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o
r
ig
i
n
al
s
i
g
n
al
is
also
af
f
ec
ted
b
y
o
t
h
er
u
n
k
n
o
w
n
r
an
d
o
m
s
ig
n
al
s
w
h
ic
h
ca
n
b
e
m
o
d
ele
d
as
ad
d
itiv
e
r
an
d
o
m
n
o
is
e.
T
h
ese
o
cc
u
r
r
en
ce
s
co
m
p
licat
e
th
e
an
al
y
s
is
a
n
d
in
ter
p
r
etatio
n
o
f
t
h
e
E
E
Gs,
a
n
d
th
e
f
ir
s
t
i
m
p
o
r
tan
t
p
r
o
ce
s
s
in
g
s
tep
w
o
u
ld
b
e
th
e
e
li
m
in
a
tio
n
o
f
t
h
e
ar
ti
f
ac
t
s
an
d
n
o
is
e.
O
u
r
g
o
al
is
to
co
n
tr
ib
u
te
to
E
E
G
ar
tif
ac
t
r
ej
ec
tio
n
b
y
p
r
o
p
o
s
in
g
an
o
r
ig
in
al
an
d
m
o
r
e
co
m
p
lete
au
to
m
at
ic
m
et
h
o
d
o
lo
g
y
co
n
s
i
s
tin
g
i
f
o
p
tim
ized
co
m
b
i
n
atio
n
o
f
s
ev
er
al
s
i
g
n
al
p
r
o
ce
s
s
in
g
an
d
d
ata
an
al
y
s
i
s
tech
n
iq
u
es.
T
h
er
e
ar
e
s
o
m
an
y
d
en
o
i
s
in
g
tech
n
iq
u
e
s
e
m
p
lo
y
ed
to
r
e
m
o
v
e
t
h
e
ar
ti
f
ac
t
s
f
r
o
m
t
h
e
E
E
G
o
r
ig
i
n
al
s
ig
n
al.
So
m
e
o
f
t
h
e
d
en
o
i
s
i
n
g
tec
h
n
iq
u
es
u
s
ed
to
r
e
m
o
v
e
th
e
n
o
is
es
ar
e
I
C
A
d
en
o
is
i
n
g
,
P
C
A
d
en
o
is
i
n
g
,
W
av
elet
b
ased
d
en
o
is
i
n
g
.
T
h
e
ab
o
v
e
s
aid
tech
n
iq
u
es
e
m
p
lo
y
ed
f
o
r
d
en
o
is
in
g
t
h
e
E
E
G
s
ig
n
al
a
n
d
th
eir
p
er
f
o
r
m
a
n
ce
ca
n
b
e
ev
alu
ated
b
y
m
ea
s
u
r
i
n
g
t
h
e
p
ar
a
m
eter
s
l
ik
e
SN
R
,
MSE
an
d
co
m
p
u
tati
o
n
ti
m
e
etc.
T
h
is
p
ap
er
is
o
r
g
a
n
ized
as
f
o
ll
o
w
s
:
T
h
e
s
ec
o
n
d
s
ec
tio
n
p
r
ese
n
ts
a
b
r
ief
h
is
to
r
y
ab
o
u
t
t
h
e
E
E
G
s
i
g
n
a
l
ar
tif
ac
ts
a
n
d
n
o
is
es
r
ej
ec
tio
n
p
r
esen
ted
in
th
e
liter
at
u
r
e.
T
h
e
th
ir
d
s
ec
tio
n
co
n
tai
n
s
t
h
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
f
o
r
d
en
o
is
in
g
.
I
n
t
h
is
p
ar
t
th
e
w
a
v
elet
d
en
o
is
in
g
is
b
r
ief
l
y
e
x
p
lain
ed
an
d
th
e
m
et
h
o
d
o
lo
g
ical
s
tep
s
in
v
o
lv
ed
t
o
ac
q
u
ir
e
th
e
n
o
is
e
r
ej
ec
ted
o
u
tp
u
t
s
i
g
n
al
i
n
a
p
r
o
p
o
s
ed
w
av
elet
tr
a
n
s
f
o
r
m
.
