
n
p
r
o
b
lem
in
s
h
o
r
t
tim
e
f
o
u
r
ier
tr
an
s
f
o
r
m
(
STFT
)
[
1
9
-
2
1
]
.
DW
T
d
ec
o
m
p
o
s
es
th
e
s
ig
n
al
i
n
to
o
r
th
o
g
o
n
al
s
et
o
f
wav
elets
u
s
in
g
f
ilter
b
an
k
s
.
T
h
e
o
u
tp
u
t
o
f
th
e
f
ilter
b
an
k
s
is
a
g
r
o
u
p
o
f
c
o
ef
f
icien
ts
u
s
ed
to
ca
lcu
late
th
e
d
etails
an
d
ap
p
r
o
x
im
atio
n
s
o
f
th
e
s
ig
n
al.
Acc
o
r
d
in
g
ly
,
th
e
o
r
ig
in
al
s
ig
n
al
ca
n
b
e
r
ec
o
n
s
tr
u
cted
f
r
o
m
th
e
s
ca
lin
g
an
d
th
e
wav
elet
co
ef
f
icien
ts
.
A
s
t
r
u
ctu
r
e
o
f
d
is
cr
ete
wav
elet
tr
an
s
f
o
r
m
a
d
ap
tiv
e
f
il
ter
(
DW
T
AF)
is
s
h
o
wn
in
Fig
u
r
e
1.
Acc
o
r
d
in
g
to
DW
T
th
eo
r
y
,
r
ec
o
n
s
tr
u
ctio
n
o
f
th
e
o
r
ig
in
a
l
s
ig
n
al
x
(
)
ca
n
b
e
p
er
f
o
r
m
ed
u
s
in
g
th
e
f
o
llo
win
g
f
in
ite
s
u
m
:
x
(
)
=
∑
∑
,
,
(
)
∈
−
1
=
0
(
1
)
wh
er
e
,
ar
e
t
h
e
wav
elet
co
ef
f
icien
ts
an
d
,
(
)
ar
e
th
e
wav
elet
f
u
n
ctio
n
s
th
at
f
o
r
m
an
o
r
th
o
g
o
n
al
b
asis
.
T
h
e
p
u
r
p
o
s
e
o
f
DW
T
ad
ap
tiv
e
f
ilter
is
to
g
en
er
ate
t
h
e
d
is
cr
ete
r
ec
o
n
s
tr
u
ctio
n
o
f
x
(
)
wh
ich
is
th
e
p
r
o
jecte
d
d
is
cr
e
te
f
o
r
m
o
f
x
(
)
in
wav
elet
s
u
b
s
p
ac
e
.
x
(
)
is
g
iv
en
b
y
:
x
(
)
=
∑
,
,
(
)
∈
(
2
)
if
v
(
)
is
th
e
ap
p
r
o
x
im
atio
n
o
f
p
r
o
j
ec
ted
x
(
)
,
th
en
v
(
)
=
∑
̂
,
,
(
)
∈
(
3
)
wh
er
e
̂
,
is
th
e
d
is
cr
ete
ap
p
r
o
x
im
atio
n
o
f
th
e
wav
elet
co
ef
f
icie
n
ts
,
,
̂
,
=
∑
x
(
)
̂
,
(
)
(
4
)
wh
er
e
̂
,
(
)
r
ep
r
esen
t
s
th
e
d
is
cr
ete
ap
p
r
o
x
im
atio
n
o
f
th
e
wav
elet
f
u
n
ctio
n
s
,
(
)
g
iv
en
th
at,
ℎ
(
,
)
=
∑
̂
,
(
)
,
(
)
∈
(
5
)
No
w,
s
u
b
s
titu
tin
g
(
4
)
a
n
d
(
5
)
i
n
(
3
)
r
esu
lts
in
v
(
)
=
∑
x
(
)
ℎ
(
,
)
(
6
)
I
n
(
6
)
is
s
im
p
ly
th
e
d
is
cr
ete
co
n
v
o
l
u
tio
n
o
f
th
e
in
p
u
t
s
ig
n
al
x
(
)
an
d
th
e
f
ilter
co
ef
f
icien
ts
ℎ
(
,
)
.
