Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
6,
No.
5,
October
2016,
pp.
2197
–
2204
ISSN:
2088-8708
2197
Empirical
Mode
Decomposition
(EMD)
Based
Denoising
Method
f
or
Heart
Sound
Signal
and
Its
P
erf
ormance
Analysis
Amy
H.
Salman
,
Nur
Ahmadi
,
Richard
Mengk
o
,
Armein
Z.
R.
Langi
,
and
T
ati
L.
R.
Mengk
o
School
of
Electrical
Engineering
and
Informatics,
Institut
T
eknologi
Bandung
Article
Inf
o
Article
history:
Recei
v
ed
May
25,
2016
Re
vised
July
11,
2016
Accepted
July
27,
2016
K
eyw
ord:
Heart
Sound
Denoising
Empirical
Mode
Decomposition
ABSTRA
CT
In
this
paper
,
a
denoising
method
for
heart
sound
signal
bas
ed
on
empirical
mode
decompo-
sition
(EMD)
is
proposed.
T
o
e
v
aluate
the
performance
of
the
proposed
method,
e
xtensi
v
e
simulations
are
performed
using
syntheti
c
normal
and
abnormal
heart
sound
data
corrupted
with
white,
colored,
e
xponential
and
alpha-stable
noise
under
dif
ferent
SNR
input
v
alues.
The
performance
is
e
v
aluated
in
terms
of
signal-to-noise
ratio
(SNR),
root
mean
square
er
-
ror
(RMSE),
and
percent
root
mean
square
dif
ference
(PRD),
and
compared
with
w
a
v
elet
transform
(WT)
and
total
v
ariation
(TV)
denoising
methods.
The
simulation
results
sho
w
that
the
proposed
method
outperforms
tw
o
other
methods
in
r
emo
ving
three
types
of
noises.
Copyright
c
2016
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Amy
H.
Salman
School
of
Electrical
Engineering
and
Informatics
Bandung
Institute
of
T
echnology
Jl.
Ganesha
No
10,
Bandung
40132,
Indonesia
Email:
amy@stei.itb
.ac.id
1.
INTR
ODUCTION
Cardio
v
ascular
disease
(CVD)
has
long
been
the
leading
cause
of
death
throughout
the
w
orld
with
an
estimate
of
17.3
million
people
died
in
2008
and
is
predicted
to
reach
23.3
million
in
2030
[1].
According
to
WHO
report,
more
than
three
quarters
of
the
death
tak
es
place
in
lo
w-
and
middle-income
countries
[2].
A
lo
w-cost
and
non-in
v
asi
v
e
diagnosis
system
based
on
heart
sound
can
be
used
to
minimize
the
risk
of
patients
going
into
se
v
ere
condition
and
reduce
the
financial
b
urden
through
an
early
accurate
diagnosis
follo
wed
by
appropriate
treatment.
This
electronic
auscultation
technique
utilizes
adv
anced
si
gnal
processing
with
f
ast
computation
capability
,
thanks
to
the
adv
ancement
of
computer
technology
.
Ho
we
v
er
,
to
produce
an
accurate
diagnosis
result
is
not
an
easy
task
since,
in
practice,
heart
sound
signal
is
al
w
ays
contaminated
with
noise
and
interference
from
v
arious
sources
such
as
background
noise,
po
wer
interference,
breathing
or
lung
sounds,
and
skin
mo
v
ements
in
the
surrounding
en
vironment.
Thus,
signal
denosing
method
is
of
paramount
importance
to
remo
v
e
all
these
unw
anted
noise.
A
poor
signal
denoising
method
can
lead
to
catastrophic
result.
The
most
widely
used
method
for
denoising
heart
sound
signal
is
based
on
w
a
v
elet
transform
(WT)
[3–5],
a
po
werful
signal
analysis
tool
with
the
ability
to
repres
ent
a
signal
simultaneously
in
the
time
and
frequenc
y
.
Despite
the
f
act
that
the
w
a
v
elet
based
denoising
method
has
been
pro
v
en
to
be
able
to
pro
vide
good
denoising
performance,
ho
we
v
er
,
it
suf
fers
from
se
v
eral
limita
tions.
It
requires
predefined
basis
function
selection
(from
too
man
y
choices)
suited
to
signal
under
consideration,
which
limits
the
fle
xibility
of
the
method.
In
addition,
the
decomposition
le
v
el
and
thresholding
technique
of
w
a
v
elet
denosing
also
need
to
be
carefully
considered.
F
ailing
to
choose
the
right
de-
composition
le
v
el
and
thresholding
technique
will
result
in
bad
denoising
performance.
V
ar
ghees
and
Ramachandran
emplo
yed
another
alternati
v
e
method
based
on
T
otal
V
ariation
(TV)
[6].
TV
method
has
been
mostly
used
for
image
denoising
due
to
its
great
benefit
of
preserving
and
enhancing
important
features
such
as
edge
in
images.
Ev
en
though
it
can
be
used
for
denoising
1D
signal,
ne
v
ertheless,
there
are
v
ery
fe
w
literatures
e
xploiting
TV
method
for
deonising
heart
sound.
The
highly
non-stationary
property
of
heart
sound
signal
is
not
suitable
to
the
nature
of
TV
method
which
performs
best
on
piece
wise
constant
signals
[7].
In
addition,
Figueiredo
et.
al.
mentioned
that
the
performance
of
TV
J
ournal
Homepage:
http://iaesjournal.com/online/inde
x.php/IJECE
Evaluation Warning : The document was created with Spire.PDF for Python.
2198
ISSN:
2088-8708
method
could
produce
better
result
than
older
w
a
v
elet
based
methods,
b
ut
it
w
as
outperformed
by
recent
state-the-art
w
a
v
elet
based
methods
[8].
