Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
72
5
~
73
4
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.9
034
7
25
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
Re
so
lv
ing
the
Issue
s
o
f
Ca
pon and APES Approach for
Projecting Enhanced Spectral Estimation
Kan
t
ipudi
MVV
Pr
asad*, Dr. H.
N. Sure
s
h**
* Visvesvaray
a
Techno
logical
Universit
y
,
Be
lga
u
m
,
India
** Departmen
t
o
f
Instrumentatio
n Bangalore
Institute Technolog
y,
Bang
alor
e, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 15, 2015
Rev
i
sed
No
v
30
, 20
15
Accepted Dec 16, 2015
There
are v
a
riou
s
applic
ations
o
n
s
i
gna
l processing that
is highly dependen
t
on precis
e
nes
s
a
nd accura
c
y
of t
h
e outcom
e
s
in s
p
ectrum
of s
i
gnals
. Henc
e,
from
the past t
w
o decades th
e
research
com
m
unit
y
has r
e
c
ognized
the
benefits, significance, as
well as
as
s
o
ciat
ed probl
em
s
in carr
y
ing
out a m
odel
for spectra
l es
tim
ation
.
W
h
ile
in-depth
inve
stigation o
f
th
e exist
i
ng
liter
a
tur
e
s shows that
ther
e a
r
e
various a
ttem
p
ts
b
y
th
e rese
arch
ers to solv
e
the
issues associa
t
ed wi
th spe
c
tra
l
est
i
m
a
tion
s
, where
m
a
jor
i
t
y
of
te
h
res
earch work
is
inclined
towards
addres
s
i
ng problem
s
as
s
o
cia
t
ed with
Capon and APES techniqu
es of spectra
l analy
s
is. Th
eref
or
e, this paper
introduces a v
e
r
y
simple techniq
u
e towards r
e
solving the issues o
f
Capon
and
APES techniqu
es. The outcome
of the
stud
y
was
analy
z
ed
using correlational
factor
and pow
er spectr
a
l d
e
nsity
to fi
nd
th
e pr
oposed s
y
stem
offers better
s
p
ectra
l
es
tim
ati
ons
com
p
ared
to
exis
t
i
ng s
y
s
t
em
.
Keyword:
APES
C
a
po
n E
s
t
i
m
a
tors
Power Sp
ectral
Den
s
ity
Sp
ectral Esti
matio
n
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
:
Kan
tipud
i MVV Prasad
Research Sc
holar
Vi
sves
va
ray
a
Tech
nol
ogi
cal
Un
i
v
ersity, Bel
g
aum
,
India
E-Mail: p
r
asadb
201
6@g
m
ai
l.co
m
1.
INTRODUCTION
In t
h
e a
r
ea of
signal
processi
ng, the
spect
ra
l estim
a
tion
plays a critical role for m
a
ny applications.
Som
e
of t
h
e e
ffect
i
v
e
exam
pl
es fo
r t
h
i
s
pu
r
pos
e ca
n
be sa
i
d
t
o
be
t
a
r
g
et
o
f
i
d
e
n
t
i
f
y
i
n
g
t
h
e
peri
odi
ci
t
y
of
a
signal in tim
e
-series, which can
be state
d
as a
prob
lem
o
f
sp
ectral
esti
m
a
tio
n
[1]. Th
e co
nv
entio
n
a
l
t
echni
q
u
es t
o
p
e
rf
orm
spect
ral
est
i
m
a
ti
ons a
d
opt
Di
scret
e
F
o
u
r
i
e
r T
r
a
n
sf
or
m
(DFT
) an
d i
t
s vari
ous
ve
rsi
ons
.
There ar
e vari
ous
researc
h
er
s t
h
at
have at
t
e
m
p
t
e
d t
o
i
n
t
r
od
uce va
ri
o
u
s
param
e
t
r
i
c
t
e
chni
que
s wi
t
h
enha
nce
d
reso
l
u
tio
n ap
pro
ach for ach
i
ev
ing
b
e
tter
po
ten
tial in
reso
l
v
in
g issu
es of
sp
ectral estim
at
io
n
s
[2
] [3
].
So
m
e
o
f
the recent effic
i
ent approac
h
e
s
that co
m
e
under the non
-pa
r
am
etric trends
are conventional Capon estim
ators
and
Am
pl
i
t
ude
an
d P
h
ase
Est
i
m
a
ti
on
(A
PE
S) t
e
c
hni
ques
[4]
.
H
o
we
ve
r,
a cl
oser
l
o
o
k
i
n
t
o
C
a
p
o
n
est
i
m
at
ors
and
Am
pl
i
t
ude and P
h
ase Est
i
m
a
ti
on (
A
PE
S) t
ech
ni
q
u
es
sho
w
s t
h
at
t
h
e
y
exhi
bi
t
pe
rf
o
r
m
a
nce equi
va
l
e
nt
t
o
co
nv
en
tio
n
a
l
DFT
app
r
o
a
ches und
er certain
co
nd
itio
ns.
In
th
is p
a
p
e
r,
we em
p
h
a
size the u
tilities o
f
sp
ectral
estim
a
tion techni
que
s as they are frequent
l
y used in
m
a
ny
m
a
jor ap
pl
i
cat
i
ons of si
g
n
al
pr
ocessi
ng
e.g
.
desi
g
n
i
n
g co
nt
rol
sy
st
em
s, bi
o-m
e
di
cal
si
g
n
al
anal
y
s
i
s
, p
r
oces
si
n
g
spee
ch, an
d fi
n
d
i
n
g l
a
t
e
nt
peri
o
d
i
c
i
t
y
.
These estim
ation tec
hni
que
s are m
o
re or le
ss inclined
t
o
ward
s tim
e fac
t
o
r
wh
ile an
al
ysis a spectrum
.
There
are also applic
ations
found
fo
r sp
ect
ral estimatio
n
s
con
s
idering
th
e sp
ati
a
l factors e.g.
localizing t
h
e
source
usi
n
g wi
rel
e
ss sens
ors
.
W
e
al
so
em
phasi
ze on
t
h
e
u
n
s
o
l
v
e
d
problem
associated wi
t
h
the sp
ectral estimatio
n
tech
n
i
qu
es th
at
calls fo
r ev
al
u
a
tio
n
o
f
th
e cu
m
u
lativ
e
po
w
e
r t
h
at
are
bei
n
g
di
st
ri
b
u
t
e
d
ove
r ce
rt
ai
n
ra
nge
o
f
fre
que
ncy
fr
o
m
a fi
xed
reco
rd
o
f
st
at
i
c
se
q
u
ence
s
of
dat
a
.