T
h
e
f
o
u
r
t
h
s
ec
tio
n
s
h
o
w
s
t
h
e
s
i
m
u
lat
io
n
r
es
u
lt o
f
t
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
i
n
Ma
tlab
a
n
d
VL
SI.
2.
RE
L
AT
E
D
WO
RK
I
n
b
io
-
m
ed
ical
s
i
g
n
al
p
r
o
ce
s
s
,
ar
tif
ac
t
s
ar
e
u
n
w
an
ted
n
o
i
s
e
ca
u
s
ed
b
y
t
h
e
o
r
ig
in
al
p
h
y
s
io
lo
g
ical
af
f
a
ir
b
ased
o
n
th
e
in
ter
e
s
t.
T
h
u
s
,
th
e
ai
m
o
f
an
al
y
s
is
d
ep
en
d
in
g
o
n
t
h
e
d
ec
is
io
n
s
h
o
u
ld
b
e
m
ad
e
as
id
en
ti
f
y
i
n
g
th
e
o
r
ig
i
n
al
a
n
d
ar
tif
ac
t
s
i
g
n
al.
Fo
r
r
eliab
le
an
aly
s
i
s
ar
tif
ac
t
s
cla
s
s
if
icatio
n
s
h
o
u
ld
b
e
co
n
s
id
er
ed
,
w
h
ic
h
if
ig
n
o
r
ed
,
m
ig
h
t
co
n
s
i
d
er
ab
ly
in
f
l
u
en
ce
t
h
e
r
esu
lt
s
an
d
th
er
ef
o
r
e
th
e
r
esu
l
tin
g
co
n
clu
s
io
n
s
.
E
E
Gs
ar
e
t
y
p
icall
y
r
ec
o
r
d
ed
in
co
n
j
u
n
c
tio
n
w
it
h
d
if
f
er
en
t
p
h
y
s
io
lo
g
ical
s
ig
n
al
s
w
h
ic
h
ca
n
i
n
ter
f
er
e
w
it
h
th
e
e
x
ac
t
E
E
Gs.
S
u
c
h
ar
ti
f
ac
t
li
k
e
o
cu
l
ar
,
m
u
s
cle,
elec
tr
ical
f
ield
ch
an
g
e
s
,
tr
an
s
m
is
s
io
n
li
n
e
i
n
ter
f
er
en
ce
,
m
o
v
e
m
e
n
ts
o
f
h
ea
d
an
d
elec
tr
o
d
es.
Fig
u
r
e.
1
illu
s
tr
ates
s
ec
tio
n
s
o
f
g
r
ap
h
ical
r
ec
o
r
d
co
n
ta
m
in
a
t
ed
b
y
t
y
p
ica
l
s
a
m
p
les
o
f
ar
ti
f
ac
ts
.
On
ce
s
o
m
e
o
f
k
n
o
w
led
g
e
co
r
r
u
p
ted
b
y
a
n
ar
tif
ac
t
h
as
b
ee
n
w
i
th
s
u
cc
e
s
s
f
u
ll
y
k
n
o
w
n
t
h
en
t
h
er
e
ar
e
d
if
f
er
en
t
w
a
y
s
w
h
ic
h
m
a
y
b
e
ad
o
p
ted
,
b
ettin
g
o
n
th
e
s
h
ap
e
o
f
th
at
ar
tif
ac
t
.
I
n
ex
tr
e
m
e
ca
s
es
th
e
w
h
o
le
ep
o
ch
th
at
co
n
tai
n
s
th
e
ar
ti
f
ac
t
m
ig
h
t
h
a
v
e
to
b
e
d
is
ca
r
d
ed
,
v
ar
io
u
s
n
o
r
m
al
ar
ti
f
ac
t
d
etec
t
o
r
is
u
s
ed
an
d
th
er
e
f
o
r
e
th
e
s
ig
n
al
s
t
h
at
is
co
n
ta
m
in
a
ted
b
y
t
h
e
ar
tif
a
ct
is
k
n
o
w
n
an
d
d
is
ca
r
d
ed
.
