Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
4, N
o
. 4
,
A
ugu
st
2014
, pp
. 55
7
~
56
0
I
S
SN
: 208
8-8
7
0
8
5
57
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
Separation of Digital Audio Si
gnals using Least-Mean-Square
(LMS) Adaptive Algorith
m
Ka
yo
de Fr
anc
i
s Aki
n
gb
ade,
Isi
ak
a
A jew
a
l
e
Al
i
m
i
Department o
f
Electrical and
Elec
tronics Engin
e
ering, Schoo
l of
Engi
neering
and
Engin
eering
Technolog
y
,
Federal University
of
Te
chnolog
y
,
Akure, Nig
e
ria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 4, 2014
Rev
i
sed
May 31
, 20
14
Accepted
Jun 20, 2014
Adaptive f
ilterin
g is one of the
fundamental
technologies in d
i
g
ital sign
al
processing (DSP) in today
’
s
comm
unication
s
y
stems and
it has b
e
en
emplo
y
ed in
a wide rang
e of
applications
s
u
ch as
adapt
i
ve nois
e
c
a
nce
lla
tion
,
adapt
i
ve
equa
liz
ation
,
an
d e
c
ho
canc
e
ll
ation
.
S
i
g
n
al s
e
p
a
ra
tion r
e
m
a
ins
a t
a
s
k
that h
a
s ca
lled
for at
tent
ion
in digi
tal sign
al processing
an
d differ
e
nt
techn
i
ques
hav
e
be
en em
plo
y
ed
in ord
e
r
to a
c
hi
eve
e
ffici
ent
and
accur
a
t
e
res
u
lt
. I
m
plem
entation o
f
adaptiv
e fil
t
eri
ng can s
e
para
te
wanted and
interf
eren
ce s
i
g
n
als
s
o
as
to im
prove perf
orm
a
nce of co
m
m
unication
s
y
s
t
em
s
.
In the light of this
, this
paper us
es
a leas
t-m
ean-s
qu
are (LM
S
)
adaptive algorith
m for separation
of audi
o signals.The simulated r
e
sults show
that
the designed
LMS based
adaptive
f
iltering
techniqueconverg
e faster th
an
conventional LMS adaptiv
e f
ilter.
Keyword:
Ad
ap
tiv
e al
go
rith
m
s
Ad
ap
tiv
e filters
DSP
FIR
IIR
LMS
Copyright ©
201
4 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
:
Kayode Fra
n
cis Akingbade
,
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
Sch
ool
o
f
E
ngi
neeri
n
g
an
d E
n
gi
nee
r
i
n
g Tec
h
nol
ogy
,
Fede
ral
U
n
i
v
e
r
si
t
y
of Tec
h
nol
ogy
,
A
k
ure
,
Ni
geri
a
Em
a
il: k
f
ak
ingb
ad
e@fu
ta.edu.ng
1.
INTRODUCTION
Di
gi
t
a
l
Si
gnal
Proce
ssi
n
g
(
D
SP
) i
s
co
nc
erne
d w
ith t
h
e theoretical and
practical
aspects of
rep
r
ese
n
t
i
ng i
n
fo
rm
ati
on be
ar
i
ng si
gnal
s
i
n
di
gi
t
a
l
fo
rm
. Al
so, i
t
i
n
v
o
l
v
es
usi
n
g c
o
m
put
ers o
r
s
p
eci
al
p
u
r
p
ose
d
i
g
ital h
a
rd
ware eith
er to
ex
t
r
act in
form
atio
n
o
r
to
tran
sform th
e sig
n
a
ls in
u
s
efu
l
form
s
[1
]. To
ach
iev
i
ng
th
is, d
i
g
ital filters rem
a
in
as t
h
e b
a
ck
bon
e fo
r d
i
g
ital sig
n
al p
r
o
cessing
.