Thi
s
pa
per
h
a
s p
r
ese
n
t
e
d a
v
e
ry
si
m
p
l
e
t
e
chni
qu
e
to
en
h
a
n
ce th
e cap
ab
ilities o
f
sp
ectral esti
matio
n
techn
i
ques co
n
s
i
d
eri
n
g
th
e case stu
d
y
o
f
Capon
and
APES
esti
m
a
t
i
o
n
p
r
ocess. Th
e
p
a
p
e
r will also
show sign
ific
an
t im
p
r
o
v
e
m
e
n
t
of power
sp
ect
ral d
e
n
s
ity as
well as
cor
r
el
at
i
onal
fa
ct
or by
i
n
t
r
o
d
u
c
i
ng
t
h
e pr
o
p
o
s
ed
t
e
c
hni
que
of spect
ral
ana
l
y
s
i
s
.
Sect
i
on 2 di
scusse
s
a
b
out
t
h
e
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
. 2, A
p
ri
l
20
16
:
72
5 – 7
3
4
72
6
researc
h
m
e
t
h
o
dol
ogy
an
d res
earch an
d di
sc
ussi
o
n
has
di
scusse
d i
n
Sect
i
on 3. Fi
nal
l
y
, Se
ct
i
on 4 m
a
kes
som
e
concl
udi
ng
re
m
a
rks a
n
d
hi
g
h
l
i
ght
s
t
h
e
di
re
ct
i
on
of
f
u
t
u
re
wo
rk
t
o
be
car
r
i
ed o
u
t
.
1.
1
Back
ground
Th
is section
will p
r
esen
t variou
s sign
ifican
t rese
arch
works in
tro
duced
b
y
th
e
research
ers m
o
st
recent
for addressing t
h
e
proble
m
s
asso
ciated with spect
ral estim
a
tions.
Niel
son et al. [5]
have
focused
on t
h
e
issu
es asso
ciated
with
Capo
n esti
m
a
to
rs and
h
a
v
e
m
ech
an
ized
a
way usin
g
a
v
a
riab
le len
g
t
h
of n
e
w filter
desi
g
n
fo
r e
n
h
a
nci
n
g t
h
e
per
f
o
r
m
i
ng o
f
s
p
e
c
t
r
al
est
i
m
a
t
i
o
ns.
The
out
c
o
m
e
of t
h
e st
ud
y
was a
n
al
y
z
e
d
usi
n
g
mean squa
red error.
Studies
towa
rd
Cap
o
n
along
with
th
e APES estim
ators wa
s al
so
witnesse
d i
n
the
literatu
re of Alty et a
l
. [6
],
wh
ere th
e au
t
h
ors
h
a
v
e
adop
ted
slid
i
n
g
win
d
o
w
b
a
sed
o
n
tem
p
o
r
al facto
r
.
Ho
we
ver
,
few
at
t
e
m
p
t
s
of be
nchm
arki
n
g
w
e
re fo
u
nd i
n
t
h
e st
udy
. Si
m
i
l
a
r pat
t
e
rn
of st
u
d
y
was al
so wi
t
n
essed
in
th
e literatu
re o
f
Ang
e
lop
o
u
l
o
s
et al. [7
]. Th
e m
a
j
o
r em
p
h
a
sis o
f
th
e study w
a
s to
in
trodu
ce th
e sign
ifican
ce
o
f
coh
e
ren
ce sp
ectru
m
an
d
to
scale down
t
h
e h
y
p
o
t
h
e
tical co
m
p
lex
ities
asso
ciated
with
Capon
and
APES.
Th
e stud
y h
a
s also
p
e
rfo
r
m
e
d
an
ex
tensiv
e an
alysis o
f
the co
m
p
u
t
atio
nal co
m
p
lex
itie
s with
resp
ect
to
th
e
len
g
t
h
of th
e
filter b
a
nk
s. Th
e stud
y was
also
fo
und
to
miss o
u
t
co
mp
arativ
e an
alysis to
sho
w
case th
e
effectiv
en
ess of th
e o
u
t
co
m
e
s
.
Literatu
res hav
e
also
prese
n
ce of certain uni
que attem
p
ts to perform
s
p
ectra
l
esti
m
a
t
i
o
n
.
Ado
p
tion
o
f
Goh
b
erg
factorization
techn
i
qu
e wa
s seen
i
n
th
e literatu
re of
Xu
e
et al. [8
],
wh
ere th
e
aut
h
ors
ha
ve
use
d
wei
ght
e
d
l
east
squa
re
d
app
r
oach
o
f
i
t
e
rat
i
v
e nat
u
r
e
. The
o
u
t
c
o
m
e of t
h
e st
u
d
y
was
anal
y
zed usi
n
g
com
put
at
i
onal
t
i
m
e
as wel
l
as si
gnal
p
o
we
r
,
but
t
h
e o
u
t
c
o
m
e of t
h
e st
ud
y
was not
f
o
u
nd t
o
analyze with respect to the
power s
p
ectral density,
wh
ich
is also
on
e of th
e significant pe
rformance
param
e
ters to showcase the
effectiv
e
n
ess
of spectral estimation techni
que
s. Tezel and Yildirum
[9] have
foc
u
se
d on the
problem
s associated
with APES technique a
nd
he
nce the
au
tho
r
s
h
a
v
e
in
tr
odu
c
e
d
an
ad
ap
tiv
e
i
m
p
u
l
se filtering
techn
i
qu
e
con
s
id
ering
th
e case stud
y of si
g
n
a
ls b
e
i
n
g g
e
n
e
rated
fro
m
t
h
e
rad
a
r im
ag
in
g.
M
o
st
rece
nt
l
y
,
t
w
o
di
m
e
nsi
onal
vi
brat
i
o
n si
gnal
s
a
n
d t
h
ei
r
ge
nerat
e
d s
p
e
c
t
r
um
have
bei
n
g
anal
y
zed
by
Dan et
al
. [1
0]
usi
n
g da
m
p
ed C
a
pon e
s
t
i
m
a
t
o
rs. The
aut
h
o
r
s ha
ve prese
n
t
e
d a sp
ect
rum
represe
n
t
a
t
i
o
n
wi
t
h
res
p
ect
t
o
fre
q
u
e
n
cy
an
d
dec
o
m
posed
pa
ram
e
t
e
rs of
pl
a
n
e
of
t
h
e
r
a
nd
om
vi
brat
i
o
n
o
f
t
h
e
real
-
w
o
r
l
d
.
