Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 1
,
Febr
u
a
r
y
201
6,
pp
. 15
1
~
15
9
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
1.8
592
1
51
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Modified Variational Mode Decomposition for Power Line
Interference Removal in ECG Signals
Neethu Moh
a
n*,
S
a
chin Ku
mar S*,
Pr
ab
ah
aran
P
o
orn
a
ch
andr
an
**, K.P Som
a
n
*
* Centr
e
for
Ex
cellence in
Computation
a
l Engin
e
eri
ng
and Networking, Amrita Vi
shwa Vidy
apeetham,
India
** Amrita C
e
nter for C
y
b
e
rsecur
i
ty
S
y
s
t
ems and
Networks,
Amrita Vishwa
Vi
dy
ap
e
e
t
ha
m,
I
n
d
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
l 14, 2015
Rev
i
sed
No
v
11
, 20
15
Accepted Nov 30, 2015
Power line interferences (PLI) occurring at
50/60 Hz can
corrupt the
biomedical reco
rdings like EC
G signa
ls and which leads to
an improper
diagnosis of disease conditions. Prope
r interfer
e
nce can
cellation
techniqu
es
are th
erefor
e req
u
ired for
the r
e
m
oval of thes
e
power line
dis
t
u
r
bances
from
biomedical recordings. The n
on-linea
r tim
e
var
y
ing
chara
c
ter
i
stics of
biomedical signals make the
in
terfer
e
nce removal a
difficult task without
com
p
rom
i
s
i
ng the a
c
tua
l
s
i
gna
l
char
act
eris
ti
cs
.
In this
p
a
per
,
a m
odified
variational mode decompos
ition based approach is proposed for
PLI removal
from
the ECG si
gnals. In this ap
proach,
th
e cen
tr
al frequen
c
y
of
an intrinsic
mode function
is fixed corr
esponding to the normalized
power lin
e
disturbance frequency
.
The experime
nta
l
res
u
lts show that the PLI
interf
eren
ce is
exac
tl
y cap
ture
d bot
h in mag
n
itude and phase and ar
e
removed. Th
e p
r
oposed approach is e
xperimented with ECG signal records
from MIT-BIH
Arrh
y
t
hmia database a
nd com
p
ared with tradit
i
onal notch
filte
ring.
Keyword:
EC
G si
gnal
s
M
ode
fi
xi
ng
M
odi
fi
e
d
vari
a
t
i
onal
m
ode
decom
posi
t
i
o
n
Po
wer li
ne inte
rfe
rence
rem
o
v
a
l
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
N
eethu
M
o
h
a
n,
C
e
nt
re
fo
r E
x
c
e
l
l
e
nce i
n
C
o
m
put
at
i
o
nal
E
n
g
i
neeri
n
g a
n
d
N
e
t
w
o
r
ki
ng
,
Am
rita Vishwa
Vidy
a
p
eetham
,
C
o
i
m
bat
o
re, I
n
di
a-
64
1
1
2
Em
a
il: n
eeth
u
m
o
h
a
n
.
ndk
m@g
m
ail.co
m
1.
INTRODUCTION
Biom
edical recordings are
usually
co
rrup
ted
with
power lin
e d
i
stu
r
b
a
nces an
d
wh
ich resu
lts an
erro
n
e
ou
s d
a
ta an
alysis. Th
e main
cau
ses o
f
p
o
wer lin
e d
i
stu
r
b
a
n
ces in
b
i
o
m
ed
ical reco
rd
ing
s
are cap
acitiv
e
and m
a
gnet
i
c
cou
p
l
i
n
g t
o
b
u
i
l
d
i
n
g
po
wer
l
i
n
es an
d t
o
no
n
po
we
r l
i
n
e n
o
i
s
e so
ur
c
e
s, nea
r
by
el
ect
ri
cal
appl
i
a
nc
es an
d m
a
i
n
s wi
ri
ng [
1
]
,
[2]
.
T
h
e po
wer l
i
n
e
i
n
t
e
rfe
rence c
ont
ai
n
s
t
h
e f
u
ndam
e
nt
al
fre
que
ncy
com
pone
nt
at
50/
60
Hz al
on
g wi
t
h
hi
ghe
r
or
der
ha
rm
oni
cs. The
rem
o
v
a
l
of t
h
e
s
e i
n
t
e
rfe
rences
f
r
o
m
t
h
e
bi
om
edi
cal
recor
d
i
n
gs i
s
a com
p
l
i
cat
ed t
a
sk si
nce t
h
e be
havi
ou
r o
f
t
h
e
s
e di
st
ur
ban
c
e
s
i
s
non st
at
i
o
nary
i
n
nat
u
re. T
h
e
PL
I ca
ncel
l
a
t
i
on i
s
i
m
port
a
nt
f
o
r
p
r
o
p
er
i
n
t
e
r
p
r
e
t
a
t
i
on o
f
ne
ur
al
si
gnal
s
.
