TELKOM
NIKA
, Vol. 11, No. 12, Decem
ber 20
13, pp.
7146
~71
5
0
e-ISSN: 2087
-278X
7146
Re
cei
v
ed
Jun
e
28, 2013; Revi
sed Aug
u
st 17, 2013; Accepted Aug
u
s
t 28, 2013
Effects of Barrier Parameter to Stochastic Resonance
Signal-to-noise Ratio in Feature Extraction
Tang Xuxian
g*
1
, Ju Chun
hua
2
1
Departme
n
t of Scientific Res
earch, Z
hej
ian
g
Gongsh
a
n
g
Univers
i
t
y
(Z
J
G
SU), No.18, Xu
ezh
e
n
g
Str.,
Han
g
zho
u
31
0
018, Ch
in
a,
Ph./F
ax: +
571-28
877
17
0/288
71
76
2
School of Co
mputer Scie
nc
e and Inform
ati
on Ein
g
in
eer
in
g, Z
hejia
ng Go
ngsh
a
n
g
Univ
e
r
sit
y
(Z
JGSU),
No.18,
Xuez
he
ng Str., Hangz
hou 3
1
0
018, C
h
in
a,
Ph./F
ax: +
571-2
887
71
7
1
/288
71
76
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: juchu
n
h
ua@
hotmai
l
.com
A
b
st
r
a
ct
Effects of bar
rier
para
m
eter
a to
o
u
tput
sign
al-to-n
o
ise
ratio
(SNR)
of bista
b
l
e
sto
c
hasti
c
reson
ance
i
n
f
eature
extracti
on w
a
s
inv
e
sti
gated
in
this
p
aper. B
a
rrier
p
a
ra
meter
a w
a
s cha
nge
d w
i
t
h
other systematic param
e
ters
fixed. The relations
hip between parameter a
an
d the
output SNR of
non-
line
a
r stochasti
c resona
nce s
ystem w
a
s studie
d
. T
h
is
rese
arch prov
ide
d
us a nove
l
w
a
y to extract th
e
features
usin
g
the n
on-
lin
ear
stochastic r
e
s
ona
nce. T
h
e
p
r
opos
ed tec
h
n
i
que
is pr
o
m
isi
ng i
n
th
e fie
l
d
app
licati
ons for
the hu
man r
e
a
l
-time status monitor
i
ng.
Ke
y
w
ords
:
ba
rrier para
m
eter
, stochastic resona
nce, sig
nal
-
t
o-nois
e
ratio, feature extracti
on, non-
lin
ear
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Stocha
stic re
son
a
n
c
e ha
s been utilized
in m
any research field
s
, su
ch a
s
mechani
cal
system
an
alysis, sig
nal proce
s
sing, bioi
nformati
cs,
etc [1
-5]. Thi
s
t
heory
hires e
x
ternal
noise
to
indu
ce
a
syn
c
hrono
us resonan
ce
withi
n
a
non
-lin
e
a
r
bi
stable
sy
stem. At this ti
me, an
evide
n
t
improvem
ent
in sign
al-to
-
n
o
ise
ratio ha
s been o
b
tain
e
d
so that
som
e
importa
nt feature
s
can b
e
extracted
un
der thi
s
be
st state. In thi
s
p
ape
r, a
n
on-lin
ea
r bi
stable
sto
c
ha
stic re
so
nan
ce
system i
s
u
s
ed to extra
c
t
the sp
ort
s
feature
s
provi
ded by a
blu
e
toot
h sta
c
k-based
wirel
e
ss
sen
s
o
r
network. Th
e system output SNR was
p
r
ese
n
ted inst
antane
ou
sly with the barrier
para
m
eter a
cha
nge
s from
0 to 8. O
u
tp
ut SNR
analy
s
is re
sult
s in
dicate th
at th
e SNR chan
g
e
s
with the ch
an
ge of barrier
para
m
eter a.