The st
udy
has
ado
p
t
e
d
a m
a
xim
i
zed resol
u
t
i
on
o
f
phas
e
an
d am
pl
i
t
ude f
o
r anal
y
z
i
n
g
bot
h
decom
pose
d
fact
o
r
and
f
r
eq
ue
ncy
.
The
o
u
t
c
om
e of t
h
e st
u
d
y
w
a
s anal
y
zed i
n
pre
s
ent
e
d o
f
noi
se t
o
s
h
o
w
opt
i
m
al
resol
u
t
i
on
of
the fre
quency. The authors have als
o
commented that their techniques
are
m
o
re applicable on ext
r
acting
spect
r
u
m
wi
t
h
preci
se am
pl
i
t
ude
. S
r
i
d
har
a
n
d
S
r
i
n
i
v
as
ul
u
[
11]
have
a
d
o
p
t
e
d e
n
ha
nced
recu
rsi
v
e
l
east
squ
a
re
t
echni
q
u
e
fo
r
achi
e
vi
n
g
e
n
h
a
nced s
p
ect
ral
resol
u
t
i
o
n
.
K
a
l
a
gn
om
os et
al
. [1
2]
ha
ve i
n
t
e
g
r
at
ed c
o
n
v
e
nt
i
ona
l
APES an
d its
en
h
a
n
c
ed
v
e
rsio
n is called as
p
a
ram
e
teri
zed APES for enha
nce spectral es
tim
a
tions over
rada
r
im
agi
ng. T
o
uz
e et
al
. [13]
h
a
ve i
n
t
r
od
uce
d
a t
h
ree di
m
e
nsi
o
nal
est
i
m
a
t
o
rs
usi
n
g C
a
po
n a
nd M
U
S
I
C
A
L
al
go
ri
t
h
m
wi
th
do
u
b
l
e
p
r
ec
i
s
i
on.
C
a
n
d
es
et
al
. [
1
4]
have
de
si
g
n
ed
a s
o
ft
t
h
res
h
ol
di
n
g
a
p
pr
oa
ch
fo
r
per
f
o
r
m
i
ng sp
ect
ral
est
i
m
a
tion
usi
ng si
ng
u
l
ar val
u
e
o
v
er
medical im
age
s
for ac
hieving an
optim
a
l
spectra
l
estim
a
tion technique.
1.
2
The Problem
In t
h
e area
of
si
gnal
p
r
oce
ssi
ng
, spect
ral
est
i
m
a
ti
on pl
ays a critical role in va
ri
ous applications e.g.
anal
y
s
i
s
of ra
d
a
r si
gn
al
, spee
ch p
r
oce
ssi
n
g
,
and
bi
ol
ogi
cal
pr
ocessi
ng
of s
i
gnal
s
et
c t
h
at
m
a
i
n
l
y
fal
l
under t
h
e
catego
r
y
of ti
m
e
-fre
que
ncy
signal a
n
aly
s
is. It was also
se
en that F
o
u
r
ier
Trans
f
orm
a
tion tech
niq
u
e is m
a
inly
ad
op
ted fo
r
t
h
e pu
rp
o
s
e of
evalu
a
tin
g
sp
ectru
m
o
f
non
-p
ar
a
m
etric type. Most rece
n
tly, th
ere is an
in
creasing
foc
u
s
o
n
i
nves
t
i
g
at
i
ng t
h
e
po
ssi
bl
e u
s
e
of
C
a
po
n est
i
m
ati
on t
e
c
h
ni
q
u
es
an
d a
d
a
p
t
i
v
e
am
pl
i
t
ude a
n
d
p
h
as
e
estim
a
tion techni
que
s (APE
S).
One
of
the
significa
nt advanta
g
es of
adoption
of s
u
ch
m
e
thod usi
n
g Capon
and
AP
ES
ov
er co
n
v
ent
i
o
n
a
l
spect
ral
est
i
m
a
ti
on t
ech
ni
que i
s
e
n
hanc
ed res
o
l
u
t
i
o
n
as wel
l
as sm
oot
he
r
feat
ure
s
of t
h
e
si
gnal
s
.
H
o
we
ver
,
s
u
ch
t
ech
n
i
ques
al
so
ha
ve
cert
a
i
n
pi
t
f
al
l
s
e.g
.
C
a
po
n a
nd
A
P
ES t
ech
ni
q
u
e
s
use
d
i
n
e
x
i
s
t
i
ng sy
st
em
have m
o
re de
p
e
nde
ncy
o
n
c
o
m
put
at
i
onal
and
pr
ocessi
ng
p
o
w
er
It was also
found t
h
at Capon
and
APE
S
techniques used ca
n re
nde
r a
significant am
ount of instability in
the system
.
The
peak locat
ions
found in t
h
e s
p
ectral an
alysis u
s
in
g APES techn
i
qu
es
are usually bia
s
ed acc
om
panied
b
y
lower reso
l
u
tio
n.
Hence
,
t
h
e
pr
o
b
l
e
m
st
at
em
ent
o
f
t
h
e
pr
o
pos
ed st
udy
i
s
– “
It
i
s
a c
o
mp
ut
at
i
o
n
a
l
l
y
c
hal
l
e
ngi
ng
t
a
sk
t
o
desi
g
n
a
n
i
n
teg
r
a
t
ed sp
ectra
l ana
lysis co
n
s
i
d
eri
n
g
bo
th
Capon
and
APES
a
p
p
r
o
a
ch
to
en
su
re co
st
-
e
ffective
com
p
ut
at
i
o
nal
an
al
ysi
s
f
o
r
t
w
o di
me
nsi
o
n
a
l
spect
ru
ms.
”
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Reso
lving
t
h
e Issu
es
o
f
C
a
pon an
d APES
App
r
oa
ch
f
o
r Projectin
g
En
han
ced
…
(Kan
tip
ud
i MVV Pra
s
ad
)
72
7
1.