Seve
ral
ap
pr
oa
ches
have
bee
n
p
r
op
ose
d
f
o
r
t
h
e rem
oval
o
f
p
o
w
e
r l
i
n
e i
n
t
e
rfe
re
nces i
n
bi
om
edi
cal
record
i
n
gs. The classical appro
a
ch
for
rem
o
v
i
ng
p
o
wer lin
e d
i
sturb
a
n
ces
is u
s
ing
a
n
o
t
ch
filter [3
], [4
]
.
Bu
t
th
is filtering
ap
pro
ach
is no
t
efficien
t
du
e t
o
th
e non
statio
n
a
ry n
a
t
u
re of th
e i
n
terferen
ces an
d also
d
u
e
to
fre
que
ncy
vari
at
i
ons i
n
t
h
e
si
gnal
.
A
n
ot
he
r com
m
on
t
e
c
hni
que
f
o
r
i
n
t
e
rfe
rence
canc
e
l
l
a
t
i
on i
s
bas
e
d
on
spect
r
u
m
est
i
m
a
t
i
on b
u
t
f
o
r real
t
i
m
e dat
a
anal
y
s
i
s
t
h
i
s
m
e
t
hod i
s
f
o
u
n
d
i
n
a
d
e
qua
t
e
[5]
.
Lat
e
r
s
e
veral
ad
ap
tiv
e i
n
ter
f
er
en
ce can
cellatio
n
app
r
o
a
ches h
a
v
e
b
een
p
r
op
o
s
ed
in
var
i
ou
s ar
ticles. I
n
[6
], pr
oposes an
alg
o
rith
m
b
a
sed
o
n
Ad
ap
tiv
e No
tch
Filter (ANF)
app
r
o
a
ch
for
fund
am
e
n
tal frequ
e
n
c
y esti
m
a
tio
n
.
Later the
h
a
rm
o
n
i
cs are
esti
m
a
ted
u
s
in
g
d
i
screte-ti
m
e
o
s
cillato
rs and th
en
th
e am
p
l
i
t
u
d
e
and
ph
ase are
m
easu
r
ed
u
s
ing
a si
m
p
le recu
rsiv
e least squ
a
re (RLS) algo
rith
m
.
A d
i
scret
e
-ti
m
e lin
ear Kalm
an
No
tch filter b
a
sed
app
r
o
a
ch
is u
s
ed
fo
r PLI rem
o
v
a
l in
[7
]. Sin
ce t
h
e filter d
e
si
g
n
is
lin
ear, th
is app
r
o
a
ch
do
es
no
t requ
ire an
y in
fo
rmatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
15
1 – 15
9
15
2
abo
u
t
t
h
e p
h
as
e and am
pl
i
t
ude of t
h
e i
n
t
e
rfe
rences
. Lat
t
i
ce
base
d seco
nd
o
r
de
r i
n
fi
ni
t
e
im
pul
se res
p
on
se (I
IR
)
n
o
t
ch
filter is
p
r
op
o
s
ed
i
n
[8] fo
r power line no
ise re
m
o
val. Man
i
ru
zzaman
et al, d
e
si
g
n
e
d
an
ad
ap
tiv
e filter
b
a
sed
on
least-mean
-squ
are co
n
c
ep
t
for th
e
rem
o
v
a
l o
f
PLI fro
m
ECG reco
rd
ing
s
[9
].
An Al
p
h
a
-Beta filter
b
a
sed
app
r
o
a
ch
is u
s
ed
in
[
1
0
]
. An
adap
tive in
ter
f
e
r
e
n
ce
can
celler
w
ith
a secon
d
o
r
d
e
r PLL is pr
oposed
i
n
[11
]
. Th
e PLL
can
h
e
l
p
to
h
a
nd
le with
th
e freq
u
e
n
c
y d
e
v
i
atio
n
s
i
n
th
e in
terferen
ce.
Th
is syste
m
is in
sen
s
itiv
e
to
b
a
selin
e fl
uctu
atio
n
s
an
d
l
a
rg
e am
p
litu
d
e
v
a
riatio
n
s
.
Wei
n
er-
H
op
f eq
uat
i
on ca
n be
use
d
fo
r fi
ndi
ng t
h
e
initial condition of the filter in [12] and base
d on th
at
an adaptive s
y
stem
is designed for interferenc
e
rem
oval
.
Vari
ous si
gnal
pr
o
cessi
ng al
go
ri
t
h
m
s
are al
so em
pl
oy
ed for E
C
G n
o
i
s
e rem
oval
[
1
3-
20]
.