2. Experimenta
l
Stocha
stic
re
son
a
n
c
e h
a
s three fu
nda
mental ele
m
e
n
ts: a no
n-lin
ear
system,
a we
a
k
coh
e
re
nt in
p
u
t sig
nal,
an
d an
a
ddition
al do
ze
external
n
o
ise so
urce. The no
n-line
a
r bi
sta
b
le
system can
be describe
d
as the motion of an
overdam
ped Bro
w
nia
n
parti
cl
e in a bistab
le
potential in th
e pre
s
en
ce of
periodi
c forci
ng:
()
()
(
)
dx
dV
x
M
It
C
t
dt
dx
(1)
Whe
r
e
x
is the
po
sition of
the Bro
w
ni
an p
a
rticl
e
,
t
is the time,
M and
C are adju
s
tabl
e
para
m
eters,
()
()
()
I
tS
t
N
t
denote
s
an i
nput si
gnal
()
St
and intrin
si
c n
o
ise
()
Nt
,
()
t
is
the external
noise, an
d
()
Vx
is the
simpl
e
st
dou
ble-well
potential with
the con
s
tant
s
a
and
b
cha
r
a
c
t
e
ri
zin
g
t
he sy
st
em.
24
11
()
24
V
x
ax
bx
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Effects of Barrier Pa
ram
e
ter to Stocha
stic Re
so
nan
ce
Signal-to
-
noi
se Ratio… (Ta
ng Xuxia
n
g
)
7147
Equation (1)
can b
e
writte
n as:
3
()
()
dx
ax
bx
MI
t
C
t
dt
(3)
The minim
a
of
()
Vx
are l
o
cated at
m
x
, where
1/
2
(/
)
m
x
ab
. A potenti
a
l barrie
r
sep
a
rate
s the
minima
with
the heig
h
t given by
2
4
a
U
b
. The barri
er top i
s
l
o
cate
d at
0
b
x
.
Whe
n
thre
e element
s of SR intera
ct coherently
, the potential b
a
rri
er
can b
e
redu
ced
and
the
Brownian pa
rticle may su
rmount the en
ergy ba
rri
e
r
and ente
r
an
other pote
n
tial well [30,33
].
The inten
s
ity of signal
s
will increa
se,
whi
c
h ma
ke
s it possible t
hat t
he weak sign
al ca
n
be
detecte
d from
noise b
a
ckg
r
ound.
Suppo
se the
input si
gnal
is
()
s
i
n
(
2
)
It
A
f
t
, where
A
is sign
al inten
s
i
t
y,
f
is
sign
al freq
ue
ncy.
D
is exte
rnal noi
se i
n
tensity. The
mo
st
comm
o
n
qua
nt
if
iers
f
o
r
st
o
c
h
a
st
i
c
resona
nce are the sp
ec
tral
amplificatio
n
and the sy
stematic o
u
tput
SNR. He
re
SNR meth
od
wa
s ado
pted
to characte
r the syste
m
ou
t
put, which h
a
s the follo
wi
ng definition:
0
2[
l
i
m
(
)
]
/
(
)
N
SN
R
S
d
S
(
4
)
()
N
S
is the n
o
ise i
n
tensity in
si
gnal fre
que
n
c
y ran
ge, an
d
()
S
is
the sign
al
power spe
c
t
r
al
dens
i
ty.
The ha
rd
wa
re system
consi
s
ts of a
we
a
r
abl
e activity reco
rding de
sig
n
using
MMA7261
QT
se
rie
s
a
c
celero
meter sensors, a
h
eart-rate
me
asu
r
ing
sen
s
or utilizi
n
g
a
comm
ercial Bluetooth mod
u
le, and a PC with fri
endly controlling
so
ftware. Three
main module
s
are
u
s
ed
wh
en the
wea
r
a
b
le d
e
vice
s
were to
be
a
dhered
to vol
unteer b
ody.
Four volunte
e
rs
(num
bered b
y
A, B, C,
and D) are
cho
s
en fr
o
m
the unive
rsity stud
ent
s to ca
rry o
u
t
experim
ents.