Th
e ex
isting
typ
e
s o
f
d
i
g
ital filters
are: Infin
ite Im
p
u
l
se Resp
on
se (IIR)
filters; an
d
Fin
ite Im
p
u
l
se Resp
on
se (FIR) filters. An
im
p
r
o
v
e
m
en
t o
n
th
ese
d
i
g
ital filters resu
lt i
n
to
th
e
u
s
e adap
tiv
e
filters
wh
ere
FIR
filters
rem
a
in
s th
e m
o
st u
s
ed
i
n
th
is
appl
i
cat
i
o
n [
2
,
3]
.
Ad
ap
tiv
e
filters are
filters th
at can
easily adju
st
th
eir
prop
erties to
su
it th
e env
i
ron
m
en
t (co
n
d
itio
ns)
unde
r whic
h they are used. T
h
e proper
ties that are adjuste
d
include: coef
ficients; step-s
ize; and length.The
y
can
b
e
im
p
l
e
m
en
ted
u
s
ing
eith
er
o
f
th
e t
w
o
av
ailab
l
e typ
e
s o
f
d
i
g
ital filters i.e. th
e In
fin
i
t
e
Im
p
u
l
se Resp
on
se
(IIR) filter o
r
t
h
e Fin
ite Im
p
u
l
se Resp
on
se (FIR).
Howe
v
e
r, th
e FIR filter is p
r
eferred
fo
r th
e i
m
p
l
e
m
en
t
a
tio
n
of the a
d
a
p
tive
filters
because
they are
m
o
re
stable and c
onverge
faster than
the
IIR
filters
[4,
5]. Som
e
of the
ad
ap
tiv
e filter
p
e
rform
s
its ta
sk
u
s
ing
corre
l
a
tio
n
p
r
i
n
cip
l
e main
ly
cro
ss
co
rrelatio
n
.
Ada
p
tive filtering m
e
thod us
ing cro
ss correlation
m
e
thod
for signal separation coupled with the
Least
M
ean
Sq
uare
ada
p
t
i
v
e a
l
go
ri
t
h
m
i
s
em
pl
oy
ed
i
n
t
h
i
s
pape
r
fo
r t
h
e s
e
parat
i
o
n
of
di
gi
t
a
l
audi
o si
g
n
al
s.
2.
DESIG
N
ME
THODOLOG
Y
Th
e cro
ss correlatio
n
m
e
th
o
d
is u
s
ed
t
o
separate
two
aud
i
o
sign
als using
ad
ap
tiv
e
filter.
A sign
al
buried in anot
her signal can be esti
m
a
ted
b
y
cro
ss co
rrelatin
g
it with
an
ad
ju
stab
le tem
p
la
te o
f
th
e secon
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
55
7
–
56
0
55
8
sig
n
a
l.
Th
e tem
p
la
te sig
n
a
l is adj
u
sted
b
y
trial an
d
error
g
u
i
d
e
d b
y
th
e
fore
k
nowledge un
til th
e fu
nctio
n
is
max
i
m
i
zed
; th
e te
m
p
late is t
h
en
t
h
e estim
a
t
e o
f
th
e
sign
al. Ad
ap
tiv
e
filter con
f
i
g
uration
em
p
l
o
y
ed
in th
is
work is shown in
Figu
re 1. Th
e filter iterativ
ely alters
its p
a
ram
e
ters so
as to
m
i
n
i
mize
th
e co
st
fun
c
ti
o
n
of
t
h
e a
d
apt
i
v
e
al
go
ri
t
h
m
of t
h
e
di
f
f
ere
n
ce
bet
w
een
t
h
e
de
si
r
e
d
o
u
t
p
ut
d(
n)
and
i
t
s
act
ual
out
put
y(n)
. Adaptiv
e
alg
o
rith
m
ad
j
u
sts th
efilter co
efficien
t i
n
clud
ed
in th
e v
ect
o
r
w
(n) Th
e
ad
aptiv
e filter aim
s
to
equ
a
te its
outp
u
t
y(n)
to
th
e d
e
si
red ou
tpu
t
d(
n)
. For
each itera
tion, t
h
e e
r
ror s
i
gnal is
give
n
by:
)
(
)
(
)
(
n
y
n
d
n
e
(1
)
Th
e erro
r sign
al is fed b
a
ck
i
n
to
th
e
filter,
wh
ere th
e
filter ch
aracteristic
s are altered
accord
i
n
g
l
y.