3
The Proposed So
lut
i
on
The m
a
i
n
p
u
r
pos
e
of t
h
e
pr
op
ose
d
sy
st
em
i
s
t
o
e
v
ol
ve
up
wi
t
h
a t
e
c
h
ni
q
u
e t
h
at
can
i
n
t
r
od
uce
a
spectral estim
a
tion tec
hni
que
s usi
n
g non-param
etric appr
o
ach. Th
e
pr
op
o
s
ed system
u
s
es
bo
th
capo
n and
APES estim
at
i
o
n techn
i
qu
e t
o
i
n
v
e
stig
ate th
e
p
r
ob
lem
s
asso
ciated
with it and
p
r
ov
id
es
a so
l
u
tio
n to reso
lve
th
e prob
lem
s
. Gen
e
rally, it is kn
own
th
at
su
ch
techn
i
q
u
e
w
o
r
k
s
on
t
h
e pri
n
ci
pl
e
of
l
o
we
r va
ri
ance
wi
t
h
resp
o
n
se o
f
l
e
sser de
fo
rm
at
ion
fo
r ens
u
ri
n
g
o
p
t
i
m
al
resol
u
t
i
on. T
h
e s
p
ect
rum
generat
e
d by
C
a
p
on
can be
considere
d
to
be a set of filters, wh
ere eac
h of the
filters is positione
d in
c
e
nter of each
other in the e
v
aluation
o
f
frequ
en
cies. Th
ere is a
h
i
gh
er
d
e
p
e
nd
en
ci
es of bo
th
frequ
e
n
c
y and
d
a
ta in
its b
a
nd
p
a
ss filters th
at separates
C
a
po
n t
ech
ni
q
u
es
of
spect
ra
l
est
i
m
a
ti
ons
fr
om
ot
her c
o
nve
nt
i
o
nal
t
echni
que
s e.
g.
p
e
ri
o
d
o
g
ram
t
h
at
i
s
pot
e
n
t
i
a
l
l
y
i
ndepen
d
e
n
t
of f
r
e
que
ncy
as we
l
l
as dat
a
usi
ng di
scret
e
m
a
t
r
i
x
of F
o
u
r
i
e
r
Tran
sf
orm
.
Theref
ore
,
th
e p
r
im
ary g
o
a
l o
f
th
is
m
a
n
u
s
cri
p
t is to
reso
lv
e th
e i
ssue
s
of C
a
p
on an
d APE
S
est
i
m
a
t
o
rs by
i
nve
st
i
g
at
i
n
g
the
dynam
i
c spectrum
formulated
fo
r showing
t
h
e
si
g
n
i
fican
t relatio
nsh
i
p
b
e
t
w
een an
y
two
sign
als. W
e
defi
ne a
t
e
rm
cal
l
e
d as c
o
rre
l
a
t
i
onal
fact
or
t
o
i
nve
st
i
g
at
e t
h
e
p
o
ssi
bl
e
r
e
l
a
t
i
onshi
p
bet
w
een
t
h
e
t
w
o
real
-
value
d
si
gnals. The
propose
d
syste
m
also targets to
pe
rf
orm
co
m
p
arative analysis of
spectral esti
m
a
ti
o
n
wit
h
respect to exis
ting techni
que
s of Peri
odogram
,
PW
elc
h
, a
nd Multitaper
m
e
thod co
nsi
d
ering Power S
p
ectral
Den
s
ity an
d correlatio
nal fact
o
r
.
2.
RESEARCH METHO
D
OL
OGY
Th
e
b
a
selin
e o
f
estim
at
io
n
techn
i
qu
es for Capon
ap
pro
ach
u
s
es filter-b
ank
deco
m
p
o
s
ition
tech
n
i
qu
es. Each
b
a
nd
in
vo
l
v
ed
in
th
e
p
r
o
c
ess calls fo
r it
s sig
n
a
ls to
b
e
esti
m
a
ted
.
Co
n
s
id
er an
inpu
t
stat
i
c
arb
itrary pro
c
ess of zer
o-m
e
a
n
th
at
will act as an
i
n
pu
t for th
e f
ilters. Hen
ce, t
h
e fun
c
tio
n rep
r
esen
ting
filter
can be now re
presente
d
as
,
Mk
=
[
m
k, 0
, m
k, 1
. .
. m
k, s-
1
]
α
(
1
)
In the a
b
ove e
q
. (1), Mk can be
conside
r
ed as function
for the
k
nu
m
b
er o
f
filters of size
s
. The va
ria
b
le
α
will rep
r
esen
t
tran
sp
o
s
ition
matrix
. Th
erefo
r
e, th
e an
ticip
ated
p
o
wer
facto
r
of th
e
ou
tpu
t
sig
n
a
l can
b
e
math
e
m
atica
l
l
y
represen
ted
as,
}
|
)
(
{|
}
|
)
(
{|
2
2
n
X
m
E
n
b
E
k
k
k
m
xx
k
C
m
.
.
(
2
)
In
th
e ab
ov
e eq
u
a
tion
(2), the v
a
riab
le
E
c
a
n be t
e
rm
ed as ant
i
c
i
p
at
ed
po
we
r of t
h
e out
put
si
g
n
al
a
nd t
h
e
vari
a
b
l
e
β
can be term
ed as conjugate tra
n
spose m
a
trix
. The covaria
n
ce
m
a
trix is represe
n
ted
by
C
xx
associated with
th
e inpu
t sign
al a
n
,
it
can
b
e
fu
rt
h
e
r written
as,
)}
(
).
(
{
n
X
n
X
E
C
xx
(
3
)
In t
h
e e
quatio
n
(2
) a
nd
(
3
),
th
e varia
b
le X
(
n
)
can
be
define
d as a trans
p
os
ed m
a
trix with an elem
ents of
x
(
n
),
x
(
n
-1),
.
. .
,
x
(
n
-
s
+
1). T
h
ere
f
ore, t
h
e syste
m
can
sh
ap
e up
th
e Fo
urier
matrix
(
γ
) c
ons
i
d
eri
n
g s
x
K
,
γ
=
[
γ
0
,
γ
1
. .
.
γ
K-1
]
(
4
)
In th
e abo
v
e
equ
a
tio
n (4
), the
v
a
riab
le
γ
k
i
s
e
qui
val
e
nt
t
o
,
]
)
1
(
exp(
....
exp(
1
[
1
s
j
j
s
k
k
(
5
)
In t
h
e ab
o
v
e e
quatio
n
(5
),
φ
k
i
s
equi
val
e
nt
t
o
2
π
k
/
K
(K=max
im
u
m
n
u
m
b
e
rs of
filters).