I
n
[
13]
,
Mateo
et al, u
tilized
th
e ad
aptab
ility o
f
A
r
tificial N
e
u
r
al Netw
ork
(AN
N
) alg
o
r
ith
m
to
t
h
e ti
m
e
v
a
ryin
g
,
non
linear features
of ECG signals for
i
n
t
e
r
f
e
r
ence rem
oval
.
A sl
i
d
i
ng
DF
T based
pha
se
l
o
cki
n
g sche
m
e
is
pr
o
pose
d
i
n
[1
4]
. A l
east
m
e
an sq
ua
re base
d ada
p
t
i
v
e i
n
t
e
rfe
rence ca
nc
el
l
e
r i
s
desi
gn
ed by
re
pl
aci
n
g
t
h
e
square
d-e
r
ror
at each sa
m
p
le by
m
ean-square
-
error of
an error
vector in the LM
S
algorithm
[15]. It is a
m
odi
fi
ed versi
on
of t
h
e exi
s
t
i
ng ada
p
t
i
v
e
cancel
l
e
r i
n
cl
ude
d wi
t
h
er
r
o
r est
i
m
at
i
on i
n
t
h
e nei
g
hb
ou
ri
n
g
sam
p
les. A State Space Rec
u
rsi
v
e Least Squa
re (SSRLS
) technique is e
m
ployed for
PLI rem
oval in [16]
,
[1
7]
. T
h
e m
a
i
n
ad
vant
a
g
e
of t
h
i
s
m
e
t
hod i
s
i
t
does
n
o
t
r
e
q
u
i
re a se
parat
e
r
e
fere
nce
po
we
r
l
i
n
e f
o
r
t
r
acki
n
g
t
h
e
PLI.
An F
F
T b
a
sed alg
o
rithm
for
fin
d
in
g the
central fre
q
u
e
n
cy
of
po
we
r l
i
n
e i
s
use
d
i
n
[
1
8]
. The
n
su
bt
ra
ct
i
ng
th
e no
ise estimated
fro
m
th
e co
rrup
ted
sig
n
a
l
for in
terferen
ce can
cell
a
tio
n
.
Em
p
i
rical
m
o
d
e
d
e
com
p
o
s
itio
n
(EMD) co
m
b
i
n
ed with filter
ap
pro
ach is
u
s
ed
for PLI remo
v
a
l i
n
[19
]
.
EMD is a d
a
ta-
d
r
i
v
en ad
ap
tive sign
al
d
eco
m
p
o
s
ition
alg
o
rith
m
an
d
i
s
u
s
ed
for cap
t
u
r
i
n
g of
p
o
wer lin
e no
ise i
n
on
e
o
f
th
e
IMF.
Fi
gu
re
1.
C
l
ean EC
G si
gnal
a
n
d
EC
G
co
rr
u
p
t
ed wi
t
h
PL
I
In
t
h
i
s
pape
r,
m
odi
fi
ed
va
ri
a
t
i
onal
m
ode d
ecom
posi
t
i
on (
V
M
D
), base
d app
r
oach
f
o
r
i
n
t
e
rfe
re
nce
rem
o
v
a
l is d
i
scu
ssed
with
experim
e
n
t
al ev
al
u
a
tio
n
on
no
isy ECG d
a
ta.
Variatio
n
a
l m
o
d
e
d
eco
m
p
o
s
ition
u
s
es
th
e con
c
ep
t of calcu
lus of v
a
riation
wit
h
Altern
ating Direction
M
e
th
od
of M
u
ltip
liers (ADM
M) fo
r
d
e
term
in
in
g
the v
a
riou
s m
o
des p
r
esen
t in
th
e sign
al. Th
e rem
a
in
in
g
sectio
n
of th
e pap
e
r is org
a
n
i
zed
as
fo
llows – sectio
n 2
d
e
scri
b
e
s
th
e
v
a
riation
a
l
m
o
d
e
d
e
co
m
p
o
s
itio
n fo
llowed
b
y
th
e
p
r
o
posed
app
r
o
a
ch
fo
r PLI
rem
oval
.
Sect
i
on
3 des
c
ri
be
s
t
h
e per
f
o
r
m
a
nce eval
uat
i
o
n
of t
h
e
pr
o
pos
ed ap
pr
oac
h
o
n
EC
G si
g
n
al
s an
d
co
m
p
ariso
n
wi
th
conv
en
ti
o
n
a
l n
o
t
ch
filtering
.
Sectio
n 4 con
c
lud
e
s t
h
e
p
a
p
e
r.
2.
PROP
OSE
D
APP
R
O
A
CH
The pr
op
ose
d
app
r
oach uses m
odi
fi
ed
vari
a
t
i
onal
m
ode
d
ecom
posi
t
i
on
f
o
r po
we
r
l
i
n
e di
st
ur
ba
nce
can
cellatio
n
.