Empirical
mode
decomposition
(EMD),
a
relati
v
ely
ne
w
non-linear
a
n
d
non-stationary
signal
analysis
method
[9],
of
fers
interesting
feature
of
adapti
v
e
and
data-dri
v
en
decomposition
capability
.
Since
its
inception,
EMD
has
attracted
man
y
rese
archers
around
the
globe
to
utilize
it
as
denoising
method
[10–12].
Ho
we
v
er
,
the
mechanism
of
discriminating
the
noise
and
useful
information
within
decomposed
signal
and
fitti
n
g
it
to
heart
sound
signal
to
get
good
signal
reconstruction
performance
remains
challenging.
In
this
paper
,
we
propose
an
EMD
based
denoising
method
for
heart
sound
signals.
T
o
measure
the
per
-
formance
of
our
proposed
method,
we
perform
repeated
simulation
o
v
er
normal
and
abnormal
synthetic
heart
sound
signal
b
urried
under
dif
ferent
types
of
noise
with
SNR
input
v
alues
ranging
from
0
to
15
dB.
The
qualitati
v
e
e
v
alu-
ation
is
performed
by
visual
inspection
while
qu
a
ntitati
v
e
e
v
aluation
is
carried
out
by
using
three
standard
metrics:
signal-to-noise
ratio
(SNR),
root
mean
square
error
(RMSE),
and
percent
root
mean
square
dif
ference
(PRD).
The
rest
of
this
paper
is
or
g
anized
as
follo
ws.
Section
2.
describes
EMD
denoising
method
wi
th
brief
intro-
duction
to
its
theoritical
background
and
mathematical
notation.
Section
3.
e
xplains
the
imulation
setting
and
data.
The
simulation
results
and
performance
analysis
of
both
qualitati
v
e
and
quantitati
v
e
are
gi
v
en
in
Section
4.
Finally
the
conclusion
is
dra
wn
in
Section
5.
2.
EMD
DENOISING
METHOD
2.1.
Empirical
Mode
Decomposition
(EMD)
Empirical
mode
decom
p
os
ition
(EMD),
since
firstly
proposed
by
Huang
in
1998
[9],
has
g
ained
popularity
as
data
analys
is
method
especiall
y
for
non-stationary
and
non-linear
signals
such
as
biomedical
(including
heart
sound)
signals.
EMD,
in
contrast
to
other
methods
such
w
a
v
elets
and
fourier
whic
h
require
predefined
basis
function,
is
fully
data-dri
v
en
method
that
does
not
require
an
y
a
priori
kno
wn
basis.
EM
D
adapti
v
ely
decomposes
a
signal
into
a
series
of
simple
oscillatory
AM-FM
components
called
as
intrinsic
mode
functions
(IMFs)
through
itera
ti
v
e
procedure
(kno
wn
as
sifting
).
An
IMF
is
defined
as
a
function
that
satisfies
tw
o
conditions:
the
number
of
e
xtrema
(maxima
and
minima)
and
zero
crossing
must
be
equal
or
dif
fer
by
at
most
1;
and
the
a
v
erage
v
alue
of
the
en
v
elopes
deri
v
ed
from
local
maxima
and
minima
is
(approximately)
zero.
Despite
EMD
still
being
lack
of
a
solid
mathematical
foundation
which
could
be
used
for
theoritical
analysis
and
performance
e
v
aluation,
it
has
been
pro
v
en
to
pro
vide
interesting
and
useful
results.
The
sifting
procedure
of
EMD
for
decomposing
the
signal
x
(
n
)
into
IMFs
is
systematically
described
as
follo
ws:
1.
Specify
all
the
local
e
xtrema
(maxima
and
minima)
of
x
(
n
)
2.
Interpolate
between
local
maxima
using
cubic
spline
line
to
form
upper
en
v
elope
e
max
(
n
)
and
local
minima
to
form
lo
wer
en
v
elope
e
min
(
n
)
3.
Calculate
the
local
mean
based
on
formed
upper
and
lo
wer
en
v
elopes,
m
(
n
)
=
(
e
max
(
n
)
+
e
min
(
n
))
=
2
4.
Substract
this
mean
from
the
original
signal
to
e
xtract
the
detail
d
(
n
)
=
x
(
n
)
m
(
n
)
.
If
d
(
n
)
does
not
satisfy
IMF
conditions
(stopping
criteria),
the
procedure
1)
to
4)
are
iterated
with
ne
w
input
signal
d
(
n
)
5.
If
d
(
n
)
satisfies
the
criteria
of
an
IMF
,
it
is
stored
as
an
IMF
,
h
i
(
n
)
=
d
(
n
)
where
i
refers
to
i
th
IMF
.
Residue
signal
is
obtained
by
substracting
the
IMF
from
the
original
signal,
r
(
n
)
=
x
(
n
)
h
i
(
n
)
6.
Perform
the
same
step
from
1)
with
the
ne
w
signal
r
(
n
)
until
the
final
residue
signal
is
constant
or
monotonic
function.
After
the
completion
of
EMD
proce
ss,
the
original
signal
can
be
written
in
terms
of
its
IMF
and
residue
signal
as
follo
ws:
x
(
n
)
=
L
1
X
i
=1
h
i
(
n
)
+
r
L
(
n
)
(1)
where
L
refers
to
decomposition
le
v
el
and
i
denotes
IMF
order
.
Lo
wer
-order
of
IMFs
contains
f
ast
osci
llation
modes
(high
frequenc
y)
while
higher
-order
of
IMFs
represent
slo
w
oscillation
modes
(lo
w
frequenc
y).