Usi
n
g
o
r
th
o
g
o
n
ality
an
d
tim
e
-
s
tead
in
ess
,
f
ilter
in
d
ices c
an
b
e
r
ewr
it
ten
as:
ℎ
(
,
)
=
ℎ
(
−
)
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
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KA
T
elec
o
m
m
u
n
C
o
m
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t E
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n
tr
o
l
Dis
crete
w
a
ve
let
tr
a
n
s
fo
r
m
r
e
cu
r
s
ive
in
ve
r
s
e
a
lg
o
r
ith
m
u
s
in
g
s
ec
o
n
d
-
o
r
d
e
r
…
(
Mo
h
a
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d
S
h
u
kri S
a
lma
n
)
3075
T
h
er
ef
o
r
e,
v
(
)
=
∑
x
(
)
ℎ
(
−
)
(
8
)
3.
DWT
S
E
CO
ND
-
O
RD
E
R
R
E
CURS
I
V
E
I
NV
E
RS
E
A
L
G
O
RIT
H
M
Fo
llo
win
g
th
e
s
tr
u
ctu
r
e
s
h
o
w
n
in
Fig
u
r
e
1
a
n
d
u
s
in
g
th
e
s
am
e
n
o
tatio
n
u
s
ed
i
n
s
ec
tio
n
2
,
t
h
e
u
p
d
ated
eq
u
atio
n
o
f
th
e
s
ec
o
n
d
-
o
r
d
er
R
I
alg
o
r
ith
m
[
1
7
]
ca
n
b
e
wr
itt
en
as:
C
(
+
1
)
=
⌈
I
−
(
)
R
(
)
⌉
C
(
)
+
(
)
p
(
)
(
9
)
wh
er
e
is
th
e
tim
e
p
ar
am
eter
(
=
1
,
2
,
.
.
.
)
,
C
(
)
r
ep
r
esen
ts
th
e
f
ilter
weig
h
t
v
ec
to
r
ca
lcu
lated
at
tim
e
,
v
(
)
=
Wx
(
)
r
ep
r
esen
ts
th
e
tr
an
s
f
o
r
m
ed
in
p
u
t
s
ig
n
al
an
d
W
r
ep
r
esen
ts
th
e
wav
elet
tr
an
s
f
o
r
m
m
atr
i
x
o
f
s
ize
×
.
(
)
r
ep
r
esen
ts
th
e
v
a
r
iab
le
s
tep
-
s
ize
[
1
6
]
wh
ich
s
atis
f
ies
th
e
co
n
v
e
r
g
en
ce
c
r
iter
io
n
[
9
]
,
th
e
au
to
co
r
r
elatio
n
m
atr
ix
R
(
)
r
ep
r
esen
ts
th
e
esti
m
ate
o
f
t
h
e
tap
-
i
n
p
u
t
v
ec
to
r
,
an
d
p
(
)
r
ep
r
esen
ts
th
e
esti
m
ate
o
f
th
e
cr
o
s
s
-
co
r
r
elatio
n
v
ec
to
r
b
etwe
en
th
e
d
esire
d
o
u
tp
u
t
s
ig
n
al
(
)
an
d
th
e
tap
-
in
p
u
t
v
ec
t
o
r
esti
m
ated
,
r
ec
u
r
s
iv
ely
,
as:
R
(
)
=
1
R
(
−
1
)
+
2
R
(
−
2
)
+
v
(
)
v
(
)
(
1
0
)
p
(
)
=
1
p
(
−
1
)
+
2
p
(
−
2
)
+
(
)
v
(
)
(
1
1
)
w
h
e
r
e
1
a
n
d
2
a
r
e
p
o
s
i
ti
v
e
c
o
n
s
tan
t
s
.
C
h
o
o
s
i
n
g
t
h
e
c
o
e
f
f
i
ci
e
n
ts
in
(
1
0
)
a
n
d
(
1
1
)
t
o
b
e
e
q
u
a
l
,
i
.
e
.