Th
e con
cep
t
of
VMD and
ho
w it is
u
tili
zed
for efficient po
wer lin
e
n
o
i
se can
cellat
i
o
n
is
di
scuss
e
d
i
n
t
h
i
s
sect
i
on.
2.
1.
V
a
ri
a
t
i
o
n
a
l
M
o
de
Dec
o
mposi
t
i
o
n
The c
o
ncept
o
f
va
ri
at
i
onal
m
ode
dec
o
m
posi
t
i
on i
s
pr
o
pose
d
i
n
[
20]
.
VM
D,
dec
o
m
pose
s
t
h
e si
gnal
i
n
t
o
va
ri
o
u
s m
ode
s or i
n
t
r
i
n
si
c
m
ode f
unct
i
o
ns (
I
M
F
'
s
) usi
ng cal
c
u
l
u
s
of
vari
at
i
o
n. Eac
h
m
ode of t
h
e
si
gnal
i
s
assum
e
d t
o
have c
o
m
p
act
fre
que
ncy
s
u
pp
o
r
t
aro
u
nd
a cent
r
al
f
r
eq
u
e
ncy
.
VM
D t
r
i
e
s t
o
fi
n
d
out
t
h
ese
cent
r
al
f
r
e
que
n
c
i
e
s an
d IM
F'
s
cent
e
re
d
o
n
t
h
ose
fre
q
u
enci
e
s
co
nc
ur
rent
l
y
usi
n
g a
n
opt
i
m
i
zat
i
on m
e
t
hod
ol
o
g
y
called
Altern
at
in
g
Direction
Meth
od
of Mu
ltip
liers
(ADMM). In
VM
D, a fun
c
tio
n
th
at can
m
eas
u
r
e the
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Modified
V
a
riational Mode Decomposition
fo
r P
o
wer
Line
Interfere
n
ce R
e
mov
a
l in …
(
N
eet
hu M
o
ha
n
)
15
3
b
a
ndw
id
th of
IMF,
()
k
ut
is calcu
lated
.
For th
at, first co
m
p
u
t
e Hilb
ert tran
sform
o
f
IMF,
()
H
k
ut
and
f
o
rm
ul
at
e
an
an
alytic functio
n
()
()
H
kk
ut
j
u
t
. T
h
e
fre
que
ncy
s
p
ect
r
u
m
of t
h
i
s
fu
nct
i
on
i
s
one
si
de
d a
n
d ass
u
m
e
d t
o
be cent
e
re
d o
n
k
. By
m
u
l
tip
lyi
n
g
th
is an
alytical sig
n
a
l with
k
j
t
e
, th
e sig
n
a
l is
freq
u
e
n
c
y translated
to
b
e
centere
d at
origin. T
h
e i
n
tegral of the
s
qua
re of t
h
e
tim
e
d
e
ri
v
a
tiv
e
o
f
t
h
is freq
u
e
n
c
y
tran
slated signal is a
m
easure o
f
ba
nd
wi
dt
h o
f
t
h
e
IM
F,
()
k
ut
. Now the problem
can be form
ulated
as an optimization
problem
as
fo
llows,
2
,
2
mi
n
(
)
*
(
)
.
k
kk
jt
tk
u
k
k
k
j
tu
t
e
t
st
u
f
(1
)
Whe
r
e
f
is th
e
o
r
i
g
in
al sign
al. Th
at is th
e sum o
f
th
e
b
a
n
d
wid
t
hs of
k
m
odes i
s
m
i
nim
i
zed s
u
b
j
ect
t
o
t
h
e
co
nd
itio
n th
at
su
m
o
f
th
e
k
m
o
d
e
s is equ
a
l to
th
e orig
inal sig
n
a
l. So
t
h
e algorith
m
t
r
ies to
find
out
k
unknown cent
r
al freque
n
cie
s
and
k
funct
i
ons ce
nt
ere
d
at
t
hose fre
q
u
enci
es
. No
w
t
h
i
s
const
r
ai
ned
o
p
tim
izat
io
n
prob
lem
is co
n
v
erted
in
t
o
an
un
con
s
trai
n
e
d prob
lem
u
s
in
g
t
h
e au
g
m
en
ted
Lag
r
ang
i
an
m
u
ltip
lier
m
e
thod. T
h
e a
ugm
ented La
grangia
n
m
u
ltiplier c
o
rres
ponds
to the a
b
ove
optim
i
zation is as
follows;
2
2
2
2
(,
,
)
(
)
*
(
)
,
k
jt
kk
t
k
k
k
kk
k
j
Lu
t
u
t
e
f
u
f
u
t
(2
)
Now this can
be sol
v
ed
via the AD
M
M
fra
m
e
wor
k
an
d t
h
e corre
sp
o
ndi
n
g
u
pdat
e
e
quat
i
ons are
o
b
t
a
i
n
ed. I
n
ADMM, s
o
lve
for one va
riabl
e
at a ti
m
e
assum
i
ng t
h
at
al
l
t
h
e ot
her
vari
a
b
les are known.