Th
erefo
r
e, when
th
e
value
of K as
well as
s
is equ
i
v
a
len
t
, th
an
t
h
e m
a
trix
F can
b
e
term
ed
as Fou
r
ier m
a
trix
. Hen
ce,
F
β
.F=
F
.F
β
=I
(unitary m
a
trix). The
r
e
f
ore,
in th
e Capon
estim
a
tors, the
system
choos
es
the coe
ffici
ents of filter
for t
h
e
p
u
rp
o
s
e of
redu
cing
th
e v
a
rian
ce
o
f
th
e
ou
tpu
t
filter
b
y
co
nsid
ering
t
h
e con
s
train
t
factor,
]
.
1
[
.
k
k
m
xx
k
m
C
m
k
(
6
)
In
th
e ab
ov
e eq
u
a
tion
(6), the v
a
riab
le
λ
can
b
e
term
ed
as Lag
r
ang
i
an
mu
ltip
lier. Th
erefore, acco
r
d
i
ng to
th
is
constraint
factor, whe
n
t
h
e
inpu
t of static arb
itrary
p
r
ocess
a
(
n
) is
su
bj
ected to
t
h
e filter
m
k
wit
h
ze
ro
di
st
ort
i
o
n at
a part
i
c
ul
a
r
f
r
e
q
uency
φ
k
as
we
ll as signals for
other fre
que
ncy than the
bas
e
line
φ
k
will ten
d
to
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
. 2, A
p
ri
l
20
16
:
72
5 – 7
3
4
72
8
b
e
atten
u
a
ted
.
Hen
c
e, th
e
o
b
jectiv
e fun
c
tion for th
e
p
u
rp
os
e of
red
u
ci
n
g
t
h
e co
nst
r
ai
nt
s
exhi
bi
t
e
d i
n
e
q
uat
i
o
n
(6)
will resu
lt i
n
,
k
xx
k
k
xx
k
C
C
m
1
1
(
7
)
Th
erefo
r
e, th
e
math
e
m
atica
l
rep
r
esen
tation
of th
e sp
ect
ru
m
can
b
e
ex
h
i
b
ited
as,
k
m
xx
k
k
k
xx
C
m
n
b
E
.
2
}
|
)
(
{|
)
(
(
8
)
Sub
s
titu
tin
g eq. (7
) to
eq
. (8
),
k
xx
k
k
xx
C
.
.
1
)
(
1
(
9
)
There
f
ore,
k
k
xx
m
xx
k
C
).
(
.
(
1
0
)
The a
b
ove
eq
u
a
t
i
on
(1
0)
can
be
no
w
ge
neral
i
zed by
c
o
nsi
d
eri
n
g
γ
k
,
w
h
e
r
e
k=
0,
1,
2
,
3…
K-
1,
C
xx
M =
γ
.
σ
xx
(
φ
)
(
1
1
)
In
th
e abov
e eq
u
a
tion
(11
)
, t
h
e v
a
riab
le M refers to
a
m
a
t
r
ix
with
elem
e
n
ts
m
o
, m
1
, m
2
… m
K-1
. The funct
i
o
n
σ
xx
(
φ
)
will refer to th
e
d
i
ag
on
al elem
en
ts o
f
σ
xx
(
φ
0
),
σ
xx
(
φ
1
)…
σ
xx
(
φ
K-1
). The desi
g
n
o
f
t
h
e pr
o
pose
d
sy
st
em
i
s
bei
n
g car
ri
e
d
o
u
t
on M
a
t
l
a
b o
n
no
rm
al
32 bi
t
m
achi
n
e.
For
p
r
eci
se ev
al
uat
i
on
of t
h
e
pr
o
pose
d
sy
st
em
, t
h
e
i
m
p
l
e
m
en
tatio
n
is being
carried
o
u
t
t
o
evalu
a
te th
e
an
alysis o
f
cro
s
s-sp
ectru
m
an
d
th
ereb
y estab
lish
the
rel
a
t
i
ons
hi
p be
t
w
een t
w
o si
g
n
al
s fo
r en
h
a
nced
sp
ectral esti
m
a
tio
n
s
. Generally, th
e cro
s
s-sp
ectru
m
is
u
s
ed
to
accom
p
lish the lag in phases
betwee
n sinus
o
idal com
pone
nts
of the signal. Hence, it is
essential to recognize
t
h
e p
o
t
e
nt
i
a
l
cor
r
el
at
i
onal
fa
ct
or at
s
p
eci
fi
c
fre
que
nci
e
s.
T
h
e p
r
op
ose
d
s
y
st
em
adopt
s t
h
e t
e
rm
C
o
rrel
a
t
i
onal
fact
or
f
o
r i
d
e
n
t
i
f
y
i
ng t
h
e
pot
ent
i
a
l
fre
q
u
enc
y
dom
ai
n bet
w
een t
h
e signals
.
In t
h
is case
the
propose
d
s
y
ste
m
con
s
i
d
er
s t
h
e p
r
esence
of t
w
o
i
nput
si
g
n
al
s
of ar
bi
t
r
ary
t
y
pe a
1
(n
) an
d a
2
(n) ass
o
ciated with s
p
ectrum
σ
a1a1
(
φ
k
) a
n
d
σ
a2a2
(
φ
k
).
Th
erefore,
th
e d
e
sign
s of th
e filter can
be rep
r
esen
ted as,
k
a
a
k
k
a
a
k
p
p
p
p
p
C
C
m
1
1
,
.
(
1
2
)
In
t
h
e abov
e eq
u
a
tion
(12), t
h
e v
a
riab
le
p
rep
r
esen
ts
v
a
lues
wo
rth
1
,
2. Th
e
ab
ov
e d
e
si
g
n
of
th
e filter
can
b
e
u
tilized
fo
r estimatin
g
th
e sp
ectru
m
o
f
a
1
(n)
an
d
a
2
(n) at a s
p
ecific fre
que
ncy of
φ
k
.
k
a
a
k
k
a
a
p
p
p
p
C
1
1
)
(
(
1
3
)
In
th
e ab
ov
e
eq
u
a
tion
,
t
h
e matrix
fo
r co
vari
ance corre
s
p
onding to a particula
r
signal a
p
(n) can
b
e
no
w
represe
n
ted as
,
)}
(
)
(
{
n
X
n
X
E
C
p
p
a
a
p
p
(
1
4
)
The m
a
the
m
atical represe
n
tatio
n of
t
h
e sign
al a
p
(n
) ca
n
be
sho
w
n as
,
X
p
(n
) =
[
x
p
(n
)
x
p
(n-
1
)
….