Fig
u
re
1
.
Ad
aptiv
e filter co
nfig
uration
2.
1. T
h
e L
e
a
s
t
Me
an
Squ
are
(L
M
S
)
Al
gori
t
hm
Th
e LM
S algorith
m
is wid
e
ly u
s
ed
du
e to its co
m
p
u
t
atio
n
a
l
sim
p
lic
ity. It is a form
o
f
ad
ap
tiv
e
filter
known as st
oc
hastic gradie
nt
-base
d
al
gorithm
s
because it em
ploys the gra
d
ie
nt vector of the
filter
ta
p weights
to
conv
erg
e
o
n
th
e
o
p
tim
al wien
er so
lu
tion
[6, 7
]
.
Th
e iteratio
n
o
f
t
h
e LMS alg
o
rith
m
lead
s to
t
h
e
u
p
d
a
te of
the ada
p
tive
filter tap
weights
according t
o
[8, 9]:
)
(
)
(
2
)
(
)
1
(
n
x
n
e
n
w
n
w
(2
)
whe
r
e
T
N
n
x
n
x
n
x
n
x
)
1
(
)
1
(
)
(
)
(
is th
e inp
u
t
v
ect
o
r
, th
e co
e
fficients
of the
adaptive
FIR
filter tap
weight v
ector at tim
e
n
is
T
N
n
w
n
w
n
w
n
w
)
(
)
(
)
(
)
(
1
1
0
an
d
µ is k
nown
as th
e step
size p
a
ram
e
ter an
d
is a
small
p
o
s
itiv
e co
nstan
t
p
a
rameter. Th
is step
size
p
a
ram
e
terco
n
t
ro
ls th
e
effect
o
f
t
h
e
u
p
d
a
ting
facto
r
an
d
determin
es bo
th th
e stab
ility a
n
d
c
on
v
e
rg
en
ceo
f
t
h
e
ad
ap
tiv
e filter
b
eco
m
e
s un
stab
le and
its
ou
tpu
t
d
i
v
e
rg
es.
The
n
u
m
b
er a
n
d
t
y
pe
of
o
p
e
r
at
i
ons
ne
ede
d
f
o
r t
h
e
LM
S alg
o
rith
m
is n
early th
e sam
e
as th
at
o
f
th
e
FIR filter
structu
r
e with
fix
e
d
co
efficien
t v
a
l
u
es,
wh
ich
is on
e
o
f
th
e
reason
s
for t
h
e algorith
m
’
s po
pu
larity. It
d
e
p
e
nd
s exp
licitly o
n
th
e statistics o
f
th
e i
n
pu
t and
d
e
sired
respon
se si
g
n
a
ls. In
effect, the iterativ
e n
a
t
u
re
o
f
th
e LMS co
efficien
t up
d
a
tes is a form
o
f
ti
m
e
-av
e
rag
i
ng
th
at sm
o
o
t
hed
th
e errors
in
th
e instan
tan
e
ou
s
g
r
ad
ien
t
calcu
latio
n
s
t
o
o
b
t
ai
n
a m
o
re
reason
ab
le esti
m
a
te
o
f
th
e tru
e
gradien
t
.
3.
IMPLEME
N
TATION OF
THE LMS ALGORIT
HM
Th
e LMS al
g
o
rith
m
is u
s
ed
in
d
e
sign
ing
adap
tiv
e filter and
th
e M
A
TLAB p
r
o
g
ram
is
u
s
ed
fo
r t
h
e
sim
u
l
a
t
i
on. T
h
e nam
e
gi
ve
n t
o
t
h
e
t
w
o a
u
di
o si
gnal
s
use
d
are;
m
y
voi
ce and
n
o
i
s
e.