The update for IMF,
()
k
ut
is,
1
2
1
ˆ
ˆˆ
,0
(1
2
(
)
)
n
ki
ik
k
uf
u
(3
)
The m
odes a
r
e
up
dat
e
d
i
n
t
h
e
fre
que
ncy
dom
ai
n. T
h
e
u
pdat
e
eq
uat
i
o
n
f
o
r
cent
r
al
f
r
e
que
n
c
y
k
is,
2
1
0
2
0
ˆ
()
ˆ
()
k
n
k
k
ud
ud
(4
)
An
d u
pdat
e
f
o
r
is,
11
ˆ
()
nn
n
k
f
ut
(5
)
Th
e Lagrang
i
an
m
u
ltip
lier
is
for ex
act reconstru
c
tion
an
d
is up
d
a
ted
as dual ascen
t [20
]
.
2.
2. M
o
dified
VM
D fo
r
PLI Rem
o
v
a
l
In t
h
i
s
ap
pr
oa
ch, a m
odi
fi
ed
VM
D al
go
ri
t
h
m
i
s
prop
ose
d
f
o
r
rem
ovi
n
g
t
h
e
5
0
/
6
0Hz
po
we
r l
i
n
e
in
terferen
c
es in
ECG
record
s.
represents t
h
e cent
r
al fre
quency c
o
rres
po
ndi
ng t
o
t
h
e
I
M
F'
s. In t
h
e m
odi
fi
ed
alg
o
rith
m
,
th
e
is fix
e
d
to
th
e no
rm
alized
freq
u
e
n
c
y correspo
nd
ing
to
50
/60
Hz. Th
e
v
a
ries in
th
e rang
e
fr
om
0 t
o
. In
t
h
e up
dat
i
n
g p
r
oce
d
ure, t
h
e
t
h
at
we have
fi
xed
rem
a
i
n
s
t
h
e sam
e
and the rem
a
i
n
i
ng
will
be update
d eac
h tim
e
. The
m
ode
s corres
ponding to each
will get updat
e
d until the algorithm
conve
rges
.
As t
h
e f
r
e
que
ncy
of t
h
e p
o
w
er l
i
n
e in
terferen
ce is 50
/6
0
H
z, t
h
e m
o
de fi
xe
d
wi
t
h
t
h
e cor
r
es
po
ndi
n
g
norm
alized fre
que
ncy
will capture this
power line
distur
bance.
All ot
her fre
quency c
o
m
ponents
pre
s
ents in
th
e sig
n
a
l will b
e
cap
tured
b
y
o
t
h
e
r IMF’s.
Si
m
ilar to
th
e
o
r
i
g
in
al th
eory [2
0
]
, co
m
b
in
in
g
all th
e IMF’s g
i
v
e
s
o
r
i
g
in
al sign
al
. Th
e erro
r
b
e
tween
th
e
origin
al sig
n
a
l and
th
e su
m
o
f
all
m
o
d
e
s is n
e
g
lig
i
b
le.
Now
,
b
y
rem
ovi
ng
t
h
e
m
ode wi
t
h
P
L
I di
st
ur
ba
nce,
t
h
e rec
o
nst
r
uct
e
d si
gnal
res
u
l
t
s
i
n
a
p
o
we
r l
i
ne i
n
t
e
r
f
ere
n
c
e
fre
e
sig
n
a
l.
On
e of
th
e m
a
in
issu
es with
th
e
orig
i
n
al VM
D algor
ith
m
is th
at, if th
e co
m
p
on
ent o
f
in
terest is o
f
less
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
15
1 – 15
9
15
4
po
we
r com
p
ar
ed t
o
ot
h
e
r c
o
m
ponent
s
pres
ent
i
n
t
h
e si
g
n
al
,
VM
D c
o
u
l
d n
o
t
rem
ove
i
t
.
Thi
s
pr
o
b
l
e
m
i
s
avoi
ded
i
n
t
h
e
m
odi
fi
ed
VM
D al
go
ri
t
h
m
.
In t
h
i
s
al
g
o
r
ithm
,
by fixing t
h
e ce
ntral
fre
quency,
we a
r
e
able t
o
capt
u
re t
h
e l
o
w p
o
w
er
com
pone
nt
s al
s
o
.
B
y
t
h
i
s
sam
e
way
,
w
e
can
e
x
t
r
act
hi
g
h
er
o
r
de
r
po
wer
ha
r
m
oni
cs
p
r
esen
t i
n
th
e sign
al.
