Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 1
,
Febr
u
a
r
y
201
5,
pp
. 64
~70
I
S
SN
: 208
8-8
7
0
8
64
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
Detection of Atrial Fibrillation
using Autoregressive modeling
K. P
a
dm
avathi*
and
K.
Sri
Ramakrishn
a**
*Departm
ent of ECE,GRIE
T,
Ind
i
a
**Departmrnt of
ECE,VRSEC
, I
ndi
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 14, 2014
Rev
i
sed
D
ec 11
, 20
14
Accepted Dec 28, 2014
Atrial fibr
ill
atio
n (AF) is the com
m
on
arrhy
t
h
m
ia that c
a
us
es
death in t
h
e
adults. We measured AR coeff
i
cients
using Burgs method for each
15 secon
d
s
e
gm
ent of EC
G. Thes
e
fea
t
ur
es
are
cl
as
s
i
fied
us
ing the
differ
e
nt s
t
a
tis
ti
ca
l
classifiers: kernel SVM and
KNN cl
assifier. The performance of the
algorithm
was
evalu
a
ted
on s
i
gnals from
MIT-BIH Atria
l
Fibrilla
tion
Database. The effect of AR mo
del or
der and d
a
ta length was tested on th
e
classification results. Th
is method shows better results
can
be used fo
r
pract
ica
l
use
in
t
h
e c
lini
c
s.
Keyword:
AR c
o
efficients
Atrial Fibrillati
o
n
B
u
r
g
m
e
t
hod
K
NN
M
I
T/
B
I
H
dat
a
base
SVM
Copyright ©
201
5 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
:
K. Padm
avathi
GRIET
Hy
de
raba
d,
I
n
di
a
+-
91
94
900
142
93
Em
ai
l
padm
a386
@
g
m
a
il
.com
1.
INTRODUCTION
Com
puterized electrocardiogra
m
cl
assification can hel
p
t
o
re
duce
health care
costs.
ECG re
sults
indicate the presence of AF a
l
arming the
st
at
us of
pat
i
e
nt
’s
heart
.
D
u
ri
ng
AF
, the
hearts
atria are quic
k
er tha
n
n
o
rm
al b
eatin
g. As th
e b
l
o
od is no
t ej
ected
co
m
p
letely
out
o
f
at
ri
a,
t
h
e
r
e
m
i
ght
be c
h
a
n
ces
of
f
o
rm
ati
on
o
f
bl
o
od cl
ot
s i
n
t
h
e at
ri
a res
u
l
t
i
ng i
n
i
n
c
r
eased risk
of stroke.
Electrocardiogram
(EC
G
) i
s
one
o
f
t
h
e
usef
ul
t
o
o
l
for
AF detection.
AF can be
detected by observi
n
g
three main
m
o
rp
hological
features
in t
h
e EC
G as
s
hown
in Figure
1. T
h
ey are
P wa
ve a
b
se
nc
e.
Inst
ea
d of
P w
a
ves fl
uct
u
at
i
n
g wave
f
o
rm
s
(f
-wa
v
es
).
Heart rate
irregu
larity.
There a
r
e se
veral m
e
thods to detect the
features
of
AF
[9]
.
M
e
t
h
o
d
s
base
d o
n
R
R
i
n
t
e
rval
a
r
e
pr
o
pose
d
i
n
[
1
]
,
[2]
.
P wa
v
e
based m
e
t
hods are p
r
ese
n
t
e
d i
n
[1]
,
[
2
5
]
. The R
R
i
n
terval
, P wa
ve
base
d
m
e
t
hods
have
som
e
l
i
m
i
t
a
t
i
ons
[8]
.
Whe
n
t
h
e EC
G c
h
an
ges q
u
i
c
kl
y
bet
w
een r
h
y
t
h
m
s or whe
n
At
ri
al
Fibrillation ta
kes place
with regular
vent
ricular rates
,
the
m
e
thods
bas
e
d on RR inte
rval fail in ac
curate
d
e
tectio
n
[2
].