2.2.
EMD
Denoising
EMD,
whose
decomposition
is
based
on
elementary
substractions,
enables
perfect
reconstruction
of
a
signal.
The
EMD
denoising
method
sta
rts
by
identifying
which
IMFs
carry
dominantly
noise
and
which
IMFs
contain
pri-
marily
useful
information.
This
is
done
by
comparing
the
actual
ener
gy
density
with
the
estimated
ener
gy
density
(to
IJECE
V
ol.
6,
No.
5,
October
2016:
2197
–
2204
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
2199
form
noise-only
model
[10])
of
IMFs.
The
actual
ener
gy
density
of
IMFs
is
calculated
as
follo
ws
E
i
=
1
N
N
X
n
=1
h
i
(
n
)
;
i
=
1
;
2
;
3
;
L
(2)
with
i
corresponds
to
IMF
order
.
The
estimated
ener
gy
density
(v
ariance)
of
IMFs
can
be
approximated
using
the
formula
[13]
belo
w
V
1
=
median
(
j
h
1
median
(
h
1
)
j
)
0
:
6745
2
(3)
V
i
=
V
1
j
;
i
=
2
;
3
;
4
;
L
(4)
where
and
equal
to
0.719
and
2.01,
respecti
v
ely
[10].
The
IMFs
whose
actual
ener
gy
density
e
xceed
the
v
alue
of
their
estimated
ener
gy
density
defined
by
noise-only
model
are
cate
gorized
as
information-dominated
signal
and
should
be
included
in
signal
reconstruction
step;
otherwise
those
IMFs
will
be
e
xcluded.
Due
to
the
f
act
that
the
noise
em
b
e
dd
e
d
in
IMFs
is
colored
(not
Gaussian
distrib
uted),
e
v
en
the
information-
dominated
IMFs
still
may
contain
noise
ha
ving
dif
ferent
ener
gy
density
.
T
o
remo
v
e
those
colored
noise,
IMF-
dependent
threshold
v
alue
is
required.
Consideri
ng
that
IMFs
ha
v
e
zero
mean
and
in
an
y
interv
al
of
zero
crossing
[
z
i
j
z
i
j
+1
]
the
absolute
am
plitude
of
i
th
IMF
is
v
ery
small,
the
thresholding
scheme
will
be
based
on
the
single
e
xtrema
h
i
(
r
i
j
)
,
where
r
i
j
corresponds
to
the
e
xtrema’
s
time
instance
on
this
inte
rv
al.
The
tresholding
scheme
which
follo
ws
the
hard
thresholding
is
e
xpressed
as
follo
ws
~
h
i
([
z
i
j
z
i
j
+1
])
=
h
i
([
z
i
j
z
i
j
+1
])
;
j
h
i
(
r
i
j
)
j
>
T
i
0
;
j
h
i
(
r
i
j
)
j
T
i
(5)
where
h
i
([
z
i
j
z
i
j
+1
])
represents
the
samples
from
time
instant
z
i
j
to
z
i
j
+1
of
t
th
IMF
.
The
threshold
v
alue
used
in
this
scheme
is
e
xpressed
belo
w
T
i
=
C
p
V
i
2
ln
N
;
i
=
1
;
2
;
3
;
L
(6)
where
C
is
0.1
found
by
empirical
simulations
and
V
i
is
estimat
ed
ener
gy
density
(v
ariance)
of
i
th
IMF
.
This
thresh-
olding
scheme
which
is
inspired
and
adapted
from
w
a
v
elet
[11]
will
set
to
zero
all
the
samples
from
time
instant
[
z
i
j
z
i
j
+1
]
if
the
single
e
xtrema
amplitude
belo
w
the
theshold
v
alue
meaning
that
there
is
no
useful
information
(only
noise)
in
the
specified
time
instant.
Otherwise,
all
the
samples
will
be
retained.
The
final
signal
reconstruction
can
be
obtained
by
summing
up
all
the
included
IMFs
(whose
act
ual
ener
gy
density
e
xceeding
its
estimated
estimated
ener
gy
as
described
pre
viously)
using
the
follo
wing
formula
^
y
=
q
X
i
=
p
~
h
(
n
)
(7)
where
p
and
q
indicates
the
lo
west
and
highest
inde
x
of
included
IMF
.
3.
SIMULA
TION
SETTING
T
o
e
v
aluate
the
qualitati
v
e
and
quantitati
v
e
performance
of
our
proposed
method,
we
performed
repeated
simulations
using
synthetic
heart
sound
data
obtained
from
Uni
v
ersity
of
Michig
an’
s
Heart
Sound
&
Murmur
Library
[14].
In
this
simulations,
three
types
of
heart
sound
signals
used
for
simulations
and
their
respecti
v
e
recording
location
are
‘Normal
S1
S2’
(Ape
x,
Supine,
Bell),
‘S3
Gallop’
(Ape
x,
Left
Ducubitus,
Bell)
and
‘S4
Gallop’
(Ape
x,
Left
Ducubitus,
Bell).
These
data
are
encoded
in
44
,100
Hz
sample
rate,
16
bits/sample,
and
1
minutes
of
data
length.
The
data
w
as
then
do
wn-sampled
into
2000
Hz
to
increase
the
computation
process
without
violating
Nyquist
theorem,
since
the
frequenc
y
content
of
heart
sound
data
is
maximum
at
around
700
Hz.
The
simulations
were
carried
out
100
times
in
each
case
using
MA
TLAB
2015a
which
runs
on
Intel(R)
Core(TM)
i7-4790
CPU
@3.6
GHz
W
indo
ws
7
en
vironment.