1
=
2
=
1
2
,
will
g
u
r
en
tee
th
at
th
e
T
h
e
n
u
m
b
er
o
f
m
u
ltip
licatio
n
s
in
th
e
s
ec
o
n
d
o
r
d
e
r
u
p
d
ate
eq
u
atio
n
s
will
b
e
th
e
s
am
e
a
s
th
e
f
ir
s
t o
r
d
er
u
p
d
ate
eq
u
atio
n
s
[
1
6
]
.
B
y
tak
i
n
g
th
e
ex
p
ec
tatio
n
o
f
(
1
0
)
,
th
e
n
e
w
eq
u
atio
n
ca
n
b
e
wr
itten
as:
R
̅
(
)
=
1
2
R
̅
(
−
1
)
+
1
2
R
̅
(
−
2
)
+
(
1
2
)
wh
er
e
R
vv
=
{
v
(
)
v
(
)
}
an
d
R
̅
(
)
=
{
R
(
)
}
.
T
h
e
p
o
les o
f
th
e
s
y
s
tem
in
(
1
2
)
ca
n
b
e
ca
lc
u
taed
u
s
in
g
:
1
=
1
4
(
−
√
2
+
8
)
2
=
1
4
(
+
√
2
+
8
)
(
1
3
)
wh
ich
h
av
e
m
ag
n
itu
d
es
less
th
an
u
n
ity
if
<
1
.
B
y
s
o
lv
in
g
(
1
2
)
u
s
in
g
th
e
in
itial
co
n
d
itio
n
s
R
̅
(
−
2
)
=
R
̅
(
−
1
)
=
R
̅
(
0
)
=
0
,
it r
esu
lts
in
,
R
̅
(
)
=
(
1
−
1
+
1
1
+
2
2
)
R
vv
(
1
4
)
wh
er
e
,
1
=
−
2
(
1
−
)
(
2
−
1
)
,
2
=
−
1
(
1
−
)
(
2
−
1
)
.
(
1
5
)
u
s
in
g
,
(
)
=
1
−
1
+
1
1
+
2
2
(
1
6
)
th
en
,
in
th
e
DW
T
s
ec
o
n
d
-
o
r
d
e
r
R
I
alg
o
r
ith
m
,
th
e
v
ar
ia
b
le
s
tep
-
s
ize
is
s
elec
ted
as:
(
)
=
0
(
)
,
(1
7)
wh
er
e
0
is
a
co
n
s
tan
t [
1
6
]
s
elec
ted
as:
0
<
=
2
(
1
−
)
R
vv
wh
er
e
is
th
e
m
ax
im
u
m
eig
en
v
alu
e
o
f
R
vv
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
ommun
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
0
7
3
-
30
79
3076
T
h
e
ad
ap
tiv
e
esti
m
atio
n
e
r
r
o
r
ca
n
b
e
d
e
f
in
ed
as:
(
)
=
(
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−
(
)
(
1
8
)
wh
er
e
,
(
)
=
v
(
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C
(
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(
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(
)
=
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(
)
ℎ
(
−
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(
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.
−
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−
1
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1
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T
h
e
m
a
j
o
r
a
d
v
a
n
t
a
g
e
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f
R
I
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b
a
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d
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l
g
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r
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t
h
m
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h
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a
u
t
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c
o
r
r
e
l
a
t
i
o
n
m
a
t
r
i
x
[
1
6
]
.
S
u
c
h
a
n
u
p
d
a
t
e
o
f
t
h
e
i
n
v
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e
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o
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r
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c
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l
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n
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t
a
b
i
l
i
t
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e
s
i
n
R
L
S
-
b
a
s
e
d
a
l
g
o
r
i
t
h
m
s
[
22
-
2
4
]
.
F
o
r
t
u
n
a
t
e
l
y
,
t
h
i
s
i
s
n
o
t
t
h
e
c
a
s
e
f
o
r
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h
e
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I
a
l
g
o
r
i
t
h
m
a
n
d
i
t
s
v
a
r
i
a
n
t
s
.