Detectin
g
th
e ab
sen
ce o
f
P
wav
e
is d
i
fficu
lt d
u
e
to
its sm
a
l
l a
m
p
litu
d
e
[25
]
. To
stud
y the atria
l
act
i
v
i
t
y
duri
n
g
AF
, fre
que
nc
y
dom
ai
n
t
ech
ni
q
u
es ha
ve b
een pr
o
pose
d
i
n
[2
2]
, [1
9]
, [
21]
,
[
20]
.
Ve
n
t
ri
cul
a
r
activity needs to be cancele
d
before
a
ppl
y
i
n
g
FFT. I
n
p
r
es
ence of
noi
se [
20]
t
h
i
s
cancel
l
a
t
i
on pr
ocess
m
a
y
be
diffic
u
lt and invol
ves
high c
o
m
putation. Morphological fea
t
ures a
r
e
di
ffic
u
lt to
detect because t
h
ey change
fr
om
pat
i
e
nt
to pat
i
e
nt
.
Fr
o
m
st
at
i
s
t
i
cal
f
eat
ures
(A
R
features
) we c
a
n easily classify AF signa
l
s. AR
coefficients
[24] are
the
sim
p
lest an
d
be
st
fe
at
ures
f
o
r
A
F
c
l
assi
fi
cat
i
on.
T
h
i
s
pape
r em
phasi
zes
o
n
t
h
e
use
o
f
AR
m
odel
i
n
g
t
o
di
scri
m
i
nat
e
bet
w
ee
n
N
o
n
-
AF a
n
d
AF
wa
ves.
Pre
v
i
ous
s
t
udi
es cl
ai
m
t
h
at
, t
h
e
usa
g
e
o
f
AR
coefficient feat
ures
yield bette
r re
sults tha
n
orig
in
al tim
e series
features [24],
[23].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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:
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0
8
Detectio
n
o
f
At
ria
l
Fib
r
illa
tion
u
s
ing
Au
toreg
r
essive
mo
d
e
l
i
n
g
(
K
. P
a
dm
a
v
at
hi
)
65
Fig
u
re
1
.
(a)
No
rm
al Syn
u
s
R
h
yth
m
; (b
)
Atri
al Fib
r
illatio
n
Fi
gu
re
2.
EC
G
C
l
assi
fi
cat
i
on f
l
ow c
h
a
r
t
anal
y
s
i
s
2.
METHOD
2.
1. D
a
t
a
The
pr
op
ose
d
al
go
ri
t
h
m
i
s
est
i
m
a
t
e
d based
on t
h
e dat
a
s
e
gm
ent
s
col
l
ect
ed fr
om
M
I
T-B
I
H
At
ri
al
Fib
r
illatio
n
Datab
a
se [16
]
. The AF classifica
tio
n
flow
d
i
ag
ra
m
as sho
w
n
i
n
Tab
l
e
1
.
Tabl
e
1. M
I
T-
B
I
H R
e
c
o
r
d
N
u
m
b
ers
Nor
m
al
Data
AF Data
1626
5,
1627
2,
162
73,
1642
0,
1648
3,
165
39,
1677
3,
1678
6,
167
95,
1705
2,
1745
3,
181
77,
1818
4,
1908
8,
190
90,
1910
3,
1914
0,
198
30.
0401
5,
0404
3,
040
48,
0412
6,
0474
6,
049
08,
0493
6,
0509
1,
051
21,
0526
1,
0442
6,
064
53,
0699
5,
0716
2,
078
59,
0787,
07
910,
08
21
5,
0821
9,
0837,
08
40
5
0843
4,
0845
5.
2.
2. N
o
i
s
e Re
mo
val
Th
e
first step
in
our algorithm
is d
i
v
i
d
i
n
g
th
e si
gn
al in
t
o
d
e
sired leng
th
.