T
o
measure
the
performance
under
v
arious
noises,
we
added
four
types
of
noises,
which
are
white,
colored
(bro
wn),
e
xponenti
al
and
alpha-stable
noise
to
the
clean
input
signal
y
(
n
)
to
form
noisy
signal
x
(
n
)
.
In
each
noise
case,
we
used
dif
ferent
input
SNR
le
v
el
of
0
;
5
;
10
,
and
15
dB.
The
noisy
heart
sound
signal,
x
(
n
)
,
is
e
xpressed
as
x
(
n
)
=
y
(
n
)
+
e
(
n
)
;
n
=
0
;
1
;
2
;
N
1
(8)
where
y
(
n
)
and
e
(
n
)
denotes
the
clean
signal
and
noise,
respecti
v
ely
.
EMD
Based
Denoising
Method
for
Heart
Sound
Signal
and
Its
P
erformance
Analysis
(Amy
.
H.
Salman)
Evaluation Warning : The document was created with Spire.PDF for Python.
2200
ISSN:
2088-8708
F
or
the
purpose
of
performance
benchmark,
we
also
performed
simulations
o
v
er
the
same
data
using
W
a
v
elet
T
ransform
(WT)
and
T
otal
V
ariation
(TV)
based
denoising
methods.
In
WT
based
simulation,
Daubechies
db10
w
a
v
elet
function
w
as
used
since
it
highly
resembles
the
heart
sound
signal,
which
lead
to
yield
better
performance.
In
addition,
db10
w
a
v
elet
has
orthogonal
property
which
enables
perfect
reconstruction
of
signal
and
ha
v
e
been
reported
to
produce
best
result
among
others
[3].
The
decomposition
le
v
el,
N
=
5
,
is
chosen
as
recommended
in
[4].
Hard
thresholding
technique
is
selected
as
it
pro
vides
better
result
compared
to
soft
thresholding
technique.
MA
TLAB
has
b
uilt-in
function
wden
for
w
a
v
elet
denoising
as
described
in
[15].
Se
v
eral
input
parameters
and
their
setting
for
this
function
are
e
xplained
in
T
able
1
[16].
P
arameter
rigsure
represents
the
selection
using
the
principle
of
Steins
Unbiased
Risk
Estimate
(SURE),
h
means
hard
thresholding,
and
mln
denotes
threshold
rescaling
using
a
le
v
el-dependent
estimation
of
the
le
v
el
noise.
T
able
1.
Input
parameters
setting
P
arameter
Description
Chosen
Setting
s
original
signal
x
(
n
)
tptr
threshold
selection
rule
rigsure
sorh
thresholding
technique
h
scal
threshold’
s
rescaling
method
mln
n
decomposition
le
v
el
5
wav
(mother)
w
a
v
elet
function
db10
As
for
TV
based
denoising
method,
a
Majorization-Minimzation
(MM)
algorithm
[7]
w
as
used
to
solv
e
a
sequence
of
optimization
problems.
The
parameter
is
set
to
0.3
based
on
the
e
xperiment
of
and
c
h
a
racteristic
heart
sound
signals.
The
algorithm
is
run
for
50
iterations
to
find
more
accurate
result.
4.
RESUL
TS
AND
AN
AL
YSIS
Figure
1(a)
and
Figure
1(b)
sho
ws
‘Normal
S1
S2’
heart
sound
signal
x
(
n
)
decomposition
into
11
IMFs
along
with
its
final
residue
signal
and
the
IMFs’
ener
gy
density
comparison
under
0
dB
le
v
el
of
white
noise,
respecti
v
ely
.
As
sho
wn
in
Figure
1(b),
only
information-dominated
IMFs
(number
3
;
4
;
5
;
6
;
7
;
and
11
)
will
be
processed
for
final
reconstruction,
which
leads
to
a
term
“partial
reconstruction”
of
a
signal.
The
qualitati
v
e
performance
e
v
aluation
of
our
proposed
method
compared
to
other
denoising
methods
were
performed
by
visual
inspection
and
comparison.
Figure
2
presents
the
input
clean
signal,
noisy
signal,
and
denoised
(reconstructed)
signal
of
‘S4
Gallop’
using
w
a
v
elet,
TV
,
and
EMD
denoising
methods.
In
each
noise
case,
only
one
simulation
result
under
5
dB
input
SNR
le
v
el
is
sho
wn.
Based
on
Figure
2,
it
is
sho
wn
that
EMD
denosing
method
performs
better
among
ot
h
e
rs
in
three
types
of
noises:
white
(a),
bro
wn
(b)
and
e
xponential
noise
(c)
as
its
denoised
signal
most
resembles
the
original
signal.
If
we
look
closely
and
zoom
in
the
figure,
we
will
kno
w
that
the
amplitude
of
denoised
signal
by
TV
method
are
slightly
reduced.
Ev
en
though
the
denoised
signal
by
TV
method
k
eeps
the
amplitude
of
its
main
components
almost
the
same
as
original
one,
the
amplitude
outside
the
main
components
interv
al
x(n)
h
1
h
2
h
3
h
4
h
5
h
6
h
7
h
8
h
9
h
10
h
11
r
(a)
EMD
based
signal
decomposition
0
2
4
6
8
10
12
−18
−16
−14
−12
−10
−8
−6
−4
IMF
log
2
(Energy)
Real Energy
Estimated Energy
(b)
Real
vs
estimated
ener
gy
density
of
IMFs
Figure
1.
Signal
decomposition
and
ener
gy
density
comparison
of
IMFs
under
0
dB
le
v
el
of
white
noise
IJECE
V
ol.
6,
No.
