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1317
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f
f
,...,
,
2
1
th
at
s
i
g
n
al
f
r
eq
u
e
n
c
y
m
a
y
b
e
les
s
t
h
an
all
s
a
m
p
li
n
g
f
r
eq
u
en
c
ies,
t
h
at
is
p
i
F
f
k
si
,...,
1
,
2
(
m
u
ltip
le
s
a
m
p
li
n
g
r
ates
ar
e
b
elo
w
th
e
N
y
q
u
i
s
t
r
ate)
.
I
f
s
a
m
p
l
in
g
f
r
eq
u
en
cie
s
ar
e
ch
o
s
en
p
r
o
p
er
ly
,
th
e
u
n
a
m
b
i
g
u
o
u
s
a
n
alo
g
f
r
eq
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en
c
y
est
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m
a
tio
n
k
F
ˆ
is
ac
h
iev
ed
.
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f
s
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Fig
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e
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lia
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eq
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s
a
f
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f
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alo
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eq
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t
h
e
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s
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ip
b
et
w
ee
n
f
r
eq
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e
n
c
y
o
f
u
n
d
er
-
s
a
m
p
led
w
a
v
ef
o
r
m
u
f
(
i
n
g
u
n
d
e
r
s
a
m
p
l
f
)
an
d
an
alo
g
f
r
eq
u
en
c
y
F
ca
n
b
e
o
b
tain
ed
as f
o
llo
w
s
:
s
u
mf
F
f
o
r
s
u
nf
F
f
(
1
)
I
n
(
1
)
,
m
an
d
n
ar
e
in
teg
er
n
u
m
b
er
s
an
d
s
f
is
s
a
m
p
li
n
g
f
r
eq
u
e
n
c
y
.
T
h
is
s
tu
d
y
ai
m
ed
to
u
n
d
er
s
ta
n
d
h
o
w
to
i
m
p
le
m
e
n
t
s
u
b
-
N
y
q
u
is
t
f
r
eq
u
e
n
c
y
d
etec
tio
n
ap
p
r
o
ac
h
o
n
t
h
e
FP
GA
to
f
in
d
a
f
r
eq
u
e
n
c
y
m
o
r
e
th
a
n
1
GH
z
.
T
h
u
s
,
w
e
n
ee
d
ed
a
h
i
g
h
-
s
p
ee
d
p
r
o
ce
s
s
in
g
ap
p
r
o
ac
h
(
ar
o
u
n
d
2
0
0
MHz
)
w
i
th
lo
w
u
s
e
o
f
FP
G
A
r
eso
u
r
ce
s
.
U
s
u
a
ll
y
,
w
h
e
n
a
s
ig
n
al
is
p
r
o
ce
s
s
ed
,
m
an
y
p
a
r
a
m
eter
s
s
h
o
u
ld
b
e
ex
tr
ac
ted
,
an
d
f
r
eq
u
en
c
y
i
s
a
m
o
n
g
t
h
e
m
.
Hen
ce
,
r
e
s
o
u
r
ce
s
o
f
FP
G
A
s
h
o
u
ld
b
e
r
es
er
v
ed
f
o
r
o
th
er
r
eq
u
ir
ed
p
r
o
ce
s
s
in
g
(
b
esid
es
f
r
eq
u
e
n
c
y
m
ea
s
u
r
e
m
e
n
t)
o
n
t
h
e
r
ec
eiv
ed
s
ig
n
al
as
m
u
c
h
as p
o
s
s
ib
le.
3.
T
E
ST
I
N
G
AND
DI
SCU
S
SI
O
N
O
F
DIFF
E
RE
N
T
M
E
T
H
O
DS O
N
F
P
G
A
Fre
q
u
en
c
y
esti
m
atio
n
p
la
y
s
an
i
m
p
o
r
tan
t
r
o
le
in
m
a
n
y
d
i
g
it
al
s
ig
n
als
p
r
o
ce
s
s
i
n
g
ap
p
licat
i
o
n
s
.