B
o
t
h
of
t
h
em
are .
w
av
fi
l
e
because that is
the only audi
o
f
ile form
at that MATL
AB ca
n take.
The
fol
l
o
wi
n
g
code
i
s
use
d
fo
r si
g
n
al
se
parat
i
on a
n
d A
1
a
n
d A
2
a
r
e t
h
e
fi
r
s
t
and
seco
n
d
a
udi
o si
g
n
al
respectively. T
h
e code
[y,e
]
=
filter(h
a
l
ms,x,A2
)
sh
ows that filter ratin
g
i
s ach
iev
e
d
u
s
i
n
g
a filter ob
j
ect
hal
m
s
an
d
th
e filter
o
b
j
ect d
e
p
e
nd
o
n
a
dap
tfilt.lms
alg
o
r
ith
m
w
ith
filter len
g
t
h
o
f
22
and step size of
0.
03
5
3
, the
freq
u
e
n
c
y
respo
n
s
e
o
f
t
h
e
filter u
s
ed showin
g th
e am
p
litu
d
e
an
d p
h
a
se respon
se o
f
the
filter
is g
i
v
e
n
by
Fig
u
re
2
an
d
Fig
u
re 3 shows
th
e step
resp
onse of th
e
f
ilter. Th
e m
a
x
i
m
u
m
s
t
ep
size fo
r th
e filter is
o
b
tain
ed
usi
n
g
mum
a
xlms
, wh
ile th
e m
a
x
i
m
u
m
mean
-sq
u
a
re lm
s step
size was
ob
tained
u
s
ing
mu
maxm
selm
s.
+
e(n)
d(n
)
y(n
)
x(n
)
Ada
p
tive Filt
er
w
(
n
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Sep
a
r
a
t
i
o
n
of
Di
gi
t
a
l
A
u
di
o
Si
g
nal
s
usi
n
g
Least
-
Lea
n
-
S
q
uar
e (
L
MS)
…
(
K
ayode
Fr
anc
i
s
Aki
n
g
b
ade)
55
9
Howev
e
r, it is adv
i
sab
l
e to
u
s
e th
e sm
al
le
r step
si
ze i
.
e
.
0.
01
beca
use
i
t
im
proves
a
ccuracy
o
f
co
nv
erg
e
n
ce t
o
m
a
tch
ch
aracteristics o
f
th
e un
kno
wn
t
o
th
e
ti
m
e
tak
e
n
fo
r it to
ad
ap
t.
Th
e
n
e
x
t
stag
e is th
e
d
e
sign
of th
e
filter th
at
p
e
rform
s
th
e co
rrelatio
n
of the second
aud
i
o sig
n
a
l
,
A2
wi
t
h
t
h
e
m
i
xed au
di
o
si
g
n
al
,
x
as s
h
o
w
n
bel
o
w:
[y,e
]
=
filter(h
a
l
ms,x,A2
)
;
Th
e correlation
co
m
p
ares the seco
nd
signal with
th
e
mix
e
d
sign
al. After wh
ich
th
e d
i
fferen
c
e
bet
w
ee
n t
h
em
i
s
obt
ai
ne
d t
h
i
s
diffe
re
nce is c
a
lled the er
ro
r,
e
wh
ile th
e
outp
u
t
is g
i
v
e
n as
y
. Th
e error is th
en
fed b
a
ck
i
n
to
t
h
e ad
ap
tive fil
t
er. Th
e iteratio
n pro
cess contin
u
e
s
un
til th
e error
v
a
lu
e
b
e
co
m
e
s 0
.
Wh
en
the
error
value
be
com
e
s zero, i
t
m
ean
s that
adaptation
has bee
n
done su
ccessfully, that is the filter ha
s
success
f
ully adapted.
Fig
u
re
2
.
Magn
itu
d
e
and
ph
ase respo
n
s
e of
th
e ad
ap
tiv
e filter u
s
ed
Fig
u
re
3
.