As
an
alter
n
at
iv
e,
i
n
s
o
m
e
i
n
s
ta
n
ce
s
,
t
h
er
e
is
a
p
o
ten
tial
to
esti
m
ate
th
e
o
r
ig
i
n
al
E
E
G
s
i
g
n
a
l
u
s
in
g
ap
p
r
o
p
r
iate
s
ig
n
al
p
r
o
ce
s
s
tec
h
n
iq
u
es
b
y
s
u
p
p
r
ess
i
n
g
th
e
ar
tif
ac
t.
T
h
e
ef
f
o
r
tles
s
w
a
y
to
eli
m
i
n
a
te
ar
tif
ac
ts
is
to
f
i
n
d
at
th
e
p
er
io
d
o
f
o
cc
u
r
r
en
ce
an
d
r
ec
o
r
d
ed
d
ata
is
eli
m
i
n
ated
.
On
e
tech
n
iq
u
e
th
at
is
u
s
ed
to
tak
e
ar
tif
ac
t
as
a
n
y
i
m
p
o
r
tan
t
d
ev
iatio
n
f
r
o
m
t
h
e
tr
ad
itio
n
al
is
to
p
er
m
i
t
d
etec
tio
n
b
y
s
ee
k
i
n
g
v
ar
iat
io
n
s
(
n
o
n
-
s
tatio
n
ar
ie
s
)
with
i
n
th
e
m
ea
s
u
r
ed
s
i
g
n
a
l.
T
h
is
tech
n
iq
u
e
s
h
o
u
ld
b
e
ap
p
lied
w
it
h
ca
r
e,
s
i
n
ce
t
h
e
Or
ig
i
n
al
E
E
G
is
its
el
f
n
o
n
s
tatio
n
ar
y
,
t
h
er
ef
o
r
e
m
aj
o
r
p
ar
a
m
eter
s
h
av
e
to
b
e
d
esig
n
ated
,
s
o
th
e
en
tire
co
n
n
ec
ted
n
o
n
-
s
tatio
n
ar
ie
s
ar
e
d
ete
cted
.
E
n
er
g
y
o
p
er
ato
r
s
m
a
y
b
e
h
elp
f
u
l
m
ar
k
er
s
o
f
s
u
d
d
en
ch
a
n
g
es
(
e.
g
.
s
p
i
k
es)
as
th
e
y
ar
e
s
e
n
s
iti
v
e
to
in
s
t
an
t
f
l
u
ct
u
atio
n
s
[
5
]
h
o
w
e
v
er
w
ill
r
eq
u
ir
e
m
o
r
e
s
en
s
iti
v
it
y
to
r
ec
o
r
d
ac
cu
r
ate
c
h
an
g
es
w
i
th
in
t
h
e
s
i
g
n
al
s
p
ec
t
r
u
m
.
A
s
et
o
f
m
at
h
e
m
atica
l
f
u
n
ct
io
n
s
th
a
t
tr
an
s
f
o
r
m
s
n
u
m
b
er
o
f
co
r
r
elate
d
v
ar
iab
les
in
to
a
s
m
aller
n
u
m
b
er
o
f
u
n
r
elate
d
v
ar
iab
les
is
k
n
o
w
n
as
P
r
in
cip
al
C
o
m
p
o
n
en
t.