.
x
p
(
n
-s+1
)]
T
(
1
5
)
The m
a
the
m
atical represe
n
tation of t
h
e cros
s
-
spect
rum
fo
r t
w
o
in
put a
r
bitrary
p
r
oce
ss a
1
(n
) and
a
2
(n
)
is,
}
{
)
(
*
)
(
,
1
)
(
,
2
2
1
n
k
n
k
k
a
a
b
b
E
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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8-8
7
0
8
Reso
lving
t
h
e Issu
es
o
f
C
a
pon an
d APES
App
r
oa
ch
f
o
r Projectin
g
En
han
ced
…
(Kan
tip
ud
i MVV Pra
s
ad
)
72
9
)
(
}
{
)
(
*
*
)
(
,
1
)
(
,
2
2
1
1
2
k
a
a
n
k
n
k
k
a
a
b
b
E
(
1
7
)
In t
h
e a
b
o
v
e e
quat
i
o
n (
1
6) a
nd (
1
7)
, b
1
, k
(n)
and b
2,k(n)
is co
n
s
i
d
ered
to b
e
o
u
t
p
u
t
fo
r filters
m
1,k
and m
2k
respect
i
v
el
y
.
T
h
e sy
m
bol
* i
n
eq
uat
i
on
(
1
6
)
rep
r
ese
n
t
s
operator
for c
o
njugate com
p
lex. Norm
alizing equation
(1
6)
,
k
a
a
k
k
a
a
m
C
m
,
2
,
1
2
1
2
1
)
(
(
1
8
)
In t
h
e a
b
o
v
e e
quat
i
o
n
(1
8
)
, t
h
e m
a
t
r
i
x
fo
r
cross
-
c
o
r
r
el
at
i
on
f
o
r i
n
p
u
t
p
r
ocess a
1
(
n
) a
nd
a2
(n
) ca
n
be
no
w
represe
n
ted as
,
)}
(
).
(
{
)
(
2
1
2
1
n
X
n
X
E
C
k
a
a
(
1
9
)
Th
erefo
r
e, su
bstitu
tio
n
(12
)
in
(18
)
]
][
[
.
)
(
1
1
1
1
2
2
1
1
2
2
2
1
1
1
2
1
k
a
a
k
k
a
a
k
k
a
a
a
a
a
a
k
k
a
a
C
C
C
C
C
(
2
0
)
Hence
,
t
h
i
s
eq
uat
i
o
n
ca
n
be
use
d
f
o
r s
p
ect
r
a
l
est
i
m
a
ti
on
f
o
r
cr
oss
-
spect
r
u
m
i
n
si
gnal
p
r
oces
si
n
g
.
In
t
h
e
next
p
h
a
se
o
f
t
h
e evalu
a
tio
n
,
th
e
pro
p
o
s
ed
system will b
e
fo
cu
sed
o
n
estab
lish
i
n
g
th
e correlatio
n
a
l
factor
b
e
tween
th
e two
static in
pu
t p
r
o
cess
o
f
arb
itrary ty
p
e
a
1
(n
) an
d a
2
(n). He
nce, t
h
e proposed s
y
ste
m
represe
n
ts the
correlational
fa
ctor m
a
the
m
atically as,
)
(
)
(
|
)
(
|
)
(
2
2
1
1
2
1
2
1
2
2
k
a
a
k
a
a
k
a
a
k
a
a
(
2
1
)
Th
e sim
ilar esti
m
a
t
i
o
n
s
for t
h
e cro
ss-correlatio
n
a
l
factor for equ
a
tio
n (20
)
will b
e
,
2
1
2
1
2
1
1
2
]
[
]
[
]
.
[
|
)
(
|
2
2
1
1
2
2
2
1
1
1
2
1
k
a
a
k
k
a
a
k
k
a
a
a
a
a
a
k
k
a
a
C
C
C
C
C
(
2
2
)
Sub
s
titu
tio
n and
n
o
rm
aliz
in
g
o
f
equ
a
tion
(13) an
d (2
2)
on
eq
u
a
tion
(2
1)
2
1
2
1
2
1
1
2
]
[
]
[
]
.
[
)
(
2
2
1
1
2
2
2
1
1
1
1
k
a
a
k
k
a
a
k
k
a
a
a
a
a
a
k
k
a
a
C
C
C
C
C
s
(
2
3
)
3.
RESULT AND DIS
C
USSI
ON
Th
e
o
u
t
co
m
e
o
f
th
e
p
r
op
o
s
ed
syste
m
is an
al
yzed
on
m
u
ltip
le scen
ari
o
s. Fi
g
u
re
1
sh
ows t
h
e ou
tco
m
e
of t
h
e exi
s
t
i
n
g
m
e
t
hod
of c
o
rrel
a
t
i
o
n
a
l
fact
or
, w
h
ere t
h
e
M
a
t
l
a
b fu
nct
i
o
n
ms
co
here
is
u
s
ed
to
estim
a
t
e th
e
m
a
gni
t
ude s
q
u
a
red c
ohe
re
nce
fact
or. T
h
e e
x
i
s
t
i
ng m
e
t
hod
of spect
ral
est
i
m
a
ti
on i
s
fo
u
nd t
o
use o
n
Wel
c
h
app
r
oach
base
d
on
pe
ri
o
d
o
g
r
am
t
echni
q
u
e.
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
. 2, A
p
ri
l
20
16
:
72
5 – 7
3
4
73
0
Fig
u
re
1
.