Fig
u
r
e
1
.
Stru
ctu
r
e
o
f
d
is
cr
ete
wav
elet
tr
an
s
f
o
r
m
tr
a
n
s
v
er
s
al
ad
ap
tiv
e
f
ilter
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
h
e
p
r
o
p
o
s
ed
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o
r
ith
m
is
c
o
m
p
ar
ed
to
th
e
R
I
,
s
ec
o
n
d
-
o
r
d
er
R
I
an
d
R
L
S
alg
o
r
ith
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s
in
th
e
n
o
is
e
ca
n
ce
llatio
n
s
ettin
g
as
s
h
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wn
in
Fig
u
r
e
2
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te
r
m
s
o
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co
n
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r
g
en
ce
r
ate
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d
m
ea
n
s
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u
ar
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r
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r
(
MSE
)
.
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n
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n
d
u
cte
d
ex
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eir
m
en
ts
,
f
ilter
l
en
g
th
f
o
r
all
im
p
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etd
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o
r
ith
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s
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eq
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R
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h
e
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i
g
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g
en
er
at
ed
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s
in
g
:
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=
1
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79
(
−
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−
1
.
85
(
−
2
)
+
1
.
27
(
−
3
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−
0
.
41
(
−
4
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0
(
)
,
wh
er
e
0
(
)
is
a
Gau
s
s
ian
p
r
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ce
s
s
with
ze
r
o
m
ea
n
an
d
v
ar
ian
ce
2
=
0
.
15
.
T
h
e
s
im
u
latio
n
r
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lts
f
o
r
Gau
s
s
ian
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d
im
p
u
ls
iv
e
n
o
is
e
ar
e
o
b
tain
ed
b
y
av
er
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i
n
g
1000
in
d
ep
en
d
e
n
t
r
u
n
s
.
Fo
r
all
ex
p
er
im
en
ts
,
th
e
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o
r
ith
m
s
ar
e
s
im
u
lated
u
s
in
g
th
e
p
ar
am
eter
s
in
T
ab
le
1
.
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
o
f
a
d
ap
tiv
e
n
o
is
e
ca
n
ce
llatio
n
c
o
n
f
i
g
u
r
atio
n
T
ab
le
1
.
Par
am
eter
s
u
s
ed
f
o
r
s
im
u
latin
g
th
e
p
r
o
p
o
s
ed
, 2
nd
o
r
d
er
R
I
,
R
I
an
d
R
L
S a
lg
o
r
it
h
m
s
in
all
ex
p
er
im
en
ts
A
l
g
o
r
i
t
h
m
0
P
r
o
p
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se
d
0
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1
0
.
9
9
2
nd
o
r
d
e
r
R
I
0
.
1
0
.
9
9
RI
0
.
0
0
0
5
0
.
9
9
R
LS
-
0
.
9
9
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
Dis
crete
w
a
ve
let
tr
a
n
s
fo
r
m
r
e
cu
r
s
ive
in
ve
r
s
e
a
lg
o
r
ith
m
u
s
in
g
s
ec
o
n
d
-
o
r
d
e
r
…
(
Mo
h
a
mma
d
S
h
u
kri S
a
lma
n
)
3077
4
.
1
.
Addi
t
iv
e
G
a
us
s
ia
n no
is
e
I
n
o
r
d
e
r
t
o
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e
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p
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p
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d
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,
t
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w
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A
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G
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C
G
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s
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e
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(
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w
h
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r
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n
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4
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e
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(
M
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=
−
30
dB
)
o
f
a
l
l
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l
g
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r
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t
h
m
s
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(
a
p
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m
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y
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350
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n
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t
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r
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t
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f
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r
t
h
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n
t
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R
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2
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r
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a
n
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a
l
g
o
r
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t
h
m
s
,
r
e
s
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t
i
v
e
l
y
)
.
4
.
2
.