T
h
er
e
ar
e
d
if
f
er
e
n
t
m
et
h
o
d
s
f
o
r
f
r
e
q
u
en
c
y
est
i
m
at
io
n
,
s
u
c
h
as
t
h
e
Di
s
cr
ete
Fo
u
r
ier
T
r
an
s
f
o
r
m
(
DFT
)
,
th
e
L
ea
s
t
Sq
u
ar
es
(
L
S),
an
d
th
e
Dir
ec
t
State
Sp
ac
e
(
DSS)
[
1
0
]
,
[
1
1
]
th
at
ar
e
ap
p
lied
in
s
eq
u
en
tial
p
lat
f
o
r
m
s
li
k
e
m
icr
o
p
r
o
ce
s
s
o
r
s
.
Dif
f
er
en
t
m
et
h
o
d
s
o
f
u
n
d
er
-
s
a
m
p
li
n
g
f
r
eq
u
e
n
cies
d
etec
t
io
n
o
n
t
h
e
FP
G
A
h
av
e
n
o
t
d
is
cu
s
s
ed
in
p
r
ev
io
u
s
s
t
u
d
ies t
h
at
w
e
ar
e
test
ed
an
d
d
is
c
u
s
s
e
d
b
elo
w
.
3
.
1
.
L
i
m
it
a
t
io
n o
f
DSS a
nd
L
S
met
ho
ds
o
n F
P
G
A
T
h
e
DSS
a
n
d
L
S
m
eth
o
d
s
ap
p
ea
r
to
w
o
r
k
b
etter
t
h
an
t
h
e
DFT
alg
o
r
ith
m
s
i
n
ce
t
h
e
al
g
o
r
ith
m
d
o
es
n
o
t
h
av
e
d
is
cr
ete
b
in
s
ize
s
.
B
u
t
th
e
co
m
p
u
tatio
n
a
l
in
te
n
s
it
y
cr
ea
tes
a
ch
alle
n
g
i
n
g
p
r
ac
tical
r
ea
l
tim
e
;
th
er
ef
o
r
e,
w
e
d
id
n
o
t u
s
e
t
h
ese
t
w
o
m
e
th
o
d
s
.
3
.
2
.
L
i
m
it
a
t
io
ns
o
f
G
o
er
t
ze
l f
ilte
r
a
nd
Sli
di
ng
DF
T
o
n F
P
G
A
ba
s
ed
o
n o
ur
t
esting
Sev
er
al
p
r
o
p
er
t
ies
o
f
t
h
e
DF
T
m
a
k
e
it
s
u
itab
le
f
o
r
a
p
ar
a
llel
i
m
p
le
m
e
n
tat
io
n
.
T
h
er
e
ar
e
d
if
f
er
en
t
k
in
d
s
o
f
DFT
r
ea
lizatio
n
,
s
u
c
h
as
th
e
Go
er
tzel
f
il
ter
,
th
e
Sli
d
in
g
D
FT
(
SDFT
)
an
d
th
e
Fas
t
Fo
u
r
ier
T
r
an
s
f
o
r
m
(
FF
T
)
an
d
th
o
s
e
r
elate
d
to
th
e
Fo
u
r
ier
T
r
an
s
f
o
r
m
.
W
e
co
m
p
ar
ed
s
e
v
er
al
m
et
h
o
d
s
o
f
Fo
u
r
ier
T
r
an
s
f
o
r
m
f
o
r
ex
tr
ac
ti
n
g
f
r
eq
u
en
cie
s
o
f
s
i
g
n
als,
an
d
ch
o
s
e
th
e
m
e
th
o
d
th
at
o
cc
u
p
ied
s
m
a
ll
ar
ea
in
th
e
FP
GA
(
g
ates)
an
d
y
ield
ed
an
ac
cu
r
ate
f
r
eq
u
en
c
y
,
w
h
ile
k
ep
t t
h
e
p
r
o
ce
s
s
i
n
g
s
p
e
ed
h
ig
h
.
T
h
e
Go
er
tzel
f
ilter
i
s
t
y
p
ica
ll
y
i
m
p
le
m
e
n
te
d
as
a
s
ec
o
n
d
-
o
r
d
er
I
I
R
b
an
d
p
ass
f
ilter
[
1
2
]
.
T
h
e
Go
er
tzel
alg
o
r
ith
m
ca
n
e
x
tr
ac
t
ar
b
itra
r
y
f
r
eq
u
e
n
c
y
co
m
p
o
n
en
ts
f
r
o
m
a
g
iv
e
n
s
ig
n
al.