Correlatio
n
a
l Factor
o
f
Ex
isting
Syste
m
The
o
u
t
c
om
e of
t
h
e st
udy
c
onsi
d
er
s t
h
e
s
a
m
e
i
nput
va
r
i
abl
e
s o
f
a
1
(n) and
a
2
(n) con
s
id
ering
th
e
set o
f
fre
que
nci
e
s f
0
, f
1
, …
,
f
N-1
. T
h
e
m
a
t
h
em
at
i
cal
rep
r
ese
n
t
a
t
i
on
of
t
h
e si
gnal
s
c
a
n
be
do
ne a
s
,
1
0
1
1
)
2
cos(
)
(
)
(
N
i
i
n
f
n
n
a
(
2
4
)
1
0
2
]
(
2
cos[
)
(
)
(
N
i
i
i
s
n
f
n
n
a
(
2
5
)
In
th
e ab
ov
e eq
u
a
tion
s
, th
e syste
m
co
n
s
id
ers
φ
1
(n) a
nd
φ
2
(n) as the Gaus
sian arbitr
a
r
y process
with variance
of 1. T
h
e
syste
m
also c
ons
i
d
ers th
e ph
ase sh
ifts of
δ
o
,
δ
1
, …,
δ
N-1
with
arb
itrary assu
m
p
tio
n
s
co
nsid
ering
1024 sam
p
les (n).
Fi
gu
re
2.
C
o
rre
l
a
t
i
onal
Fact
o
r
of
Pr
o
pose
d
Sy
st
em
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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ECE
I
S
SN
:
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8-8
7
0
8
Reso
lving
t
h
e Issu
es
o
f
C
a
pon an
d APES
App
r
oa
ch
f
o
r Projectin
g
En
han
ced
…
(Kan
tip
ud
i MVV Pra
s
ad
)
73
1
Fi
gu
re
2
sh
o
w
s t
h
e
out
c
o
m
e
fo
r c
o
r
r
el
at
i
on
f
actor
fo
r th
e pr
opo
sed
m
echanism of s
p
ectral
est
i
m
a
ti
on.
Th
e sy
st
em
consi
d
ers
t
h
e
wi
nd
ows
l
e
n
g
t
h
of
10
0
-
2
0
0
wi
t
h
sam
p
l
e
s of
fre
que
nci
e
s a
s
f
o
=0.02,
f
1
=0.03, f
2
=0
.0
4,
f
3
=0.05, f
4
=0
.0
6. Th
e mark
ers are g
i
ven
in
ten
tion
a
lly in the analysis to have a clear
v
i
su
alizatio
n of th
e sp
ectru
m
b
e
ing g
e
n
e
rated
.
Hen
ce, th
e correlation
a
l
facto
r
for th
e
p
r
op
o
s
ed
system
is
fo
u
nd t
o
have
si
gni
fi
ca
nt
pea
k
s as
com
p
are
d
t
o
t
h
e e
x
i
s
t
i
n
g sy
st
em
. In
or
der t
o
fu
rt
he
r
per
f
o
r
m
com
p
arat
i
v
e
analysis, we also exte
nd t
h
e sim
u
lation study conside
r
ing all th
e
m
a
j
o
r ex
istin
g
system e.g
.
Peri
o
dog
ram
,
PW
elch, an
d
Mu
ltitap
e
r m
e
th
od
with
t
h
e
p
r
op
o
s
ed
m
ech
an
ism
o
f
sp
ectru
m
esti
m
a
ti
o
n
s
u
s
ing
capo
n and
APES
m
e
t
hod.
The
out
c
o
m
e
s o
f
al
l
t
h
e
s
e m
e
t
h
o
d
s a
r
e e
x
h
i
bi
t
e
d
i
n
Fi
gu
r
e
3-7
,
w
h
ere
t
h
e
anal
y
s
i
s
i
s
do
ne
with
resp
ect to Po
wer Sp
ectral Den
s
ity (PSD) for b
e
tter
v
i
sual
i
zat
i
on o
f
t
h
e spect
r
u
m
bei
ng ge
ne
rat
e
d
by
al
l
t
h
e i
n
di
vi
d
u
al
m
e
t
hods
o
f
s
p
e
c
t
r
um
est
i
m
a
t
i
ons
.
Fig
u
r
e
3
.
Po
w
e
r
Sp
ectr
a
l
D
e
nsity o
f
Per
i
odog
r
a
m
Meth
o
d
Figure
4. Powe
r Spectral
Density of PWelch Method
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
. 2, A
p
ri
l
20
16
:
72
5 – 7
3
4
73
2
Fig
u
re
5
.
Po
wer Sp
ectral
Density o
f
M
u
ltita
p
e
r Meth
od
Th
e
o
u
t
co
m
e
o
f
PSD for Perio
dog
ram
,
PW
elch
, an
d
M
u
ltitap
e
r m
e
th
o
d
sho
w
s th
e sp
ectru
m
co
u
l
d
n
o
t
ex
ceed
m
o
re t
h
an
0.
1
Wat
t
/
Hz
o
f
P
S
D
wi
t
h
i
n
t
h
e
r
a
nge
o
f
0.
1-
0.
5
Hz
o
f
f
r
e
que
n
c
y
.
Fi
gu
re
6.
P
o
we
r S
p
ect
ral
Den
s
i
t
y
of C
a
po
n
M
e
t
h
o
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Reso
lving
t
h
e Issu
es
o
f
C
a
pon an
d APES
App
r
oa
ch
f
o
r Projectin
g
En
han
ced
…
(Kan
tip
ud
i MVV Pra
s
ad
)
73
3
Fig
u
re 7
.
Po
wer
Sp
ectral Density
o
f
APES Meth
od
Fi
gu
re
6 a
n
d
Fi
gu
re
7 s
h
ow
s t
h
e P
S
D
f
o
r
t
h
e C
a
p
o
n
an
d
APE
S
m
e
t
hod
of
spect
r
u
m
est
i
m
a
ti
ons.
The
out
c
o
m
e
sho
w
s
som
e
en
hance
d
val
u
e
s
of
PS
D f
o
r
bot
h t
h
e
m
e
t
hod a
s
com
p
ared
t
o
t
h
e exi
s
t
i
n
g sy
st
em
of
Periodo
gram
, PW
elch, an
d
Mu
ltitap
e
r m
e
t
h
od
.
4.
CO
NCL
USI
O
N
Th
is p
a
p
e
r h
a
s atte
m
p
ted
to
sig
n
i
fy th
at spectral esti
m
a
t
i
o
n
and
en
suring
its effectiv
en
ess
p
l
ays a
cri
t
i
cal
rol
e
i
n
m
a
ny
appl
i
cat
i
ons
o
f
si
g
n
al
p
r
oces
si
n
g
.