Addi
t
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im
pu
ls
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Man
-
m
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e
n
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s
u
ch
as
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n
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er
wate
r
ac
o
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s
tic
n
o
is
e,
ad
d
e
d
to
th
e
r
ec
ei
v
ed
s
ig
n
al
m
ak
es
it
h
ar
d
to
m
o
d
el
th
e
s
ig
n
al
u
s
in
g
Gau
s
s
ian
d
is
tr
ib
u
tio
n
.
T
o
o
v
er
co
m
e
th
is
p
r
o
b
lem
,
s
u
ch
ty
p
e
o
f
n
o
is
e
is
b
eliev
ed
to
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etter
m
o
d
elled
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s
in
g
a
Gau
s
s
ian
m
ix
tu
r
e
m
o
d
el.
T
h
e
im
p
u
l
s
iv
e
n
o
is
e
p
r
o
ce
s
s
is
g
en
e
r
ated
b
y
th
e
p
r
o
b
a
b
ilit
y
d
en
s
ity
f
u
n
ct
io
n
[
2
5
]
.
=
(
1
−
)
(
0
,
2
)
+
(
0
,
2
)
with
v
a
r
ian
ce
2
=
(
1
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2
+
2
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er
e
(
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is
a
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s
s
ian
p
r
o
b
a
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ilit
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en
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i
ty
f
u
n
ctio
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r
o
m
ea
n
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d
v
ar
ian
ce
2
th
at
r
e
p
r
esen
ts
th
e
n
o
m
in
al
b
ac
k
g
r
o
u
n
d
n
o
is
e.
(
0
,
2
)
r
ep
r
esen
ts
t
h
e
im
p
u
ls
iv
e
co
m
p
o
n
e
n
t
o
f
th
e
n
o
is
e
m
o
d
el,
wh
er
e
is
th
e
p
r
o
b
ab
ilit
y
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d
≥
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is
th
e
s
tr
en
g
th
o
f
t
h
e
im
p
u
ls
iv
e
n
o
is
e
co
m
p
o
n
en
ts
,
r
esp
ec
tiv
ely
.
I
n
o
r
d
er
to
test
th
e
r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
ed
al
g
o
r
ith
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,
a
n
d
to
s
tu
d
y
th
e
ef
f
ec
ts
o
f
th
e
im
p
u
ls
iv
e
co
m
p
o
n
en
ts
(
o
u
tlier
s
)
o
f
t
h
e
n
o
is
e
p
r
o
ce
s
s
in
th
e
n
o
is
e
ca
n
ce
llatio
n
s
ettin
g
,
an
im
p
u
ls
i
v
e
n
o
is
e
p
r
o
ce
s
s
is
g
en
er
ated
b
y
th
e
af
o
r
em
e
n
tio
n
ed
p
r
o
b
a
b
ilit
y
d
en
s
ity
f
u
n
ctio
n
with
=
0
.
2
an
d
=
100
.
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y
,
th
e
s
ig
n
a
l
is
as
s
u
m
ed
to
b
e
d
is
to
r
ted
b
y
an
ad
d
itiv
e
wh
ite
im
p
u
ls
iv
e
n
o
is
e
(
AW
I
N)
p
r
o
ce
s
s
.
T
h
en
,
th
e
s
am
e
ex
p
er
im
en
t
is
r
ep
ea
ted
wh
ile
ass
u
m
in
g
th
e
s
ig
n
al
is
co
r
r
u
p
ted
b
y
a
co
r
r
elate
d
im
p
u
ls
iv
e
n
o
is
e
cr
ea
ted
u
s
in
g
th
e
af
o
r
em
en
tio
n
ed
AR
(
1
)
.
I
n
b
o
th
F
ig
u
r
es
5
an
d
6
it
ca
n
b
e
s
ee
n
th
at
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
c
o
n
v
er
g
e
s
to
s
am
e
MSE
(
MSE
=
−
30
dB
)
o
f
th
e
2
nd
o
r
d
er
R
I
an
d
R
I
alg
o
r
ith
m
s
with
f
aster
co
n
v
er
-
g
en
ce
r
ate
(
ap
p
r
o
x
im
ately
400
an
d
600
iter
atio
n
s
f
aster
th
an
2
nd
o
r
d
er
R
I
an
d
R
I
alg
o
r
ith
m
s
,
r
esp
ec
tiv
ely
)
.