T
r
an
s
f
o
r
m
atio
n
o
f
th
e
o
u
tp
u
t r
esp
o
n
s
e
f
o
r
th
e
Go
er
tz
el
alg
o
r
ith
m
is
a
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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n
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eq
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ta
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t
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o
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ess
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t.
T
h
e
f
il
ter
ca
n
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e
r
ea
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w
it
h
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t
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u
f
f
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g
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b
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a
m
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ca
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o
ce
s
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r
ec
eiv
ed
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e
ca
n
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s
o
f
t
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s
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cc
e
s
s
i
v
e
w
in
d
o
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eq
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ce
s
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ch
o
f
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h
N
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th
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Sli
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SDFT
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.
T
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is
ap
p
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iate
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b
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3
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atio
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2
)]
(
)
(
)
1
(
[
)
(
(
4
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W
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tr
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m
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Go
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w
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lar
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r
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n
t
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FP
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Xi
lin
x
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s
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f
t
w
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e.
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t
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ates
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FP
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m
e
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le
m
s
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n
g
o
f
w
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cr
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m
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m
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n
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ital
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w
ith
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ix
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p
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t
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ith
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w
er
e
a
n
al
y
ze
d
b
y
B
er
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in
an
d
Steen
aa
r
t
(
1
9
8
9
)
[
1
4
]
.
Du
e
to
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s
[2
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[7
-
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tr
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to
ex
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ac
t
i
n
p
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t
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e
n
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u
r
e
2
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a)
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e
2
(
b
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.
A
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H
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A
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f
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(
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(
b
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Fig
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r
e
2
.
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lo
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r
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f
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(
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co
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w
a
v
e
f
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r
m
o
f
p
r
ev
io
u
s
s
tu
d
ie
s
[2
]
,
[7
-
9
]
an
d
(
b
)
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
f
r
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w
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P
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eq
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en
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m
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SI
M
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S AN
D
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UL
T
S
4
.
1
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P
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at
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h
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c
o
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[
1
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]
,
(
av
ailab
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in
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e
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ls
)
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th
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b
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s
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m
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2
0
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n
t
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.
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ith
a
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s
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f
b
s
=
2
0
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z
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2
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4
8
=
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6
kHz
,
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e
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r
w
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ld
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ce
ed
b
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.
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g
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1
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4
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z
(
a
)
(
b
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I
Q
f
̃
u
1
F
F
Fig
u
r
e
3
.
Un
d
er
-
s
a
m
p
li
n
g
f
r
eq
u
en
c
y
d
etec
tio
n
(
a
)
p
r
ev
io
u
s
s
t
u
d
ies [
2
]
,
[7
-
9
]
n
ee
d
m
o
r
e
AD
C
an
d
I
n
p
h
ase/
Qu
ad
r
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r
e
eq
u
ip
m
e
n
ts
(
b
)
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Hig
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f
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en
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f
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4
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ac
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f
f
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ize
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h
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f
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7
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.
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s
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o
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n
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g
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r
e
3
,
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e
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s
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t
h
e
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T
w
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th
2
0
4
8
p
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ts
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tr
ac
t
t
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f
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.
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en
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s
ed
t
h
e
r
elati
o
n
s
h
ip
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et
w
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n
t
h
e
r
e
m
in
d
er
s
o
f
a
n
alo
g
s
i
g
n
al
f
r
e
q
u
en
c
y
,
i.e
.
,
1
~
u
f
,
2
~
u
f
,
an
d
3
~
u
f
to
ex
tr
ac
t
th
e
r
ea
l
f
r
eq
u
en
c
y
o
f
th
e
a
n
alo
g
s
i
g
n
a
l
(
F
f
ana
l
o
g
)
.
T
h
e
q
u
an
tit
y
o
f
co
n
s
u
m
ed
g
at
es f
o
r
i
m
p
le
m
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n
tatio
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f
2
0
4
8
-
p
o
in
t F
FT
is
p
r
esen
ted
in
T
ab
le
1
.