5,
October
2016:
2197
–
2204
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
2201
0
0.5
1
1.5
-1
0
1
Input Signal
0
0.5
1
1.5
-1
0
1
Noisy Signal
0
0.5
1
1.5
Amplitude
-1
0
1
Wavelet Denoising
0
0.5
1
1.5
-1
0
1
TV Denoising
Time
0
0.5
1
1.5
-1
0
1
EMD Denoising
(a)
White
noise
with
SNR
5
dB
0
0.5
1
1.5
-1
0
1
Input Signal
0
0.5
1
1.5
-1
0
1
Noisy Signal
0
0.5
1
1.5
Amplitude
-1
0
1
Wavelet Denoising
0
0.5
1
1.5
-1
0
1
TV Denoising
Time
0
0.5
1
1.5
-1
0
1
EMD Denoising
(b)
Bro
wn
noise
with
SNR
5
dB
0
0.5
1
1.5
-1
0
1
Input Signal
0
0.5
1
1.5
-1
0
1
Noisy Signal
0
0.5
1
1.5
Amplitude
-1
0
1
Wavelet Denoising
0
0.5
1
1.5
-1
0
1
TV Denoising
Time
0
0.5
1
1.5
-1
0
1
EMD Denoising
(c)
Exponential
noise
with
SNR
5
dB
0
0.5
1
1.5
-1
0
1
Input Signal
0
0.5
1
1.5
-1
0
1
Noisy Signal
0
0.5
1
1.5
Amplitude
-1
0
1
Wavelet Denoising
0
0.5
1
1.5
-1
0
1
TV Denoising
Time
0
0.5
1
1.5
-1
0
1
EMD Denoising
(d)
Alpha-stable
noise
with
SNR
5
dB
Figure
2.
V
isual
performance
comparison
of
‘S4
Gallop’
heart
sound
signal
denoising
methods
is
slightly
changed
compared
to
the
original
signal.
As
for
alpha-stable
noise
as
sho
wn
in
Figure
2(d),
WT
and
TV
denoising
methods
pefrorms
better
than
EMD
method.
In
order
to
obtain
more
e
xact
comparison,
a
quantitati
v
e
performance
w
as
e
v
aluated
based
on
three
metrics
namely
signal-to-noise
ratio
(SNR),
r
o
ot
mean
square
error
(RMSE),
and
percent
root
mean
s
q
ua
re
dif
ference
(PRD),
T
able
2.
Performance
comparison
of
denoising
methods
for
‘S3
Gallop’
heart
sound
data
Noise
Input
SNR
(dB)
RMSE
PRD
(%)
T
ype
SNR
WT
TV
EMD
WT
TV
EMD
WT
TV
EMD
White
0
8.9463
7.6747
9.9222
0.0391
0.0452
0.0352
35.7720
41.3448
32.1339
5
12.7895
11.8554
13.2863
0.0251
0.0280
0.0240
22.9760
25.5490
21.9542
10
16.6698
13.6183
17.6169
0.0161
0.0228
0.0145
14.6864
20.8534
13.2708
15
20.5798
14.2784
20.9220
0.0102
0.0211
0.0101
9.3646
19.3253
9.3160
Bro
wn
0
-1.3465
-1.3822
0.58753
0.1329
0.1334
0.1071
121.4947
121.9054
97.8917
5
3.4123
3.1738
5.0755
0.0768
0.0786
0.0641
70.1732
71.8188
58.5944
10
8.3727
7.5069
9.8494
0.0431
0.0471
0.0374
39.4378
43.0857
34.1929
15
13.1883
10.8689
15.1542
0.0246
0.0316
0.0205
22.499
28.8733
18.6951
Exponential
0
-0.9209
-0.8023
6.2413
0.1217
0.1200
0.0537
111.2174
109.7049
49.0467
5
4.0152
4.1953
10.1811
0.0689
0.0675
0.0349
63.0014
61.7036
31.8804
10
8.8459
8.4530
14.5646
0.0395
0.0413
0.0223
36.1247
37.7918
20.3669
15
13.6832
11.6200
18.3461
0.0226
0.0287
0.0157
20.6983
26.2448
14.3572
Alpha-stable
0
9.8326
10.1323
8.0622
0.0440
0.0423
0.0564
40.2600
38.6638
51.5371
5
15.7833
13.0523
11.3505
0.0220
0.0272
0.0392
20.1374
24.8517
35.8671
10
20.1803
13.8206
14.2772
0.0158
0.0259
0.0336
14.4564
23.6848
30.6898
15
25.2577
14.3523
18.3497
0.0073
0.0213
0.0262
6.6370
19.4375
23.9710
EMD
Based
Denoising
Method
for
Heart
Sound
Signal
and
Its
P
erformance
Analysis
(Amy
.
H.
Salman)
Evaluation Warning : The document was created with Spire.PDF for Python.
2202
ISSN:
2088-8708
which
are
calculated
as
follo
ws:
S
N
R
=
10
log
10
P
N
n
=1
[
y
(
n
)]
2
P
N
n
=1
[
y
(
n
)
^
y
(
n
)]
2
(9)
R
M
S
E
=
s
P
N
n
=1
[
y
(
n
)
^
y
(
n
)]
2
N
(10)
P
R
D
=
v
u
u
t
P
N
n
=1
[
y
(
n
)
^
y
(
n
)]
2
P
N
n
=1
[
y
(
n
)]
2
100
(11)
where
y
(
n
)
denotes
the
clean
original
signal,
^
y
(
n
)
refers
to
t
he
denoised
(reconstructed)
signal,
and
N
represents
the
length
of
the
signal.
SNR
is
defined
as
the
ratio
of
the
po
wer
of
a
signal
(useful
information)
and
the
po
wer
of
noise
(irrele
v
ant
signal).