I
n
ad
d
itio
n
,
it
is
n
o
ted
th
at
ev
en
th
o
u
g
h
th
e
R
L
S tr
ies to
co
n
v
er
g
e
at
th
e
b
e
g
in
n
in
g
,
it st
ar
ts
to
s
lo
wly
d
iv
er
g
e
a
f
ter
al
m
o
s
t
800
iter
atio
n
s
.
Fig
u
r
e
3
.
T
h
e
en
s
em
b
le
MSE
f
o
r
th
e
p
r
o
p
o
s
ed
,
R
I
,
2
n
d
o
r
d
er
R
I
a
n
d
R
L
S a
lg
o
r
ith
m
s
in
AW
GN
Fig
u
r
e
4
.
T
h
e
en
s
em
b
le
MSE
f
o
r
th
e
p
r
o
p
o
s
ed
,
R
I
,
2
n
d
o
r
d
er
R
I
a
n
d
R
L
S a
lg
o
r
it
h
m
s
in
AC
GN
Fig
u
r
e
5
.
T
h
e
en
s
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S
[1
]
A.
M
a
n
n
a
n
,
e
t
a
l
.,
“
A
d
a
p
ti
v
e
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Ra
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h
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mp
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Dig
it
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l
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E),
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0
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[2
]
A.
N.
S
.
Be
l
g
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rz
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t
a
l.
,
“
A
p
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p
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.
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7
.
[3
]
T.
G
o
wri,
e
t
a
l.
,
“
Eff
icie
n
t
re
d
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c
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in
EC
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sig
n
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l
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ter
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1
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p
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0
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[4
]
B.
Wi
d
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w,
e
t
a
l
.
,
“
Ad
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Pre
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Ha
ll
I
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.
,
NJ
,
1
9
8
5
.
[
5
]
B
.
A
l
-
S
h
e
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k
h
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.
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,
2019
.
[
6
]
C
.
V
.
S
i
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,
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t
a
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.
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[7
]
X.
G
u
a
n
,
e
t
a
l
.,
“
QX
-
LM
S
a
d
a
p
ti
v
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F
IR
fil
ters
fo
r
sy
ste
m
id
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,
”
2
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In
ter
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ig
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ss
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g
(CIS
P
2
0
0
9
),
p
p
.
1
-
5
,
2
0
0
9
.
[8
]
A.
Zh
a
n
g
,
e
t
a
l
.,
“
Re
we
ig
h
ted
lp
c
o
n
stra
in
t
LM
S
-
b
a
se
d
a
d
a
p
ti
v
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sp
a
rse
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a
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l
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stim
a
ti
o
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ra
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o
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m
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n
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sy
ste
m
,
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IET
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o
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n
ica
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n
s
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l.
1
4
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o
.
9
,
p
p
.
1
3
8
4
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1
3
9
1
,
2
0
2
0
[9
]
S
.
Ha
y
k
i
n
,
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A
d
a
p
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v
e
F
il
ter T
h
e
o
ry
,
”
Pre
n
ti
c
e
Ha
l
l,
Up
p
e
r S
a
d
d
le
Ri
v
e
r,
NJ
,
2
0
0
2
.
[1
0
]
S
.
P
a
n
d
a
,
e
t
a
l
.,
“
Im
p
u
lsiv
e
n
o
ise
c
a
n
c
e
ll
a
ti
o
n
fro
m
c
a
rd
iac
sig
n
a
l
u
sin
g
m
o
d
ifi
e
d
WL
M
S
a
l
g
o
ri
th
m
b
a
se
d
a
d
a
p
ti
v
e
fil
ter,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
C
irc
u
it
s,
S
y
ste
ms
a
n
d
S
ig
n
a
l
Pro
c
e
ss
in
g
,
v
o
l
.
1
1
,
p
p
.