T
ab
le
1
Sy
n
t
h
esi
s
r
esu
l
ts
o
f
a
2
0
4
8
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p
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in
t FFT
co
r
e
p
ip
elin
ed
s
tr
ea
m
in
g
I
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n
X
C
5
v
s
x
9
5
T
u
s
ed
p
r
e
v
io
u
s
ap
p
r
o
ac
h
es [
2
]
,
[7
-
9
]
an
d
p
r
o
p
o
s
ed
ap
p
r
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ac
h
(
u
s
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es f
o
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4
0
9
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f
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R
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M
s
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2
4
4
3
Fo
r
ex
tr
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tin
g
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alo
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eq
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en
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y
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f
r
o
m
th
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r
e
m
i
n
d
er
s
1
~
u
f
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2
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u
f
,
an
d
3
~
u
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
i
n
Step
5
-
1
to
5
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5
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as
u
s
ed
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e
test
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th
e
i
m
p
le
m
e
n
tati
o
n
b
y
i
n
p
u
t
s
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g
n
al
w
i
th
f
r
eq
u
en
c
y
2
/
)
2
)
4
4
(
(
3
2
1
s
s
s
f
f
f
184
)
192
200
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2
M
H
z
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d
th
e
h
a
v
e
m
in
i
m
u
m
d
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ta
n
ce
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ased
o
n
(
8
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th
at
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al
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ac
c
o
r
d
in
g
to
E
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u
atio
n
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)
.
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t
m
a
y
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e
d
et
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ted
in
co
r
r
ec
tl
y
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s
2
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4
4
(
(
3
2
1
'
s
s
s
f
f
f
F
184
)
192
200
(
2
M
H
z
600
b
ased
o
n
(
8
)
.
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t
ca
n
b
e
f
o
u
n
d
f
r
o
m
E
q
u
at
io
n
(
1
0
)
th
at
g
o
o
d
f
r
eq
u
en
c
y
e
s
ti
m
atio
n
m
et
h
o
d
(
n
ea
r
th
e
C
r
a
m
er
-
R
ao
b
o
u
n
d
)
allo
w
s
c
o
r
r
ec
t
d
etec
tio
n
o
f
f
r
eq
u
en
c
y
b
y
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
u
n
t
il
th
e
p
o
in
t
w
h
er
e
d
ev
iatio
n
o
f
f
r
eq
u
e
n
c
y
i
s
b
elo
w
3
2
8
(
6
5
dB
)
.
T
h
e
m
i
n
i
m
u
m
d
is
ta
n
ce
b
et
w
ee
n
t
h
e
r
e
m
in
d
er
s
o
f
ea
c
h
f
r
eq
u
en
c
y
i
n
t
h
e
b
an
d
w
it
h
r
esp
ec
t
to
f
s1
=1
8
4
,
f
s2
=1
9
2
,
f
s3
=2
0
0
MHz
ar
e
8
MHz
(
7
)
.
T
h
er
ef
o
r
e,
m
a
x
i
m
u
m
to
ler
an
ce
o
f
ea
ch
f
r
eq
u
en
c
y
to
d
etec
t f
r
eq
u
en
c
y
u
n
iq
u
e
l
y
i
s
3
2
8
MHz
.
R
es
u
lts
o
f
tes
tin
g
f
o
r
s
i
g
n
al
s
w
it
h
d
i
f
f
er
en
t
p
u
ls
e
w
id
t
h
s
a
n
d
p
er
io
d
s
o
f
r
ep
etitio
n
eq
u
al
to
1
0
0
u
s
w
er
e
ev
al
u
ated
an
d
t
h
e
m
i
n
i
m
u
m
p
o
w
er
f
o
r
f
r
eq
u
en
c
y
e
x
tr
ac
tio
n
u
n
iq
u
el
y
(
Fi
g
.
4
)
w
a
s
n
ea
r
-
70
d
B
m
f
o
r
g
r
ea
ter
p
u
l
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e
w
id
t
h
.
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t
is
s
h
o
w
n
t
h
at
in
cr
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p
u
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w
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h
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ter
s
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h
e
m
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m
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m
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o
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f
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le
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ls
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u
n
ti
l
th
e
n
u
m
b
er
o
f
s
a
m
p
le
p
u
l
s
es
is
les
s
t
h
an
t
h
e
F
FT
len
g
t
h
.
T
h
e
s
i
m
u
latio
n
r
es
u
lt
s
in
F
ig
.