RMSE
is
used
to
measure
the
accurac
y
of
denoising
method
in
preserving
the
quality
of
information
in
the
denoised
signal
by
calculating
the
sample
standard
de
viation
of
the
dif
fe
rences
between
denoised
signal
and
original
signal.
PRD
is
frequently
used
as
a
method
of
quantifying
the
distortion
or
the
dif
ference
between
the
original
and
the
reconstructed
signal.
The
PRD
indicates
reconstruction
fidelity
by
point
wise
comparison
with
the
original
data.
A
denoising
method
is
said
to
perfom
better
if
at
a
particular
input
SNR,
the
v
alue
of
output
SNR
is
lar
ger
while
the
v
alue
of
RMSE
and
PRD
are
smaller
.
Comparati
v
e
simulation
results
of
three
denoising
methods
(WT
,
TV
,
and
EMD)
o
v
er
‘S3
Gallop’
heart
sound
data
on
the
basis
of
SNR,
RMSE,
and
PRD
are
sho
wn
in
T
able
2.
The
simulation
result
v
alues
were
rounded
into
4
digits
after
comma.
Highlighted
(bold)
v
alues
indicates
the
best
performance
among
others.
It
is
sho
wn
that
for
three
cases
of
noises
(white,
bro
wn,
and
e
xponential)
under
dif
ferent
input
SNR
v
alues
(
0
;
5
;
10
;
and
15
dB),
EMD
denoising
method
consistently
yields
lar
gest
SNR
v
alue,
and
smallest
RMSE
and
PRD
v
alues
(see
bold
v
alues).
F
or
instance
in
white
noisy
en
vironment
with
0
dB
input
SNR
le
v
el,
EMD
method
sho
ws
SNR
v
alue
9.9222
dB,
RMSE
0.0352
and
PRD
32.1339
%
where
as
WT
(TV)
method
sho
ws
8.9463
(7.6747)
dB
SNR,
0.0391
(0.0452)
RMSE,
and
35.7720
%
(41.3448
%)
PRD.
The
performance
of
EMD
method
in
these
three
types
of
noises
for
other
heart
sound
signals
(‘Normal
S1
S2’
and
‘S4
g
allop’)
o
v
er
input
SNR
le
v
el
range
(
0
dB
-
15
dB)
is
superior
as
well
compared
to
WT
and
TV
methods.
Ho
we
v
er
,
for
heart
sound
signals
contaminated
with
alpha-stable
noise,
EMD
method
does
not
perform
well
compared
to
its
counterparts
especially
for
input
SNR
le
v
el
0
-
10
dB.
In
this
type
of
noise,
on
a
v
erage,
WT
method
outperforms
other
tw
o
methods,
e
xcept
for
the
case
of
0
dB
input
SNR
where
TV
method
produces
the
best
performance
on
all
three
metrics.
Alpha-stable
noise
being
used
in
this
simulation
represents
the
impulsi
v
e
noise
or
disturbance
characterized
by
high
amplitude
and
short
time
duration
within
arbitrary
location
along
the
data.
This
impulsi
v
e
disturbance
usually
occurs
when
there
is
quick
mo
v
ement
or
friction
between
chest
skin
and
stethoscope
during
recording
heart
sound
data.
This
alpha-stable
noise
has
four
parameters:
(characteristic
e
xponent),
(sk
e
wness),
(scale)
and
(location)
[17].
P
arameter
indicates
the
tail
of
distrib
ution
while
specifies
whether
the
distrib
ution
is
right-
or
left-sk
e
wed.
In
this
simulation,
we
used
=
1
:
6
,
=
1
,
=
0
:
1
and
=
0
.
Graphical
visualization
of
comparati
v
e
simulation
results
of
‘S4
Gallop’
heart
sound
signal
under
four
types
of
noises
is
depicted
in
Figure
3.
Figure
3(a-c)
sho
ws
the
comparati
v
e
output
SNR,
RMSE
and
PRD
v
alue
of
three
denoising
methods
with
respect
to
dif
ferent
input
SNR
le
v
els
in
white
n
oi
sy
en
vironment.
It
is
sho
wn
that
EMD
method
(blue
line
with
triangle
point)
on
a
v
are
ge
performs
better
than
WT
(black
line
with
rectangle
point)
and
TV
(red
line
with
circle
point),
indicated
by
lar
ger
output
SNR
v
alue
and
smaller
RMSE
and
PRD
v
alues.
The
same
trend
is
also
observ
ed
in
simulation
results
o
v
er
bro
wn
and
e
xponential
noisy
signal
as
sho
wn
in
Figure
3(d-f)
and
Figure
3(g-i).
EMD
is
equi
v
alent
to
dyadic
filter
structure
which
can
ef
fecti
v
ely
decompose
fractional
Gaussian
noise
processes
such
as
white
and
colored
(bro
wn)
noises.
This
leads
to
ef
fecti
v
e
denoising
method
o
v
er
dif
ferent
class
of
fractional
Gaussian
noises
[18–20].
Moreo
v
er
,
EMD
method
does
not
require
an
y
predefined
basis
function
and
is
fully
data-dri
v
en
which
of
fers
more
fle
xibility
and
adaptability
to
an
y
signal
under
consideration.
Ho
we
v
er
,
EMD
method
does
not
perform
well
compared
to
its
counterparts
under
alpha-stable
noise
simulation
as
shw
on
in
Figure
3(j-l).
According
to
our
observ
ation
during
repeated
simulations,
we
chose
constant
v
alue
C
=
0
:
6
in
threshold
v
alue
calculation
within
EMD
denoising
mechanism
to
obtain
good
performance.
This
constant
v
alue
appli
es
well
on
three
types
of
noises
(white,
bro
wn
and
e
xponential).