2
2
3
-
2
2
9
,
2
0
1
7
.
[1
1
]
C.
Li
u
,
e
t
a
l
.,
“
A
v
a
riab
le
ste
p
si
z
e
imp
ro
v
e
d
m
u
lt
ib
a
n
d
-
str
u
c
tu
re
d
su
b
b
a
n
d
a
d
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p
t
iv
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f
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ter
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l
g
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th
m
with
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b
b
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n
d
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p
u
t
se
lec
ti
o
n
,
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In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
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.
1
1
,
p
p
.
2
0
2
-
2
0
9
,
2
0
1
7
.
[1
2
]
Y.
Xia
o
,
“
S
tab
il
iza
ti
o
n
o
f
a
M
o
d
if
ied
LM
S
Al
g
o
rit
h
m
fo
r
Ca
n
c
e
li
n
g
No
n
li
n
e
a
r
M
e
m
o
ry
Eff
e
c
ts,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
S
ig
n
a
l
Pro
c
e
ss
in
g
,
v
o
l.
6
8
,
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p
.
3
4
3
9
4
-
4
9
,
2
0
2
0
.
[
1
3
]
D
.
B
.
H
a
d
d
a
d
,
e
t
a
l
., “
l
2
-
n
o
r
m
f
e
a
t
u
r
e
l
e
a
s
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m
e
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n
s
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u
a
r
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t
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m
,
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l
e
c
t
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c
s
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e
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s
,
v
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l
.
5
6
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o
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0
,
p
p
.
5
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6
-
5
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9
,
2
0
2
0
.
[1
4
]
S
.
Ha
y
k
in
,
e
t
a
l
.,
“
Ad
a
p
ti
v
e
trac
k
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n
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o
f
li
n
e
a
r
t
ime
-
v
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t
sy
ste
m
s
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y
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x
ten
d
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d
RL
S
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l
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h
m
s,”
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EE
T
ra
n
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s
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S
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Pro
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in
g
,
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5
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p
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1
1
1
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8
,
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9
9
7
.
[1
5
]
M
.
S
.
Ah
m
a
d
,
e
t
a
l
.,
“
Re
c
u
rsiv
e
i
n
v
e
rse
a
d
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p
ti
v
e
fil
terin
g
a
lg
o
rit
h
m
,
”
Dig
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l
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ig
n
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Pro
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ss
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l
se
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ier),
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o
.
4
,
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p
.
4
9
1
-
4
9
6
,
2
0
1
1
.
[1
6
]
M
.
S
.
S
a
lma
n
,
e
t
a
l
.,
“
Re
c
u
rsiv
e
in
v
e
rse
a
lg
o
rit
h
m
:
M
e
a
n
-
sq
u
a
re
-
e
rro
r
a
n
a
ly
si
s,”
Dig
it
a
l
S
ig
n
a
l
Pro
c
e
ss
in
g
(El
se
v
ier),
v
o
l.
6
6
,
p
p
.
10
-
1
7
,
2
0
1
7
.
[1
7
]
M
.
S
.
Ah
m
a
d
,
e
t
a
l
.,
“
Re
c
u
rsiv
e
in
v
e
rse
a
d
a
p
ti
v
e
fil
ter
wit
h
se
c
o
n
d
o
rd
e
r
e
stim
a
ti
o
n
o
f
a
u
to
c
o
rr
e
latio
n
m
a
tri
x
,
”
T
h
e
1
0
th
IEE
E
In
ter
n
a
ti
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n
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l
S
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o
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ig
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l
Pro
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g
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n
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n
fo
rm
a
t
io
n
T
e
c
h
n
o
l
o
g
y
,
p
p
.
4
8
2
-
4
8
4
,
2
0
1
0
.
[1
8
]
S
.
M
a
ll
a
t,
“
Wa
v
e
let
fo
r
a
v
isio
n
,
”
Pro
c
e
e
d
in
g
s o
f
th
e
IEE
E
,
v
o
l
.
8
4
,
n
o
.
4
,
p
p
.
6
0
4
-
6
1
4
,
1
9
9
6
.