As t
h
ere a
r
e va
ri
o
u
s
m
e
t
hods
f
o
r
per
f
o
r
m
i
ng spe
c
t
r
al
estim
a
tions, he
nce, it is critical to unde
rstand the best m
e
thod to
do s
o
. From
the literature, we ha
ve se
en that
t
h
ere a
r
e va
ri
o
u
s m
e
t
hods a
n
d m
a
jori
t
y
of
t
h
e re
searc
h
ers
are f
o
un
d t
o
be
m
o
re i
n
cl
i
n
ed
on C
a
p
on
an
d
APE
S
est
i
m
a
ti
on t
ech
ni
q
u
es.
We
ha
ve al
so i
d
ent
i
f
i
e
d a p
r
obl
em
in i
m
pl
em
ent
a
tion
o
f
C
a
p
on a
nd
APE
S
est
i
m
at
i
o
n
t
echni
q
u
es
wi
t
h
res
p
ect
t
o
c
o
m
put
at
i
onal
need
s. He
nce,
t
h
i
s
pape
r ha
s per
f
o
r
m
e
d an eval
uat
i
on
of t
h
e
problem
associated with va
rious s
p
ectral esti
mation tec
hni
ques a
n
d propos
ed a sim
p
le sol
u
tion to e
n
hance the
powe
r spectral
density as well as correlational factor as
a
mean to showc
a
se the
propos
ed enha
nced
version
of C
a
po
n an
d
APES est
i
m
at
ion t
e
c
hni
ques
.
Ou
r st
u
d
y
sh
ows t
h
at
cor
r
e
l
at
i
on fact
o
r
i
s
one
of t
h
e
w
i
del
y
ado
p
t
e
d t
e
c
hni
que
s t
o
fi
n
d
t
h
e si
gni
fi
ca
nt
r
e
l
a
t
i
onshi
p am
on
g va
ri
o
u
s si
gnal
s
.
W
e
al
so
fo
un
d t
h
at
ess
e
nt
i
a
l
pri
n
ci
pl
e
of
C
a
po
n i
s
n
o
t
t
o
t
a
l
l
y
used
f
o
r
car
ry
i
n
g
o
u
t
s
p
ect
ral
anal
y
s
i
s
.
T
h
e
out
c
o
m
e
of
ou
r st
udy
sh
o
w
s t
h
at
a CAPON esti
mato
r in
corporates
m
o
re d
a
ta in
its si
g
n
a
l
wh
ile APES
op
ti
m
a
l reso
lu
tio
n
o
f
t
h
e frequ
e
n
c
ies
p
r
esen
t in
one sp
ectru
m
.
Howev
e
r, we also
fou
n
d
certain
p
itfall
in
th
e
o
u
t
come wh
ich
sho
w
s th
e
o
v
e
restim
at
io
n ch
arecteristics o
f
CAPON
on min
i
m
a
l a
m
p
l
it
u
d
e
v
a
lu
es. Th
erefore, we will lik
e to
so
l
v
e th
is
pr
o
b
l
e
m
i
n
fut
u
re
usi
n
g en
ha
nced
versi
o
n o
f
R
ecursi
v
e Le
ast
Squa
re t
echni
que
s. O
u
r
f
u
t
u
re di
rect
i
o
n
of t
h
e
stu
d
y
will b
e
fo
cu
sed
on
ach
iev
i
ng fu
rt
h
e
r low co
m
p
lex
ities in
com
p
u
t
atio
n
wit
h
efficien
t speed
o
f
con
v
e
r
ge
nce
f
o
r
o
u
r
ne
xt
e
n
hance
d
ve
rsi
o
n
of
R
ecu
rsi
v
e
Least
Sq
ua
re t
echni
que
s t
a
r
g
et
i
ng t
h
e
t
i
m
e
-vary
i
n
g
freq
u
e
n
c
ies
with
im
p
u
l
se co
m
p
on
en
ts in th
e
sig
n
a
ls.
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eg
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.
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[10]
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.
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13.
BIOGRAP
HI
ES OF
AUTH
ORS
Kantipudi MVV Prasad recei
ved his B.Te
c
h
degree in E
l
ec
tronics & c
o
m
m
unications
Engineering fro
m ASR College of Engineer
ing,
Tanuku, India, the M.Te
ch degree in Digital
Electronics and Communication S
y
stems from
Godavari
Institute of Engineering
& Techno
log
y
,
Rajahmundr
y
,
I
ndia. Curr
ently
pursuing his Ph
.D from BITS,
VTU and working as Assistant
Professor in Department of Electronics & co
mmunications, R
K
University
.
Rajkot, having
teaching exp
e
rience
around 6
y
e
ars. He has
au
thored
and
co-author
ed
man
y
pap
e
rs in
Interna
tiona
l Jou
r
nals, In
tern
atio
nal
Conf
eren
ces
and Nat
i
onal
Co
nferenc
e
s
.
I have
r
ece
ived
m
y
BE
(E
&C)
and M
.
Te
ch (B
io Me
dica
l Instrume
nta
ti
on)
from University
of
M
y
sore. I got m
y
Ph.D (ECE) fr
om Anna unive
rsity
of Techno
lo
g
y
. Co
imbotore
(TN). I had th
e
opportunity
to
serving as a Ch
airman for Boar
d
of Examiners, and Board of
Studies etc. for
Vis
v
es
wara
ya
T
echni
cal
Univers
i
t
y
and Bang
alor
e Univers
i
t
y
Kar
n
atak
a.
I worke
d
as
L
ectu
r
er
,
Associate prof
essor and Professor and Research
/ PG co-ord
i
n
ator
in Bang
al
ore inst
itut
e
of
techno
log
y
, Ban
g
alore
,
affi
li
ate
d
to vis
v
ewara
y
a techno
logi
cal
univers
it
y, K
a
rn
atak
a .during
1989 to till dat
e
. Presentl
y
,
I am
a Chairm
an
of the Board of exam
ination (I
T/ML/BMI) for
Visveswaray
a
technolog
ical un
iv
ersity
, With
more than 30
y
ears of academic resear
ch and
administrative
experien
ce b
l
end
e
d with prog
re
s
s
ive views, org
a
nization
a
l str
e
ngths. I
am a
member of IEEE, Bio
Medical Society
of
Indi
a, IS
TE, IMAPS &
Fellow member
of IETE.
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