After seg
m
en
tatio
n
,
we
co
nsid
ered
each
seg
m
en
t as
a co
lu
m
n
o
f
a m
a
trix
fo
r com
p
act n
o
t
atio
n and
u
s
ed
sgolay filterin
g
[15
]
to
rem
ove t
h
e
bas
e
l
i
n
e wa
nde
r
p
r
esent
i
n
t
h
e
si
gnal
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-87
08
IJEC
E V
o
l
.
5, No
. 1, Feb
r
uar
y
20
1
5
:
6
4
– 70
66
Fi
gu
re
3.
U
p
si
gnal
:
B
a
sel
i
n
e
noi
se
si
g
n
al
,
D
o
w
n
si
gn
al
:
B
a
sel
i
n
ewa
nde
r
r
e
m
oved
si
g
n
al
2.
3. Fea
t
ure
E
x
tr
acti
on
2.
3.
1. C
o
mpu
t
ati
o
n of
A
R
c
o
effi
ci
ents
Aut
o
re
gre
ssi
ve
m
odel
i
s
base
d
on
t
h
e
pri
n
ci
pl
e o
f
l
i
n
ea
r
pr
edi
c
t
i
on.
I
n
AR
m
odel
[1
7]
ea
ch sam
p
l
e
i
s
pre
d
i
c
t
e
d
base
d
on t
h
e l
i
n
ea
r
com
b
i
n
at
i
on
of
pre
v
i
o
us
sam
p
l
e
s. Let
f
1
,
f2
,
f3
, ..
.,
fn
be
t
h
e
t
i
m
e
seri
es. T
h
e
p
th
o
r
d
e
r au
t
o
reg
r
essiv
e
tim
e series (written
as
AR
(p
))
o
f
F(n
)
is g
i
v
e
n b
y
t
h
e th
e eq
u
a
ti
o
n
.
(1
)
Wh
ere P is th
e
m
o
d
e
l ord
e
r
(
n
) is assu
m
e
d
to
b
e
wh
ite Gau
ssian
noise wi
th zero m
ean and
va
riance
2
. Th
e
AR
m
odel
par
a
m
e
t
e
rs
j
are
calculated using
Yule
-W
al
ker, Burg
s m
e
thods and the s
e
lected
m
odel orde
r
expe
ri
m
e
nt
al
ly.
2.
3.
2. Yul
e
-w
a
l
ker
Me
th
od (
Y
W)
(2
)
is Pred
icted
v
a
lu
e
(3
)
(4
)
j
is p
r
ed
icted
to
m
i
n
i
mize error
(
n
). Mean squ
a
re v
a
l
u
e
of th
e error
will b
e
m
i
n
i
m
u
m
if
0
(5
)
R
=
r
(6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Detectio
n
o
f
At
ria
l
Fib
r
illa
tion
u
s
ing
Au
toreg
r
essive
mo
d
e
l
i
n
g
(
K
. P
a
dm
a
v
at
hi
)
67
=
R
-1
r
(7
)
2.
3.
3. B
u
rg
’s
meth
o
d
Input signal F(
n)
, n=1, 2, .
..,
N, and let us consi
d
er the
ba
ckwa
r
d
and forwa
r
d linea
r pr
edictions
of
or
der
k
= 1, 2,
...m
(8
)
(9
)
whe
r
e
m
and
m
are
the
forward and
bac
k
ward pr
ediction coefcie
n
ts
res
p
ectively
;
1
,…,
(1
0)
(1
1)
Whe
r
e
m
and
m
are the forward and
backward
pred
ictio
n
resi
d
u
a
ls.
No
te th
at
m
= 1
m
= 1 by
de
fi
ni
t
i
on.
Th
e
FIR
p
r
ed
ictio
n
erro
r filter or
th
e lattice filter is g
i
v
e
n b
y
th
e set
o
f
recursiv
e equ
a
tion
s
f
m
(
n
) =
f
m
-1
n
+
k
m
b
m
-1
(
n
– 1)
(1
2)
b
m
(
n
) =
k
m
f
m
–1
(
n
– 1)
(1
3)
m
=
1,2,
3.