[1
9
]
M
.
G
a
rrid
o
,
“
Th
e
fe
e
d
fo
rwa
rd
sh
o
rt
-
ti
m
e
F
o
u
rier
tran
sf
o
rm
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Circ
u
i
ts
a
n
d
S
y
st
e
ms
II:
Exp
re
ss
Briefs
,
v
o
l
.
6
3
,
n
o
.
9
,
p
p
.
8
6
8
-
8
7
2
,
2
0
1
6
.
[2
0
]
P
.
Z
h
a
n
g
,
e
t
a
l
.,
“
P
a
ra
m
e
tri
c
a
u
d
io
e
q
u
a
li
z
e
r
b
a
se
d
o
n
sh
o
rt
-
ti
m
e
F
o
u
rier
tran
sf
o
rm
,
”
IEE
E
1
7
t
h
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Co
mm
u
n
ica
t
io
n
T
e
c
h
n
o
l
o
g
y
(ICCT),
p
p
.
1
6
4
8
-
1
6
5
1
,
2
0
1
7
.
[2
1
]
W.
L
u
,
e
t
a
l
.
,
“
De
c
o
n
v
o
l
u
ti
v
e
sh
o
rt
-
ti
m
e
F
o
u
rier
tran
sfo
rm
s
p
e
c
tro
g
ra
m
,
”
IEE
E
S
i
g
n
a
l
Pro
c
e
ss
in
g
L
e
tt
e
rs
,
v
o
l.
1
6
,
n
o
.
7
,
p
p
.
5
7
6
-
5
7
9
,
2
0
0
9
.
[2
2
]
G
.
O.
G
l
e
n
ti
s,
e
t
a
l
.,
“
Eff
icie
n
t
lea
st
sq
u
a
re
s
a
d
a
p
ti
v
e
a
lg
o
rit
h
m
s
fo
r
F
IR
tran
sv
e
rsa
l
fil
terin
g
,
”
IEE
E
S
ig
n
a
l
Pro
c
e
ss
in
g
M
a
g
a
zin
e
,
p
p
.
1
3
-
4
1
,
1
9
9
9
.
[2
3
]
A.
Ra
ste
g
a
rn
ia,
“
Re
d
u
c
e
d
-
c
o
m
m
u
n
ica
ti
o
n
d
iffu
si
o
n
RLS
fo
r
d
is
t
rib
u
te
d
e
stim
a
ti
o
n
o
v
e
r
m
u
lt
i
-
a
g
e
n
t
n
e
two
r
k
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Circ
u
it
s
a
n
d
S
y
ste
ms
II:
Exp
re
ss
Briefs
,
v
o
l.
6
7
,
n
o
.
1
,
p
p
.
1
7
7
-
1
8
1
,
2
0
2
0
.
[2
4
]
A.
Ge
b
h
a
rd
,
e
t
a
l
.,
“
A
ro
b
u
st
n
o
n
li
n
e
a
r
RLS
ty
p
e
a
d
a
p
ti
v
e
fil
ter
f
o
r
se
c
o
n
d
-
o
r
d
e
r
-
in
term
o
d
u
l
a
ti
o
n
d
ist
o
rti
o
n
ca
n
c
e
ll
a
ti
o
n
i
n
F
DD
LT
E
a
n
d
5
G
d
irec
t
c
o
n
v
e
rsio
n
tran
sc
e
iv
e
rs,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
M
icr
o
w
a
v
e
T
h
e
o
ry
a
n
d
T
e
c
h
n
iq
u
e
s
,
v
o
l.
6
7
,
n
o
.
5
,
p
p
.
1
9
4
6
-
1
9
6
1
,
2
0
1
9
.
[2
5
]
H.
De
li
c
,
e
t
a
l.
,
“
Ro
b
u
st
d
e
tec
ti
o
n
in
DS/
CDMA,
”
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Veh
ic
u
la
r
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
5
1
,
n
o
.
1
,
p
p
.
1
5
5
-
1
7
0
,
2
0
0
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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rica
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t
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n
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