During
th
is op
eration
,
it m
u
st b
e
o
b
s
erv
e
d th
at
th
e n
e
arb
y
freq
u
e
n
c
ies are
no
t all
affected. So
t
h
e propo
sed m
e
t
h
odo
log
y
, acts
as a
v
e
ry sh
arp no
tch
filter to
rem
o
v
e
th
e sp
ecified
freq
u
e
n
c
y.
Mo
dified V
M
D alg
o
rithm
1
.
In
itialize
11
1
ˆ
ˆ
ˆ
,,
,
0
kk
k
un
2
.
In
itialize
2
ˆ
as the norm
alized freque
ncy c
o
rres
ponding to 50/
6
0 Hz
Repe
at
1
nn
3.
for
1:
kK
do
4.
up
dat
e
ˆ
k
u
fo
r all
0
1
1
2
ˆ
ˆ
ˆˆ
2
ˆ
12
(
)
n
nn
ii
n
ik
i
k
k
n
k
fu
u
u
5.
up
dat
e
k
fo
r all
0
6.
i
f
2
k
,
th
en
no
u
pdate
o
f
else
2
1
1
0
2
1
0
ˆ
()
ˆ
()
n
k
n
k
n
k
ud
ud
7.
end
8.
Dual a
s
cent
for all
0
11
ˆ
ˆˆ
ˆ
()
nn
n
k
k
fu
9.
until
c
o
nverge
nce:
22
1
22
ˆˆ
ˆ
nn
n
kk
k
k
uu
u
3.
RESULTS
A
N
D
DI
SC
US
S
I
ON
The
per
f
o
r
m
a
nce of
the
pr
o
p
o
se
d ap
p
r
oac
h
is evaluate
d
with M
I
T
-
B
I
H
Ar
r
h
y
t
hm
ia database [
2
1]
.
The EC
G si
gn
al recor
d
s co
n
t
aining
po
wer
line distur
ba
nc
es at 60 Hz is consi
d
ere
d
for the experim
e
nting
pu
r
pose
.
It do
es not co
ntain
any
ha
rm
onics. In fi
gu
re 2
,
it shows a f
r
a
m
e of EC
G re
cor
d
2
28
with
60 Hz
po
we
r distu
r
ba
nce alo
n
g
with
its po
wer s
p
e
c
tral den
s
ity
(PSD
) pl
ot. F
r
o
m
the PSD
plo
t
, the p
r
ese
n
ce
of
6
0
Hz po
we
r distu
r
ba
nces
ca
n be s
een as a sm
all
lobe
at 60Hz.
This EC
G sig
n
a
l is then
gi
ve
n to
m
odified
VM
D al
go
rith
m
,
where t
h
e s
econ
d
m
ode is
fixe
d
with
no
rm
alized
fre
que
ncy
of 6
0
Hz. VM
D
crea
tes
IM
F'
s
base
d on
the par
a
m
e
ters
s
u
ch as
t
o
tal
n
u
m
b
er
o
f
m
odes,
bandwidth c
o
nstraint, ti
m
e
st
ep of th
e dual ascent etc. The
m
odes thus
ob
tained a
r
e sh
ow
n in fi
gu
re 3. T
h
e
second m
ode i
s
m
a
de to ope
rate for
60 Hz
. The
powe
r
disturbance
s
at 60Hz
will get c
a
ptured i
n
the
sam
e
m
ode. This ca
n
be clearly
vi
sible fr
om
figu
re 3
.
It is
obse
rve
d
that
t
h
e reconstructe
d
si
gnal has som
e
loss of
height (or m
a
gnitude
) at the location
where
there are R-
pe
aks. T
h
e hei
g
h
t
s of R
-
p
eaks
are really cruci
a
l for
analysis purpose. The lost m
a
gnitude
o
f
the
peak ca
n be se
en in the m
ode corre
sp
o
ndi
ng
to interfere
nce
.
So a
threshol
ding step is introduc
e
d
in
the p
r
o
p
o
s
e
d m
e
thod
ol
og
y
to avoid the l
o
ss o
f
inf
o
rm
ation. T
h
e im
por
tance
of
thre
sh
oldi
n
g
ca
n
be
u
nde
rsto
od
by
o
b
se
rvi
n
g
the
sm
all peak
like
sig
n
al sam
p
les in
the sec
o
nd
m
ode
at
several locations. T
h
ese locat
ions are m
a
rke
d
with re
d ri
ng
s in fig
u
re
3.