The
wea
r
abl
e
device
s
are
fixed on th
e voluntee
rs’
bo
dies, e
a
ch vo
lunteer sit
s
o
n
the chai
r for 15 minute
s
then expe
rim
ents sta
r
t. Ac
tivity varieties incl
ude: sta
nding, walkin
g,
runni
ng, and
football playing. The accel
e
rom
e
ters
on
ly give us the refere
nce pa
ramete
rs h
e
re.
To digitize th
e record
ed Q
R
S wave, the ECG signal i
s
sam
p
led at 512 Hz. Hea
r
t rate signal i
s
divided into continuo
us 1
-
minute se
gm
ent
of 8-se
co
nds
step. Instant heart rat
e
(
H
(
t
)), the
1-
minute incre
a
s
e (
∆
HR
1 minute
), and mean
heart rate (
()
N
H
t
), defined a
s
(5
)~(7
):
60
n
()
.
s
f
Ht
t
(
5
)
1
15
0
()
(
)
.
2
N
N
kN
s
k
Ht
H
t
Nf
(
6
)
T
m
i
nut
e
HR
(
)
(
T
)
(
)
.
tH
t
H
t
(
7
)
Whe
r
e n
= 3,
N
= 30
0.
Noi
s
e inten
s
i
t
y is just a para
m
eter of
SR model.
SR model i
s
used a
s
a
data
pro
c
e
ssi
ng method
in
th
is re
sea
r
ch. We use
()
s
i
n
(
2
)
()
()
I
tA
f
t
W
t
N
t
as in
put
matrix. It has a sin
u
soid
signal
si
n(
2
)
Af
t
, accelerometer
se
nsor respon
se
data
()
Wt
,
and i
n
trin
sic
noise
()
Nt
. Noise
intensity
cha
nge
s
within t
he
ran
ge [0,9
00]. SNR b
e
twee
n th
e
output and in
put is cal
c
ul
ated. A graphi
cal illustrati
o
n
of SR pro
c
e
s
sing i
s
sh
own
in Figure 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 12, Dece
mb
er 201
3: 714
6 – 7150
7148
Figure 1. Gra
phical Illustrat
i
on of Data Analysi
s
Metho
d
3. Resul
t
s
and
Discus
s
ion
In the past twenty years, stoch
a
sti
c
re
so
nan
ce h
a
s bee
n used
as engi
nee
ri
ng data
pro
c
e
ssi
ng m
e
thod in
nu
mbers
of re
search fiel
ds
Bistable
sto
c
hasti
c resona
nce
theo
ry h
a
s
been wi
dely investigate
d
by resea
r
che
r
s from many
countrie
s
[6-1
2
]. In
this pape
r, experime
n
ts
are hel
d to explore the re
lations
hip bet
wee
n
barrie
r
paramete
r
a
and stocha
stic resona
nce
whe
n
input
si
gnal inten
s
ity A is fixed. Action me
asurements
of four volunte
e
rs are tra
n
smitted
to PC for fu
rther a
nalysi
s
t
h
rou
gh Blu
e
tooth dev
i
c
e
s
. The exp
e
rim
ental data
of volunteer B
i
s
cho
s
e
n
and
the systemat
ic barrie
r
pa
ramete
r
a
varie
s
from 0
to 8. Analysis results a
r
e
displ
a
yed in
Figure 2 to Fi
gure
7. Whe
n
param
eter
a
put up at a lo
w level (n
o m
o
re tha
n
3.2),
no obviou
s
ei
gen pea
k ap
pears. With the value vari
es from 4.8 to 8.0, the output SNR curv
e
pre
s
ent
s feat
ure pe
aks g
r
adually an
d we can see t
hat four a
c
tivities of the sel
e
cted volu
nte
e
r
can
be
di
scri
minated
from
ea
ch
othe
r.
The
optimize
d
sy
stemati
c
barrier value
is a
bout
f
0
=8.
0
.