Ho
we
v
er
,
based
on
our
simulation,
the
performance
of
EMD
denoising
method
under
alpha-stable
noise
can
be
impro
v
ed
by
increasing
the
constant
v
alue
C
up
to
1.5.
In
addition,
to
miti
g
ate
this
impulsi
v
e
disturbance
in
heart
sound
analysis,
an
adapti
v
e
selection
algorithm
based
on
Heron’
s
formula
can
be
emplo
yed
in
the
subsequent
process
[21].
IJECE
V
ol.
6,
No.
5,
October
2016:
2197
–
2204
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
2203
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
8
1
0
1
2
1
4
1
6
1
8
2
0
2
2
O
u
t
p
u
t
S
N
R
(
d
B
)
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(a)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
0
.
0
1
0
0
.
0
1
5
0
.
0
2
0
0
.
0
2
5
0
.
0
3
0
0
.
0
3
5
0
.
0
4
0
0
.
0
4
5
0
.
0
5
0
R
M
S
E
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(b)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
5
1
0
1
5
2
0
2
5
3
0
3
5
4
0
4
5
P
R
D
(
%
)
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(c)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
-
4
-
2
0
2
4
6
8
1
0
1
2
1
4
O
u
t
p
u
t
S
N
R
(
d
B
)
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(d)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
0
0
.
1
2
0
.
1
4
0
.
1
6
R
M
S
E
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(e)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
2
0
4
0
6
0
8
0
1
0
0
1
2
0
1
4
0
P
R
D
(
%
)
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(f)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
-
5
0
5
1
0
1
5
2
0
O
u
t
p
u
t
S
N
R
(
d
B
)
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(g)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
0
0
.
1
2
0
.
1
4
R
M
S
E
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(h)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
2
0
4
0
6
0
8
0
1
0
0
1
2
0
P
R
D
(
%
)
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(i)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
8
1
0
1
2
1
4
1
6
1
8
2
0
2
2
2
4
2
6
O
u
t
p
u
t
S
N
R
(
d
B
)
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(j)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
0
.
0
0
0
.
0
1
0
.
0
2
0
.
0
3
0
.
0
4
0
.
0
5
0
.
0
6
0
.
0
7
R
M
S
E
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(k)
-
2
0
2
4
6
8
1
0
1
2
1
4
1
6
0
1
0
2
0
3
0
4
0
5
0
6
0
P
R
D
(
%
)
I
n
p
u
t
S
N
R
L
e
v
e
l
(
d
B
)
W
T
T
V
E
M
D
(l)
Figure
3.
Performance
comparison
o
v
er
‘S4
Gallop’
heart
sound
signal
under
(a-c)
white
(d-f)
bro
wn
(g-i)
e
xponential
and
(j-l)
alpha-stable
noise
EMD
Based
Denoising
Method
for
Heart
Sound
Signal
and
Its
P
erformance
Analysis
(Amy
.
H.
Salman)
Evaluation Warning : The document was created with Spire.PDF for Python.
2204
ISSN:
2088-8708
5.
CONCLUSION
Empirical
Mode
Decomposition
(EMD)
based
denois
ing
method
is
proposed
in
this
paper
.
Its
performance
and
analysis
compared
to
other
tw
o
methods
based
on
w
a
v
elet
transform
(WT)
and
total
v
ariation
(TV)
are
presented.
F
our
types
of
noises
with
input
SNR
le
v
el
0
dB,
5
dB,
10
dB
and
15
dB
are
artificially
added
to
clean
original
nor
-
mal
and
abnormal
heart
sound
signal
s
obtained
from
the
Uni
v
ersity
of
Michig
an
Health
System.
Based
on
e
xtensi
v
e
simulations,
our
proposed
EMD
based
denoising
method
consistently
yields
better
performance
in
terms
of
three
stan-
dard
metrics:
signal-to-noise
ratio
(SNR),
root
mean
square
error
(RMSE),
and
percent
root
mean
square
dif
ference
(PRD)
under
white,
colored
(bro
wn)
and
e
xponential
noises.
As
for
alpha-stable
noise,
on
a
v
erage,
WT
and
TV
based
denoising
methods
perform
better
than
EMD
method.
REFERENCES
[1]
G.
Redlarski,
D.
Gradole
wski,
and
A.
P
alk
o
wski,
“
A
system
for
heart
sounds
classification,
”
PloS
one
,
v
ol.
9,
no.
11,
p.
e112673,
2014.
[2]
WHO,
Global
status
r
eport
on
noncommunicable
diseases
2014
.
W
orld
Health
Or
g
anization,
2014.
[3]
L.
H.
Cherif,
S.
Debbal,
and
F
.
Bereksi-Re
guig,
“Choice
of
the
w
a
v
elet
analyzing
in
the
phonocardiogram
signal
analysis
using
the
discrete
and
the
pack
et
w
a
v
elet
transform,
”
Expert
Systems
with
Applications
,
v
ol.
37,
no.
2,
pp.
913–918,
2010.
[4]
S.
R.
Messer
,
J.
Agzarian,
and
D.
Abbott,
“Optimal
w
a
v
elet
denoising
for
phonocardiograms,
”
Micr
oelectr
onics
J
ournal
,
v
ol.
32,
no.
12,
pp.
931–941,
2001.
[5]
F
.
Liu,
Y
.
W
ang,
and
Y
.
W
ang,
“Research
and
implementation
of
heart
sound
denoising,
”
Physics
Pr
ocedia
,
v
ol.
25,
pp.
777–785,
2012.
[6]
V
.
N.
V
ar
ghees
and
K.