...
p. Whe
r
e
K
m
are the reflection coefficie
n
ts of the
m
th
recu
rsio
n
step. Th
e in
itial v
a
lu
es o
f
the
residuals are
f
0
(
n
) =
b
0
(
n
) =
f
(
n
)
2
∑
1
∑
(1
4)
m
(
k
) =
m
–1
(
k
) +
k
m
m
–1
(
k
–
m
) (
1
5
)
m
(0)
=
1;
m
(
m
) =
k
m
,
whe
r
e m
=
1 t
o
p a
n
d
k=
1 t
o
m
.
Al
l
-
p
o
l
e
p
r
edi
c
t
i
on co
ef
fi
ci
ent
s
m
e
t
hod ex
cel
i
n
com
p
ari
s
on
t
o
t
h
e a
u
t
o
co
rrel
a
t
i
o
n m
e
t
h
o
d
bec
a
use
t
h
ey
decrease
the t
o
tal prediction
errors a
n
d the data se
quence is not s
u
bjected
to
an
y
w
i
nd
ow
f
u
n
c
ti
o
n
.Th
e
ad
v
a
n
t
ag
e
o
f
th
e form
er
meth
od
is th
at it is co
m
p
u
t
atio
n
a
lly efficien
t, stab
le and h
a
s h
i
gh
freq
u
e
n
c
y
reso
l
u
tio
n. Th
e selectio
n
o
f
the Au
toregressi
v
e
m
o
d
e
l or
d
e
r is of forem
o
st i
m
p
o
r
tan
ce in
th
e classificatio
n of
AF.
The c
o
rre
ct num
ber of
Aut
o
re
gre
ssive
coefficients
are d
e
term
in
ed
u
s
ing
trial and erro
r m
e
th
o
d
. Th
e
coef
fi
ci
ent
s
of
or
der
4
,
8, 1
6
a
r
e used
f
o
r
o
u
r
st
udy
.
2.
4. Cl
as
si
fi
ca
ti
on
The
perform
ance of two
diffe
r
ent cl
a
s
s
i
f
i
er
s
S
V
M an
d k-NN
ar
e
o
b
t
a
i
ne
d
with the
AR
coefficients
as i
n
put
.
2.
4.
1. Kernel Supp
ort
Vec
t
r
o
r Mac
h
ines (KSVM)
A ke
rnel Support Vect
or Ma
chine [26] is a supe
rv
ise
d
machine learning t
echnique applicable for
classificatio
n
.
It is an
ex
amp
l
e for no
n-p
r
o
b
a
b
ilistic
b
i
n
a
ry lin
ear classifier, estab
lish
e
d
fro
m
Sta
t
istical
Learn
i
n
g
Th
eory [27
]
. It exh
i
b
its h
i
gh
accu
racy and
h
a
s cap
ab
ility to
d
eal with
h
i
g
h
d
i
m
e
n
s
io
n
a
l d
a
t
a
sequences
. T
h
e
support
vect
or m
achine m
a
kes use
of
pattern rec
o
gn
ition a
m
ong two
point classes by
Support
Vectors (SV).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 1, Feb
r
uar
y
20
1
5
:
6
4
– 70
68
Kernels are
functions that pe
rform
s
som
e
mat
h
em
ati
cal
operat
i
ons
o
n
x
1
,
x2
de
pen
d
i
n
g
on t
h
e sel
ect
i
o
n o
f
t
h
e
k
e
rn
el fun
c
tion.
(1
6)
(1
7)
Gaus
sian
ke
rne
l
can
be e
x
pres
sed as
(1
8)
Fi
gu
re
4.