4
s
h
o
w
s
u
n
d
er
s
a
m
p
li
n
g
f
r
eq
u
en
c
y
d
et
ec
tio
n
f
o
r
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
an
d
p
r
ev
io
u
s
ap
p
r
o
ac
h
h
av
e
s
a
m
e
p
er
f
o
r
m
an
c
e
w
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ile
p
r
o
p
o
s
ed
ap
p
r
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ac
h
h
as
l
ess
h
ar
d
w
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n
co
m
p
ar
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w
it
h
t
h
e
p
r
ev
io
u
s
s
t
u
d
ies
(
s
ee
Fi
g
u
r
e
3
(
a)
,
3
(
b
)
an
d
T
ab
le
2
)
.
Fig
4
.
Min
i
m
u
m
p
o
w
er
d
etec
t
ab
le
w
it
h
n
e
w
u
n
d
er
-
s
a
m
p
li
n
g
f
r
eq
u
en
c
y
d
etec
tio
n
m
et
h
o
d
o
n
th
e
FP
GA
f
o
r
d
if
f
er
e
n
t p
u
l
s
e
w
id
t
h
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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3
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u
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e
2
0
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:
1
3
1
6
–
1
3
2
5
1324
C
o
m
p
ar
is
io
n
b
et
w
ee
n
p
r
o
p
o
s
ed
an
d
p
r
ev
io
u
s
s
t
u
d
ies
f
o
r
u
n
d
er
s
a
m
p
li
n
g
f
r
eq
u
e
n
c
y
d
etec
tio
n
ca
n
b
e
s
u
m
m
ar
ized
as
T
ab
le
2
.
A
s
y
o
u
ca
n
s
ee
n
u
m
b
er
o
f
u
s
ed
ADC
p
er
s
a
m
p
li
n
g
f
r
eq
u
e
n
cies
f
o
r
p
r
ev
io
u
s
s
t
u
d
ies
th
at
u
s
ed
co
m
p
le
x
av
e
f
o
r
m
(
h
as
I
n
p
h
ase
an
d
Qu
ad
r
at
u
r
e
p
ar
ts
)
w
as
d
o
u
b
le
o
f
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
f
r
o
m
r
ea
l
w
a
v
e
f
o
r
m
.
Fu
r
t
u
r
e
m
o
r
e,
ex
tr
a
eq
u
ip
m
en
t
w
a
s
n
ee
d
ed
in
p
r
ev
io
u
s
s
t
u
d
ies
to
o
b
tain
co
m
p
le
x
w
av
e
f
o
r
m
.
Si
n
ce
i
m
p
le
m
en
ta
tio
n
o
f
FF
T
f
o
r
co
m
p
lex
a
n
d
r
ea
l
n
u
m
b
er
s
o
n
F
P
GA
is
s
a
m
e
an
d
s
a
m
e
co
r
e
I
P
is
u
s
ed
f
o
r
th
e
m
th
e
av
er
a
g
e
u
s
ag
e
o
f
r
esu
r
ce
s
f
o
r
b
o
th
ap
p
r
o
ac
h
es a
r
e
s
am
e.
T
ab
le
2
.
C
o
m
p
ar
is
io
n
b
et
w
ee
n
p
r
o
p
o
s
ed
an
d
p
r
ev
io
u
s
s
tu
d
ie
s
ap
p
r
o
ac
h
es
M
e
t
h
o
d
N
o
.
A
D
C
p
e
r
saml
i
n
g
f
r
e
q
u
e
n
c
i
e
s
Ex
t
r
a
e
q
u
i
p
me
n
t
A
v
e
r
a
g
e
F
P
G
A
R
e
so
u
c
e
u
s
a
g
e
o
n
o
n
X
C
5
v
sx
9
5
T
C
o
ml
e
x
w
a
v
e
f
o
r
m
u
n
d
e
r
samp
l
i
n
g
[
2
,
7
,
8
,
9
]
2
Eq
u
i
p
me
n
t
f
o
r
c
o
n
v
e
r
t
r
e
c
e
i
v
e
d
si
g
n
a
l
t
o
c
o
m
p
l
e
x
w
a
v
e
f
o
r
m
8%
P
r
o
p
o
se
d
me
t
h
o
d
1
N
o
n
e
e
d
8%
I
n
s
en
s
o
r
n
et
w
o
r
k
s
,
en
er
g
y
co
n
s
u
m
p
tio
n
an
d
co
s
t
o
f
h
a
r
d
w
ar
e
i
m
p
le
m
en
ta
tio
n
ar
e
im
p
o
r
ta
n
t
f
ac
to
r
es
[
1
9
]
,
[
2
0
]
.