Hence
,
by
fin
d
i
ng a thre
sh
old
as an
avera
g
e
on e
n
ergy
, t
hose
sm
all peaks ca
n
be ext
r
acted,
a
nd is a
d
ded
ba
ck to t
h
e rec
o
nstr
ucted si
gna
l. No
w
the rec
o
nstructed signal
will be the
clear E
C
G signal
without PL
I. Figure
4
shows PSD
of PL
I re
m
ove
d
reco
nstr
ucted
EC
G signal. F
r
om
the PSD it
can be o
b
se
rve
d
that the lobe at 60Hz is not prese
n
t. T
h
is exhi
bits
the p
o
we
r
of m
odi
fied
VM
D a
l
go
rithm
to exactly
take out th
e specifie
d
f
r
e
que
ncy
an
d t
h
e
near
by
f
r
eq
ue
ncies
are
not all a
ffe
cted.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Modified V
a
riational
Mode
D
ecom
p
osition for P
o
wer
Line
Interfere
n
ce R
e
mov
a
l in …
(
N
eethu M
o
ha
n
)
15
5
Consi
d
er a
not
her sce
n
ari
o
,
whe
r
e the EC
G signal
co
ntains 5
0
Hz
p
o
w
er line
noise
s alon
g with
harm
onics in it
. I
n
this case, t
h
e sec
o
n
d
m
o
d
e
of
VM
D al
g
o
rithm
is fixed
fo
r capt
u
ri
ng
f
r
eq
ue
ncies o
f
50
Hz
and
the t
h
ir
d m
ode
is fi
xed
f
o
r
captu
rin
g
t
h
e
od
d
harm
onics
of
1
5
0
Hz
pre
s
ent in t
h
e si
gn
al. The
sig
n
al a
n
d
its
PSD
plot are
give
n in fi
gu
re
5. The c
o
r
r
es
po
n
d
in
g m
odes obtaine
d are
give
n in fi
gu
re
6. Fr
om
the
m
odes
obtaine
d,
it is obs
er
ved
that t
h
e sec
o
nd a
n
d
third m
odes
ca
ptu
r
ed
the
p
o
w
e
r line
fu
n
d
am
ental fre
q
u
enc
y
an
d
the odd
harm
onics present in
the no
isy
EC
G
signal exactly
.
Hence
,
fo
r rec
onst
r
uctio
n,
re
m
oving th
ose
m
odes
will result in a
PLI
free
signal
. Figure
7 shows the nois
y a
n
d noise
rem
oved ECG signa
l
s along
with t
h
e PSD
plot.
Figu
re 2.
EC
G
signal with PL
I
at 60
Hz
an
d cor
r
es
po
n
d
in
g PSD
Figu
re
3.
IM
F
’
s o
b
taine
d
th
ro
ug
h m
odifie
d
VM
D
o
f
rec
o
r
d
22
8
The
propose
d
m
odified VM
D algorithm
is com
p
ared
with the conventi
onal
notch filtering
a
p
proach.
In
notch
filtering, whe
n
the i
n
terfe
re
nce fundam
e
ntal fre
quency is slight
ly deviated
from
the 50/
60
Hz, the
notc
h
filters fa
il to rem
ove the interfe
re
nce
prese
n
t in
the
signal. From
t
h
e e
xpe
rim
e
nts, it can
also
observe
d
that the
notc
h
filters com
p
letely fails to pic
k
up t
h
e
devia
tions
occuring in hi
gh
er order
ha
rm
onics of
t
h
e
interfe
rence
.
H
o
we
ve
r the
p
r
op
ose
d
al
go
rithm
successf
u
lly rem
oves the
interfe
rence
s
unde
r
both situa
tions.
Figu
re
8.a a
n
d
8.
b re
pre
s
ents
the PS
D pl
ot
of t
h
e p
r
o
p
o
se
d m
odified
V
M
D alg
o
rithm
and
fig
u
re
8
.
c
and
8.
d
represe
n
ts
the traditional notch filtering
PSD plot. Fr
om
the pl
ots it ca
n
be see
n
t
h
at the
notc
h
filtering
co
m
p
letely f
a
il
s to
p
i
ck
up
the in
ter
f
e
r
e
n
ce
wh
en
th
e
f
unda
m
e
n
t
al f
r
e
q
u
e
n
c
y is sligh
tly d
e
v
i
ated fr
o
m
6
0
Hz.
Whe
r
e as the
proposed approa
ch
successfully rem
oves the
interfe
re
nce
present in t
h
e si
gna
l.
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. 1, Feb
r
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20
1
6
: 15
1 – 15
9
15
6
Figu
re
4.
(a
),
(
b
)
N
o
isy
rec
o
r
d
22
8 a
n
d its P
S
D; (
c
),
(
d
)
de
noise
d
reco
r
d
22
8 a
n
d P
S
D
o
f
den
o
ised
p
o
r
tion
Figu
re 5.