Ke
rn
el
t
r
i
c
k
Li
near
ke
rnel
c
a
n
be e
x
p
r
esse
d as
(1
9)
(2
0)
k
e
rn
el fun
c
tions can
b
e
app
lied
to
no
n-lin
ear d
a
ta so
th
at non-linea
r feature
s
are co
nv
erted in
to
lin
ear featu
r
es
as sh
o
w
n
i
n
Fi
gu
re
4.
B
y
usi
n
g
ker
n
el
t
r
i
c
k
feat
u
r
es c
a
n
be
rep
r
ese
n
t
e
d i
n
a
hi
g
h
di
m
e
nsi
onal
feat
ur
e
space.Li
near cl
assifier m
e
thods used
t
o
produce non-linear classification is
the m
a
j
o
r advantage
of
kernel
s.As
EC
G i
s
an
o
n
e
di
m
e
nsi
onal
si
gnal
,
x1 i
s
x
2
are t
h
e f
eat
ur
es of a t
w
o
di
st
i
n
ct
EC
G rec
o
r
d
i
n
gs.
Li
nea
r
an
d
Gaus
si
an
ke
rne
l
s are a
ppl
i
e
d
o
n
t
h
e ECG signal with
SVM cl
assifier.
2.
4.
2. K-
Ne
ar
est Nei
g
h
b
o
u
r
(K
NN
)
In
t
h
e
K-
nea
r
e
s
t
nei
g
h
b
o
r
s
ru
l
e
, a ne
w
vect
o
r
y
of a
ne
w
cl
ass is classifie
d
base
d
on
the distance from
nearest
mean
vector. The distance from
v
ector y a
n
d the ce
ntroid of the
m
th
cluster
z
l
is calcul
a
ted as the
Euclidea
n
distance
(2
1)
m
i
s
t
h
e cl
ust
e
r i
nde
x,
n i
s
t
h
e n
u
m
b
er of
t
h
e param
e
t
e
rs used a
n
d l
t
h
e param
e
t
e
r i
ndex
.
Vect
or y
can
b
e
classified in to
class k at
which
s
m
is m
i
nim
u
m
.
W
e
selected the
value
of
k
as 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Detectio
n
o
f
At
ria
l
Fib
r
illa
tion
u
s
ing
Au
toreg
r
essive
mo
d
e
l
i
n
g
(
K
. P
a
dm
a
v
at
hi
)
69
3.
RESULTS
The
5,15 and
30 second length se
quence
s
from
each
rec
o
rding a
r
e considere
d
a
nd
AR coefficients
are calculated. The effect
of
m
odel
o
r
d
e
r on
classificatio
n resu
lts is in
v
e
stig
ated
. Fo
r t
h
e SVM an
d
K-NN
classifiers, 280 recordings are
given
fo
r trai
n
i
ng
(2
/
3
o
f
total reco
rd
i
n
gs) an
d
93
(1
/3
of to
tal reco
rd
i
n
g
s
) are
gi
ve
n f
o
r t
e
st
i
n
g
.
T
h
ree m
o
d
e
l
i
ng o
r
ders a
r
e use
d
t
o
di
ffe
rent
i
a
t
e
t
h
e p
r
op
ose
d
m
e
t
hod wi
t
h
ot
he
r m
e
t
h
o
d
s.
Classification accuracies
for diffe
re
nt
m
odel orders a
n
d differe
n
t leng
ths
are s
h
own in 2
to 4 Ta
bles.
The
res
u
l
t
s
o
f
t
h
ese m
e
t
hod
s are
sh
o
w
n
i
n
Ta
bl
es
2 t
o
4.
It
i
s
e
v
i
d
e
n
t
t
h
at
t
h
e
b
u
r
g
’
s
m
e
t
hod
wi
t
h
K
N
N
cl
assi
fi
er sh
ow
s best
resul
t
s
a
m
ong t
h
e t
w
o
cl
assi
fi
ers i
rres
p
ect
i
v
e o
f
t
h
e l
e
ngt
h
of
dat
a
seq
u
ence f
o
r m
odel
or
der
8
.
4.