Ou
r
p
r
o
p
o
s
ed
s
i
m
p
le
h
ar
d
w
ar
e
ca
n
s
a
v
e
co
s
t
a
n
d
en
er
g
y
.
T
h
er
ef
o
r
e,
it
is
u
s
e
f
u
l
f
o
r
s
en
s
o
r
s
in
s
e
n
s
o
r
n
et
w
o
r
k
s
.
5.
CO
NCLUS
I
O
NS
T
h
is
p
ap
er
ex
am
i
n
ed
an
d
d
is
cu
s
s
ed
d
if
f
er
e
n
t
m
et
h
o
d
s
f
o
r
esti
m
atio
n
o
f
s
u
b
-
s
a
m
p
led
f
r
eq
u
en
c
y
o
n
th
e
FP
G
A
.
W
e
im
p
le
m
e
n
ted
d
if
f
er
en
t
m
et
h
o
d
s
o
n
th
e
F
P
GA
f
o
r
Su
b
-
Sa
m
p
lin
g
f
r
eq
u
en
ci
e
s
d
etec
tio
n
,
in
cl
u
d
in
g
L
ea
s
t
Sq
u
ar
es,
Dir
ec
t
State
Sp
ac
e,
Go
er
tzel
f
ilt
er
,
Sli
d
in
g
D
FT
,
P
h
ase
ch
an
g
es
o
f
FF
T
,
p
ea
k
a
m
p
lit
u
d
e
o
f
FF
T
.
Sh
o
r
tco
m
i
n
g
a
n
d
ad
v
an
ta
g
es
o
f
ea
ch
m
eth
o
d
d
u
r
in
g
t
h
e
i
m
p
le
m
e
n
tat
io
n
o
n
FP
GA
w
er
e
d
is
cu
s
s
ed
an
d
te
s
ted
.
No
te
th
at,
s
h
o
r
tco
m
i
n
g
s
o
f
t
h
ese
m
e
th
o
d
s
ar
e
n
o
t
d
is
c
u
s
s
ed
s
p
ec
i
f
icall
y
i
n
p
r
ev
io
u
s
s
tu
d
ie
s
.
Fi
n
all
y
,
an
ap
p
r
o
p
r
ia
te
m
et
h
o
d
f
o
r
u
n
d
er
-
s
a
m
p
l
in
g
f
r
eq
u
en
c
y
d
etec
tio
n
o
n
th
e
FP
GA
w
a
s
c
h
o
s
en
.
I
m
p
le
m
e
n
tatio
n
an
d
m
o
d
if
ic
atio
n
o
f
co
d
es
o
n
th
e
FP
GA
ar
e
ti
m
e
-
co
n
s
u
m
i
n
g
p
r
o
ce
d
u
r
es
an
d
r
eq
u
ir
e
k
n
o
w
led
g
e
o
f
h
ar
d
w
ar
e.
T
h
er
ef
o
r
e,
th
i
s
w
o
r
k
ca
n
h
elp
c
h
o
o
s
e
an
ap
p
r
o
p
r
iate
ap
p
r
o
ac
h
f
o
r
i
m
p
le
m
e
n
tatio
n
o
f
s
u
b
-
s
a
m
p
lin
g
f
r
eq
u
e
n
c
y
d
ete
ctio
n
o
n
th
e
FP
G
A
f
r
o
m
L
e
ast
Sq
u
ar
es,
Dir
ec
t
State
Sp
ac
e,
Go
er
tzel
f
ilter
,
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.