Im
p
u
lse resp
on
se
of th
e
Ad
ap
tiv
e filter u
s
ed
4.
SIMULATION RESU
LT AN
D
ANA
LY
SIS
Th
e LMS is u
s
ed
for up
d
a
tin
g
th
e filter co
efficien
ts. Th
e LMS algo
rith
m
is s
i
mu
lated
u
s
i
n
g
MATLAB
.
The filter len
g
t
h
o
f
22
and step
size
0
.
03
53
is u
s
ed
. Th
e MATLAB cod
e
written
was run
so
th
at
th
e b
e
tterp
erform
an
ce is ach
iev
e
d b
y
v
a
rying
th
e filter le
ng
th
and
step size. Figu
re 4 and
Fi
g
u
re
5
sh
ow t
h
e
pl
ot
of
sepa
rat
i
on
of
t
h
e
fi
rs
t
(desi
r
ed
) a
n
d
t
h
e sec
o
nd
(
n
oi
se) a
u
di
o si
gnal
s
. It
i
s
o
b
s
erve
d t
h
at
aft
e
r t
h
e
rem
oval of the
noise signal, the desire
d input signal an
d the desire
d
out
put signal
are
close to each
othe
r.
Also
, t
h
e ad
ap
t
i
v
e
filter ou
tput an
d
th
e
n
o
i
se sig
n
a
l are
close. Th
is sh
ows t
h
at in
ad
ap
tiv
e n
o
i
se rem
o
v
a
l
,
th
e
o
u
t
p
u
t
of th
e fi
lter is sim
p
ly t
h
e
n
o
i
se sign
al wh
ile
th
e co
rrelatio
n
resu
lt is th
e
d
e
sired
o
u
t
p
u
t
sign
al.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
55
7
–
56
0
56
0
Fi
gu
re
4.
Se
par
a
t
i
on
of
t
h
e
Fi
r
s
t
Au
di
o Si
gna
l
:
t
h
e Desi
re
d
Si
gnal
Fi
gu
re
5.
Se
par
a
t
i
on
of
t
h
e
Se
con
d
A
udi
o Si
gnal
:
t
h
e
N
o
i
s
e
Si
g
n
al
5.
CO
NCL
USI
O
N
Ad
ap
tiv
e filters are v
e
ry i
m
p
o
r
tan
t
to
o
l
s in
Dig
ital Sig
n
a
l Processing
. The asp
ect o
f
Mix
e
d
Aud
i
o
Si
gnal
sepa
rat
i
o
n
has
bee
n
l
o
oke
d i
n
t
o
i
n
t
h
i
s
pa
per.
T
h
e
LM
S al
g
o
ri
t
h
m
has been
e
m
pl
oy
ed beca
use
of
i
t
s
si
m
p
licit
y. The im
p
l
e
m
en
tati
o
n
of t
h
is al
go
rith
m
resu
lts
in
reliab
l
e ad
ap
tiv
e
no
ise rem
o
v
a
l fro
m
i
m
p
a
ired
audi
o si
gnal
s
.
REFERE
NC
ES
[1]
Vijay
,
K.M. and
Douglas, B
.
W. (
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itain.
[2]
Monson, .H.
(19
96), “Statistical
Digital
Signal Pr
ocessing and
Mo
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”
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.
[3]
S. Chaudhar
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an
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, vol. 3
,
Issue-2, pp.
208-211, 2013
,
[4]
Scott, C. D. (199
9), “Introduction
to Ad
ap
tiv
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[5]
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K. L. Yad
a
v, Per
f
ormance Ev
alu
a
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[6]
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ilt
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ts
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.
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rmalized
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e
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ation
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,
IEEE workshop on
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and S
y
stems
, pp
. 161-16
4, 2004
.
[8]
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a
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rnat
i
o
nal
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012
[9]
J. W
.
Lee and
G. K.Lee
,
Desi
gn of an Adaptive Filte
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y
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i
c Stru
cture for ECG
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International Jo
urnal of Con
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. 1
,
pp
. 137-
142, 2005
.
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