EC
G
signal with PL
I
at 50
Hz
an
d its
harm
onics a
n
d
co
rre
sp
o
ndi
ng
PS
D
of
the
signal
Fig
u
r
e
6
.
Modes ob
tain
ed
thro
ugh
m
o
d
i
f
i
ed
VMD
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Modified V
a
riational
Mode
D
ecom
p
osition for P
o
wer
Line
Interfere
n
ce R
e
mov
a
l in …
(
N
eethu M
o
ha
n
)
15
7
Figu
re
7.
(a
),
(
b
)
N
o
isy
EC
G
signal a
n
d its P
S
D; (
c
), (d) EC
G signal a
f
ter
noise
cancellation a
n
d its PSD
3.
1. Si
gn
al
to
Noi
s
e
R
a
ti
o
The
per
f
o
r
m
a
nce of t
h
e p
r
o
p
o
se
d ap
pr
oac
h
is also evaluat
e
d in term
s of
inp
u
t an
d o
u
tp
ut sig
n
al to
noise ratio
(S
NR
). T
h
e in
pu
t SNR
(SNR
in
) is calculated
by finding the ratio
of the
power of the clean E
C
G
signal t
o
the
powe
r
of t
h
e int
e
rfe
rence
signa
l
.
When th
e
p
o
w
er lin
e dist
ur
bance
inc
r
ease
s, the
value
of
input
SNR
will be low. T
h
e output SNR (SNR
out
) is calculated
by finding the
ratio
of the
power
of the esti
m
a
ted
signal to t
h
e powe
r
of the
error in the estim
ation. Th
e c
o
r
r
ectness
o
f
the p
r
op
ose
d
a
p
p
r
oach is c
h
e
c
ked
b
y
vary
in
g the S
N
R
in
f
r
o
m
-
1
0
dB to
3
0
d
B
and th
e co
rr
espond
ing
SNR
out
va
lues are tabulated in Ta
ble 1.
To do
the expe
rim
e
nts, EC
G signal
reco
rd
10
1 o
f
M
I
T-B
I
H A
r
r
h
y
t
h
m
ia database is chosen.
W
h
ile it was observe
d
that, for low SNR
in
signal, t
h
e last
m
ode of
the VM
D
d
o
es
n’t co
ntain a
n
y
signal in
fo
rm
ation.
Hence
,
du
rin
g
reco
nstr
uctio
n,
av
oidin
g
t
h
is
m
ode gives
a s
i
gnal
with im
pro
v
e
d
S
N
R
out
.
Table
1. R
e
s
u
lts o
f
e
v
aluatio
n
on
EC
G
rec
o
r
d
1
0
1
Signal Record
SNR
in
SNR
ou
t
101
28.
698
2
49.
858
5
101
22.
677
6
47.
610
8
101
16.
657
0
44.
084
7
101
11.
796
3
30.
594
7
101
2.
6776
22.
698
3
101
-
0
.
8442
20.
520
7
101
-
6
.
8648
14.
624
0
101
-
9
.
3636
12.
116
9
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I
S
SN:
2
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-87
08
IJEC
E V
o
l. 6, No
. 1, Feb
r
uar
y
20
1
6
: 15
1 – 15
9
15
8
Figure
8. (a
),
(b) Perform
ance of m
odified VMD
al
gorithm
;
(c),
(d) Pe
rform
a
nce of tra
d
itional
notc
h
filter
4.
CO
NCL
USI
O
N
The pr
o
pose
d
app
r
oach usi
n
g
m
odified va
r
i
ati
onal m
ode decom
positio
n
clearly
rem
oves the
50/
60
Hz inter
f
ere
n
c
e
and its
harm
onics
fr
om
the EC
G rec
o
r
d
i
ngs.
By co
rr
ectly f
i
x
i
ng
th
e
bounda
ries for the
signal
in VM
D m
o
de calculation, it accurate
ly
extracts the
specified fre
q
uenc
y, wit
h
out altering the
nea
r
by
fre
que
ncies. Du
rin
g
the re
con
s
tructio
n o
f
sig
n
al
by
e
x
cluding the
m
ode that captured t
h
e noise and
harm
onics, it is sho
w
n that the reco
nstr
u
c
ted sign
al ha
ve a hi
gh S
N
R
out
co
m
p
ared to SNR
in
. F
r
om
the
obs
er
vation
s
m
a
de it can be conclu
de
d tha
t
, the pro
p
o
sed
m
odified VM
D base
d ap
pr
o
ach is appr
o
p
ri
ate for
powe
r line interfe
rence ca
ncellation from
ECG signals. It can also conclude
that the proposed appraoc
h
acts
as a
very sharp notch
filter
by
rem
oving the
specified frequency.
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0
8
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a
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ecom
p
osition for P
o
wer
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n
ce R
e
mov
a
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o
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