RE
F
E
R
E
NC
E
S
[1
]
M
a
ro
o
si
A
,
Biza
k
i
H.K.,
“
Dig
it
a
l
F
re
q
u
e
n
c
y
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t
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m
in
a
ti
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o
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m
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d
o
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u
lt
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so
rs
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it
h
L
o
w
S
a
m
p
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n
g
R
a
tes
”
,
IEE
E
S
e
n
so
rs
J
o
u
rn
a
l
,
2
0
1
2
;
1
2
(5
)
:
1
4
8
3
-
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4
9
5
[2
]
X
iao
L
,
X
ia
X
.G
,
Hu
o
H,
“
Ne
w
Co
n
d
it
io
n
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o
n
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c
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iev
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e
M
a
x
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m
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f
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u
lt
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le I
n
teg
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rs”
,
IEE
E
S
i
g
n
a
l
Pro
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g
L
e
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rs
,
2
0
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5
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2
(
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2
):
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1
9
9
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0
3
.
[3
]
Li
W
.
C
,
Wan
g
X
.
Z
,
W
a
n
g
X
.
M
,
M
o
ra
n
B,
“
Dista
n
c
e
Esti
m
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ti
o
n
u
sin
g
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ra
p
p
e
d
P
h
a
se
M
e
a
su
re
m
e
n
ts
in
N
o
ise
”
,
IEE
E
T
ra
n
s.
S
ig
n
a
l
Pro
c
e
ss
,
2
0
1
3
;
6
1
:
1
6
7
6
-
1
6
8
8
.
[4
]
Ak
h
laq
A
,
M
c
Kill
ia
m
R
,
S
u
b
ra
m
a
n
ian
R,
“
Ba
sis
Co
n
stru
c
ti
o
n
f
o
r
Ra
n
g
e
Esti
m
a
ti
o
n
b
y
P
h
a
se
N
w
r
a
p
p
in
g
”
,
IEE
E
S
ig
n
a
l
Pro
c
e
ss
.
L
e
tt
e
r
,
2
0
1
5
;
2
2
:
2
1
5
2
-
2
1
5
6
.
[5
]
M
a
rq
u
e
s
P
.
A
.
C
,
Dia
s
J.
E.
M
.
B
,
“
V
e
lo
c
it
y
Esti
m
a
ti
o
n
o
f
F
a
st
M
o
v
in
g
T
a
rg
e
ts
u
sin
g
a
S
in
g
le
S
A
R
S
e
n
so
r”
,
IEE
E
T
ra
n
s.
Aer
o
sp
El
e
c
tro
n
S
y
st
,
2
0
0
5
;
4
1
:
75
–
8
9
.
[6
]
Zo
lt
o
w
sk
i
M
.
D
,
M
a
th
e
w
s
C.
P
.
,
“
Re
a
l
-
T
i
m
e
F
re
q
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n
c
y
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n
d
2
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m
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ti
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p
a
ti
o
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e
m
p
o
ra
l
S
a
m
p
li
n
g
”
,
IEE
E
T
r
a
n
s.
S
ig
n
a
l
Pro
c
e
ss
,
1
9
9
4
;
4
2
:
2
7
8
1
–
2
7
9
1
.
[7
]
X
iao
L
,
X
ia
X.
-
G.
,
“
A
G
e
n
e
ra
li
z
e
d
Ch
in
e
se
Re
m
a
in
d
e
r
T
h
e
o
re
m
f
o
r
Tw
o
I
n
teg
e
rs
”
,
IEE
E
S
ig
n
a
l
Pro
c
e
ss
.
L
e
tt
,
2
0
1
4
;
2
1
:
55
–
5
9
.
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.
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,
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ia
X.
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J.
,
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IEE
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tt
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–
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[9
]
X
iao
L
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X
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X
.
G
.
,
“
A
Ne
w
R
o
b
u
st
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w
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in
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re
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y
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m
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ti
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ro
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e
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m
p
led
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f
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r
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s
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l
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,
2
0
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5
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1
7
:
2
4
2
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2
4
6
.
[1
0
]
Ba
rb
o
sa
D
,
M
o
n
a
ro
R.
M
,
Co
u
r
y
D.V
,
Ole
sk
o
v
icz
M,
“
M
o
d
if
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L
e
a
st
M
ea
n
S
q
u
a
re
A
lg
o
rit
h
m
f
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r
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d
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p
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e
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re
q
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n
c
y
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m
a
ti
o
n
i
n
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o
w
e
r
S
y
ste
m
s
”
,
IEE
E
Po
we
r
a
n
d
E
n
e
rg
y
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
2
0
0
8
;
p
p
.