Football
playi
ng o
w
n
s
th
e
highe
st SNR
pea
k valu
e th
an the
othe
r
activities, a
n
d
stan
ding
o
w
ns
the lowest. Accordi
ngly, football playing
lead
s
to fast
est he
art rate
and
standin
g
pre
s
e
n
ts th
e
lowe
st. With
t
he in
crea
se
o
f
barrie
r
p
a
ra
meter
a
, BSR pea
ks lo
cate
d noi
se
intensities increase.
The sy
stema
t
ic barrie
r
pa
ramete
r
a
d
e
t
ermine
s the
position
of SNR p
e
a
ks.
Based
on thi
s
con
c
lu
sio
n
, we can u
s
e thi
s
ch
ara
c
te
rist
ic to analyze heart rate fea
t
ures.
Figure 2. Output SNR Curves Rel
a
ted
with
Systematic B
a
rri
er Parame
ter
a
=0
Figure 3. Output SNR Curves Rel
a
ted
with
Systematic B
a
rri
er Parame
ter
a
=1.6
Gene
rally sp
eaki
ng, sto
c
h
a
stic
re
son
a
n
c
e
o
c
curs
in
non-li
nea
r system
s,
wh
en a
sm
all
perio
dic (sinu
s
oid
a
l) fo
rce i
s
a
pplie
d tog
e
ther
with
a l
a
rge
wi
de
ba
nd
stocha
stic force
(noi
se
).
The
system
resp
on
se i
s
d
r
iven by the
combinatio
n of
the two force
s
that
com
pet
e/coo
perate t
o
make the
system switch b
e
twee
n the two sta
b
le
sta
t
es. The deg
ree of orde
r is related to the
amount of p
e
r
iodi
c fun
c
tio
n
that it sho
w
s i
n
t
he sy
stem re
spo
n
se. Whe
n
the
perio
dic fo
rce
is
cho
s
e
n
small
enoug
h in order to not ma
ke the sy
ste
m
respon
se
switch, the p
r
e
s
en
ce of a no
n-
negligibl
e
n
o
i
s
e i
s
requi
re
d
for it to h
app
en. W
hen th
e
noise i
s
sma
ll very few
switche
s
o
c
cur,
mainly at ran
dom with no
signifi
cant pe
riodi
city
in the system re
sp
onse.
Whe
n
the noi
se is v
e
ry
stron
g
a l
a
rg
e numb
e
r
of swit
che
s
o
c
cur for e
a
ch
perio
d of th
e sin
u
soid a
nd the
syste
m
0
20
40
60
80
10
0
12
0
140
16
0
18
0
-1
15
-1
10
-1
05
-1
00
-9
5
-9
0
-8
5
-8
0
-7
5
-7
0
-6
5
-6
0
N
o
is
e
in
t
e
n
s
it
y
SN
R
(
d
b
)
f
o
ot
ba
l
l
r
unn
i
n
g
wal
k
i
n
g
s
t
an
di
n
g
0
20
40
60
80
10
0
120
14
0
160
18
0
-1
15
-1
10
-1
05
-1
00
-9
5
-9
0
-8
5
-8
0
-7
5
-7
0
-6
5
-6
0
N
o
is
e
in
t
e
n
s
it
y
SN
R
(
d
b
)
f
o
ot
bal
l
ru
nni
ng
w
a
lk
in
g
s
t
and
i
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Effects of Barrier Pa
ram
e
ter to Stocha
stic Re
so
nan
ce
Signal-to
-
noi
se Ratio… (Ta
ng Xuxia
n
g
)
7149
respon
se d
o
e
s
not sh
ow
re
markabl
e peri
odicity.