Ramachandran,
“
A
no
v
el
heart
sound
acti
vity
detection
frame
w
ork
for
automated
heart
sound
analysis,
”
Biomedical
Signal
Pr
ocessing
and
Contr
ol
,
v
ol.
13,
pp.
174–188,
2014.
[7]
“T
otal
v
ariation
denoising
(an
MM
algorithm),
”
T
echnical
Report,
Polytechnic
Uni
v
ersity
,
Mar
.
2014.
[8]
M.
A.
Figueiredo,
J.
B.
Dias,
J.
P
.
Oli
v
eira,
and
R.
D.
No
w
ak,
“On
total
v
ariation
denoising:
A
ne
w
majorization-
minimization
algorithm
and
an
e
xperimental
comparisonwith
w
a
v
alet
denoising,
”
in
2006
IEEE
International
Confer
ence
on
Ima
g
e
Pr
ocessing
.
IEEE,
2006,
pp.
2633–2636.
[9]
N.
E.
Huang,
Z.
Shen,
S.
R.
Long
et
al.
,
“The
empirical
mode
decomposition
and
the
hilbert
spectrum
for
non-
linear
and
non-stationary
time
series
analys
is,
”
in
Pr
oceedings
of
the
Royal
Society
of
London
A:
Mathematical,
Physical
and
Engineering
Sciences
,
v
ol.
454,
no.
1971.
The
Ro
yal
Society
,
1998,
pp.
903–995.
[10]
G.
Rilling,
P
.
Flandrin,
and
P
.
Goncalv
es,
“Detrending
and
denoising
with
empirical
mode
decomposition,
”
in
Pr
oceedings
of
the
Eur
opean
signal
pr
ocessing
confer
ence
(EUSIPCO04)
,
v
ol.
2,
2004,
pp.
1581–1584.
[11]
Y
.
K
opsinis
and
S.
McLaughlin,
“De
v
elopment
of
EMD-based
denoising
methods
inspired
by
w
a
v
elet
threshold-
ing,
”
IEEE
T
r
ansactions
on
Signal
Pr
ocessing
,
v
ol.
57,
no.
4,
pp.
1351–1362,
2009.
[12]
M.
A.
Kabi
r
and
C.
Shahnaz,
“Denoising
of
ECG
signals
based
on
noise
reduction
algorithms
in
EMD
and
w
a
v
elet
domains,
”
Biomedical
Signal
Pr
ocessing
and
Contr
ol
,
v
ol.
7,
no.
5,
pp.
481–489,
2012.
[13]
W
.
W
u
and
H.
Peng,
“
Application
of
EMD
denoising
approach
in
noisy
blind
source
separation,
”
J
ournal
of
Communications
,
v
ol.
9,
no.
6,
2014.
[14]
Heart
Sound
&
Murmur
Libr
ary
,
Uni
v
ersity
of
Michig
an
Health
System,
Ann
Arbor
,
MI.
[Online].
A
v
ailable:
http://www
.med.umich.edu/lrc/psb
open/repo/primer
heartsound/primer
heartsound.html
[15]
M.
Misiti,
Y
.
Misiti,
G.
Oppenheim,
and
J.-M.
Poggi,
W
avelet
T
oolbox
User’
s
Guide
,
Re
v
.
4.14
(Rel.
2014b),
The
MathW
orks,
Inc.,
Oct.
2014.
[16]
A.
H.
Salman,
N.
Ahmadi,
R.
Mengk
o,
A.
Z.
R.
Langi,
and
T
.
L.
R.
Mengk
o,
“Performance
comparison
of
denoising
methods
for
heart
sound
signal,
”
in
2015
International
Symposium
on
Intellig
ent
Signal
Pr
ocessing
and
Communication
Systems
(ISP
A
CS)
.
IEEE,
2015,
pp.
435–440.
[17]
M.
V
eillette,
Alpha-Stable
distrib
utions
,
Boston
Uni
v
ersity
,
Aug.
2015.
[18]
Z.
W
u
and
N.
E.
Huang,
“
A
study
of
the
characteristics
of
white
noise
using
the
empirical
mode
decomposi-
tion
method,
”
Pr
oceedings
of
the
Royal
Society
of
London.
Series
A:
Mathematical,
Physical
and
Engineering
Sciences
,
v
ol.
460,
no.
2046,
pp.
1597–1611,
2004.
[19]
P
.
Flandrin
and
P
.
Goncalv
es,
“Empirical
mode
decompositions
as
data-dri
v
en
w
a
v
elet-lik
e
e
xpansions,
”
Inter
-
national
J
ournal
of
W
avelets,
Multir
esolution
and
Information
Pr
ocessing
,
v
ol.
2,
no.
04,
pp.
477–496,
2004.
[20]
P
.
Flandrin,
P
.
Gonc
¸
alv
es,
and
G.
Rilling,
“EMD
equi
v
alent
filter
banks,
from
interpretation
to
applications,
”
Hilbert-Huang
T
r
ansform
and
Its
Applications
,
pp.
57–74,
2005.
[21]
A.
H.
Salman,
N.
Ahmadi,
R.
Mengk
o,
A.
Z.
Langi,
and
T
.
L.
Mengk
o,
“
Automatic
se
gme
n
t
ation
and
detection
of
heart
sound
components
S1,
S2,
S3
and
S4,
”
in
4th
International
Confer
ence
on
Instrumentation,
Communi-
cations,
Information
T
ec
hnolo
gy
,
and
Biomedical
Engineering
(ICICI-BME
2015)
.
IEEE,
2015,
pp.
103–107.
IJECE
V
ol.
6,
No.
5,
October
2016:
2197
–
2204
Evaluation Warning : The document was created with Spire.PDF for Python.