T
h
e
P
r
in
cip
al
C
o
m
p
o
n
en
t
An
al
y
s
is
(
P
C
A
)
is
a
p
r
im
ar
y
ele
m
e
n
t
th
at
ac
co
u
n
t
s
f
o
r
th
e
m
a
x
i
m
u
m
a
m
o
u
n
t
o
f
th
e
v
ar
iab
ilit
y
w
it
h
i
n
th
e
d
ata
as
p
o
s
s
ib
le,
an
d
ev
er
y
s
u
cc
ee
d
in
g
ele
m
e
n
t
ac
co
u
n
t
s
f
o
r
th
e
m
a
x
i
m
u
m
a
m
o
u
n
t
o
f
t
h
e
r
e
m
a
in
i
n
g
v
ar
ia
b
ilit
y
as
p
o
ten
t
ial.
P
r
in
cip
al
co
m
p
o
n
e
n
t
s
ar
e
ab
s
o
lu
te
a
n
d
in
d
ep
en
d
e
n
t
to
p
r
o
v
id
e
th
e
r
ec
o
r
d
in
g
d
ataset
th
at
i
s
n
o
r
m
a
ll
y
cir
cu
lated
.
P
C
A
is
m
o
r
e
ac
cu
r
ate
to
t
h
e
r
elati
v
e
le
v
el
o
f
th
e
in
itial
v
ar
iab
les
[6
-
9
]
.
Dep
en
d
in
g
o
n
th
e
ap
p
licatio
n
,
it i
s
ad
d
itio
n
a
ll
y
n
a
m
ed
as
d
is
ti
n
ct
Kar
h
u
n
e
n
–
L
o
èv
e
tr
a
n
s
f
o
r
m
,
t
h
e
Ho
telli
n
g
tr
an
s
f
o
r
m
o
r
P
r
o
p
er
o
r
th
o
g
o
n
al
d
ec
o
m
p
o
s
itio
n
.
T
h
e
m
at
h
e
m
at
ical
m
et
h
o
d
u
ti
lized
in
P
C
A
is
ter
m
ed
a
s
E
i
g
en
an
al
y
s
is
.
I
t
ten
d
s
to
s
o
l
v
e
th
e
E
i
g
e
n
v
alu
e
s
a
n
d
eig
e
n
v
ec
to
r
o
f
a
s
q
u
ar
e
s
y
m
m
etr
ic
m
atr
i
x
w
i
th
s
u
m
o
f
s
q
u
ar
e
an
d
cr
o
s
s
p
r
o
d
u
ct.
T
h
e
eig
e
n
v
ec
to
r
is
r
elate
d
to
th
e
b
ig
g
est
E
i
g
en
v
alu
e
s
an
d
h
a
s
co
n
s
tan
t
d
ir
ec
tio
n
b
ec
au
s
e
it
i
s
t
h
e
f
ir
s
t
p
r
in
cip
al
ele
m
en
t.
T
h
e
eig
en
v
ec
to
r
r
elate
d
to
th
e
s
e
co
n
d
lar
g
est
E
i
g
e
n
v
a
lu
e
s
d
eter
m
i
n
e
th
e
d
ir
ec
tio
n
o
f
t
h
e
s
ec
o
n
d
p
r
in
cip
al
co
m
p
o
n
e
n
t.
T
h
e
ad
d
itio
n
o
f
t
h
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I
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IJ
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3
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ad
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d
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is
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tio
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o
f
t
h
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E
MG
s
ig
n
als:
Stan
d
ar
d
Dev
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n
,
Me
an
,
Av
er
ag
e
p
o
w
er
,
an
d
r
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f
ab
s
o
lu
te
m
ea
n
o
f
th
e
co
ef
f
icie
n
ts
i
n
ea
ch
s
u
b
-
b
a
n
d
s
a
m
p
le
s
.
4.
RE
SU
L
T
S
T
h
e
r
esear
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tu
d
y
w
as
to
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i
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i
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n
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ai
n
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r
ec
o
r
d
in
g
r
eq
u
ir
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lin
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in
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o
r
m
a
tio
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r
o
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m
a
n
y
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h
a
n
n
el
s
(
s
ta
n
d
ar
d
ch
an
n
el
s
3
2
-
4
4
)
,
th
e
i
n
p
u
t
s
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r
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s
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g
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s
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