Between the
s
e two con
d
ition
s
, there exist
s
a
n
optimal value
of the noi
se t
hat co
ope
rati
vely con
c
urs
with the p
e
rio
d
ic fo
rcin
g in
orde
r to m
a
ke
almost exa
c
tl
y one switch
per
peri
od
(a maximum
i
n
the si
gnal
-to-noi
se
ratio
)
. In this stu
d
y,
stocha
stic re
son
a
n
c
e i
s
u
s
ed to
extract the
feature
informatio
n of human
bo
dy status. Th
e
prop
osed techniqu
e is promisin
g in the field
appl
ication
s
for the huma
n
real-time
statu
s
monitori
ng. We have arrange
d a lon
g
-term pl
an to
investigate
the usage o
f
this method
in
human b
ody monitori
ng.
Figure 4. Output SNR Curves Rel
a
ted
with
Systematic B
a
rri
er Parame
ter
a
=3.2
Figure 5. Output SNR Curves Rel
a
ted
with
Systematic B
a
rri
er Parame
ter
a
=4.8
Figure 6. Output SNR Curves Rel
a
ted
with
Systematic B
a
rri
er Parame
ter
a
=6.4
Figure 7. Output SNR Curves Rel
a
ted
with
Systematic B
a
rri
er Parame
ter
a
=8.0
4. Conclu
sion
The effe
cts o
f
system
atic
barrier
a
to
BSR are inv
e
stigate
d
in
this
pap
er
ba
sed
on
WSN
sign
al
measurement
device
s
. Wit
h
a
varia
b
le systematic
b
a
rrier paramete
r
a
rang
e fro
m
0 to
8.0, BSR non
-line
a
r sy
stem
output
SNR curve
s
are
calculate
d
for furth
e
r a
nalysi
s
. With
an
incr
ea
se of
p
a
ram
e
t
e
r
a
,
BSR pea
ks l
o
cate
d noi
se
intensitie
s in
cre
a
se gradu
ally. Thus, we
coul
d co
ncl
u
de that syste
m
atic ba
rri
er
para
m
eter
a
determi
ne
s the scatterin
g
instan
ce of S
NR
pea
ks. Thi
s
method i
s
p
r
omisin
g in h
u
man bi
oinf
o
r
matics a
naly
s
is. In thi
s
st
udy, stocha
stic
resona
nce i
s
used to
extract the
featu
r
e i
n
fo
rm
ation
of
h
u
ma
n body status.
The pro
p
o
s
e
d
techni
que i
s
promi
s
in
g in the field appli
c
ations
for the
human
real
-time statu
s
mo
nitoring.
0
20
40
60
80
10
0
12
0
140
16
0
18
0
-1
15
-1
10
-1
05
-1
00
-9
5
-9
0
-8
5
-8
0
-7
5
-7
0
-6
5
-6
0
N
o
is
e
in
t
e
n
s
it
y
SN
R
(
d
b
)
f
o
ot
ba
l
l
r
unn
i
n
g
wal
k
i
n
g
s
t
an
di
n
g
0
20
40
60
80
100
12
0
14
0
16
0
18
0
-
115
-
110
-
105
-
100
-9
5
-9
0
-8
5
-8
0
-7
5
-7
0
-6
5
-6
0
N
o
is
e
in
t
e
n
s
i
t
y
SN
R
(
d
b
)
f
o
ot
bal
l
ru
nn
i
n
g
w
a
lk
in
g
s
t
a
ndi
n
g
0
20
40
60
80
100
12
0
14
0
16
0
18
0
-11
5
-11
0
-10
5
-10
0
-9
5
-9
0
-8
5
-8
0
-7
5
-7
0
-6
5
-6
0
N
o
is
e
in
t
e
n
s
it
y
S
NR (
d
b
)
f
o
ot
ba
l
l
ru
nn
i
n
g
w
a
lk
in
g
s
t
a
ndi
n
g
0
20
40
60
80
10
0
12
0
14
0
160
180
-
115
-
110
-
105
-
100
-95
-90
-85
-80
-75
-70
-65
-60
N
o
is
e
i
n
t
e
n
s
it
y
S
N
R (db)
f
oot
bal
l
r
unni
ng
w
a
lk
in
g
s
t
and
i
n
g
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Vol. 11, No
. 12, Dece
mb
er 201
3: 714
6 – 7150
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