CO
NCL
USI
O
N
In
th
is p
a
p
e
r t
h
e u
s
e of AR m
o
d
e
lin
g
for Atrial Fib
r
illatio
n
arrh
yth
m
ia
d
e
tectio
n
is ex
am
in
ed
. A
com
p
arison
of the
perform
ance
of SVM a
n
d kNN classi
fi
ers
o
n
si
gnal
s
f
r
om
M
I
T-B
I
H
At
ri
al
Fi
bri
l
l
a
t
i
on
Database is depicted. Anal
ysis effect of various
m
odel
orde
r’s
fo
r
di
ffe
rent
dat
a
segm
ent
l
e
n
g
t
h
s i
s
per
f
o
r
m
e
d. A
m
ong t
h
e t
w
o
cl
assi
fi
ers
K
NN
wi
t
h
B
u
r
g
’s m
e
t
hod ac
h
i
eved t
h
e be
st
resul
t
s
.
T
he m
i
nim
u
m
m
i
scl
a
ssi
fi
ed segm
ent
s
were
achi
e
ve
d i
n
5,
15
,
30
sec
o
n
d
segm
ent
s
fo
r t
h
e m
odel
or
der
8,
w
h
i
c
h
p
r
o
v
e
s
t
o
be
th
e b
e
st classificatio
n
ob
tained
.B
u
r
g
’
s m
e
t
h
od
sh
ows goo
d
resu
lts fo
r sh
ort d
a
ta seg
m
en
ts with
SVM
cl
assi
fi
er,Y
ul
e Wal
k
e
r
m
e
t
h
o
d
s
h
ows
go
o
d
resul
t
s
f
o
r dat
a
segm
ent
s
o
f
l
e
ngt
h 3
0
sec
o
n
d
s fo
r
m
odel
o
r
de
r 6
wi
t
h
KN
N cl
a
ssi
fi
er.
Sel
ect
i
n
g
t
h
e m
odel
or
der
an
d
seg
m
ent
l
e
ngt
h
d
e
pen
d
s
o
n
t
h
e
req
u
i
r
e
d
preci
s
i
on a
n
d
av
ailab
ility o
f
th
e co
m
p
u
t
at
io
n
a
l reso
urces.Th
is algo
rithm can
b
e
u
s
ed
for real ti
me d
e
tectio
n
of AF
si
gnal
s
.
T
he f
o
r
m
er proce
d
ure
s
for f
eat
ure e
x
t
r
act
i
on suc
h
a
s
vent
ri
c
u
l
a
r a
c
t
i
v
i
t
y
cancel
l
a
t
i
on an
d det
ect
i
on o
f
R
pea
k
,
w
h
i
c
h
are t
e
di
ous
i
n
n
a
t
u
re ca
n
be el
i
m
i
n
at
ed.
Tabl
e
2. C
l
assi
fi
cat
i
on
fo
r M
o
del
o
r
der
4
Accurac
y
Data
length
YW+S
VM
Burg+SVM
YW+
KNN
Burg+KNN
5
Sec
76.
9
92.
3
46.
1
38.
4
15
Sec
92.
3
76.
9
92.
3
92.
3
30
sec
92.
3
92.
3
76.
9
76.
9
Tabl
e
3. C
l
assi
fi
cat
i
on
fo
r M
o
del
o
r
der
6
Accurac
y
Data
length
YW+S
VM
Burg+SVM
YW+
KNN
Burg+KNN
5
Sec
76.
9
92.
3
53.
8
61.
5
15 Sec
84.
6
100
69.
2
92.
3
30
sec
92.
3
100
100
92.
3
Tabl
e
4. C
l
assi
fi
cat
i
on
fo
r M
o
del
o
r
der
8
Accurac
y
Data
length
YW+S
VM
Burg+SVM
YW+
KNN
Burg+KNN
5
Sec
76.
9
92.
3
84.
6
100
15 Sec
84.
6
100
84.
6
100
30 sec
92.
3
100
92.
3
100
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