1
-
6
.
[1
1
]
Jin
g
D
,
Ju
n
W
,
H
a
n
C
,
Da
lu
L
,
Ha
n
W
,
“
Esti
ma
ti
n
g
th
e
Fre
q
u
e
n
c
y
in
Po
we
r
S
y
ste
m
b
a
se
d
o
n
S
ta
te
S
p
a
c
e
Rec
u
rs
ive
L
e
a
st S
q
u
a
re
s”
,
ICI
EA
2
0
0
8
,
IEE
E
Co
n
f
o
n
I
n
d
u
strial
El
e
c
tro
n
ics
a
n
d
A
p
p
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ica
ti
o
n
s
,
2
0
0
8
;
1
4
4
4
-
1
4
4
7
.
[1
2
]
Op
p
e
n
h
e
im
A
.
V
,
S
c
h
a
fe
r
R.
W
,
Bu
c
k
J.
R.
,
“
Dis
c
re
te
-
T
i
m
e
S
ig
n
a
l
P
ro
c
e
ss
in
g
”
,
P
e
a
rso
n
Ed
u
c
a
ti
o
n
,
In
c
.
,
2
n
d
e
d
it
io
n
,
1
9
9
9
.
[1
3
]
Ja
c
o
b
se
n
E
,
L
y
o
n
s
R,
“
T
h
e
S
li
d
in
g
DFT
”
,
IEE
E
S
ig
n
a
l
Pro
c
e
ss
M
a
g
a
zin
e
,
2
0
0
3
;
2
0
:
74
-
8
0
.
[1
4
]
Be
ra
ld
in
J
,
S
tee
n
a
a
rt
W,
“
O
v
e
r
f
l
o
w
A
n
a
l
y
sis
o
f
a
F
ix
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d
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n
t
I
m
p
le
m
e
n
tatio
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f
th
e
G
o
e
rtze
l
A
l
g
o
rit
h
m
,
IEE
E
T
ra
n
.
Circ
u
it
s
a
n
d
S
y
ste
ms
,
1
9
8
9
;
3
6
:
3
2
2
-
3
2
4
.
[1
5
]
Bro
w
n
,
J.
C
,
P
u
c
k
e
tt
e
M.S.
,
“
A
Hig
h
Re
so
lu
ti
o
n
F
u
n
d
a
m
e
n
ta
l
F
re
q
u
e
n
c
y
D
e
ter
m
in
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ti
o
n
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a
se
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o
n
P
h
a
se
Ch
a
n
g
e
s
o
f
th
e
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o
u
rier T
ra
n
sf
o
r
m
”
,
T
h
e
Jo
u
rn
a
l
o
f
th
e
A
c
o
u
stica
l
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o
c
iety
o
f
Am
e
rica
,
1
9
9
3
;
9
4
:
6
6
2
-
6
6
7
.
[1
6
]
He
rse
l
m
a
n
P
.
L
,
Cil
l
iers
J.
E.
,
“
A
Di
g
it
a
l
In
sta
n
tan
e
o
u
s
F
re
q
u
e
n
c
y
M
e
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su
re
m
e
n
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n
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e
u
si
n
g
Hig
h
-
S
p
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e
d
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n
a
lo
g
u
e
-
to
-
Dig
it
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l
Co
n
v
e
rters
a
n
d
F
ield
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r
o
g
ra
m
m
a
b
le
G
a
te
Arra
y
s”
,
S
o
u
th
Af
ric
a
n
J
o
u
rn
a
l
o
f
S
c
ien
c
e
,
2
0
0
6
;
1
0
2
:
3
4
5
–
3
4
8
.
[1
7
]
Ho
lm
S,
“
Op
ti
m
u
m
F
F
T
-
b
a
se
d
F
re
q
u
e
n
c
y
A
c
q
u
isit
io
n
w
i
th
A
p
p
li
c
a
ti
o
n
to
COS
P
A
S
-
S
A
RS
AT
”
,
IEE
E
T
ra
n
s.
Aer
o
sp
El
e
c
tro
n
S
y
st
,
1
9
9
3
;
2
9
:
4
6
8
-
4
7
5
.
[1
8
]
Emm
e
rt
J,
“
An
FF
T
A
pp
ro
x
im
a
ti
o
n
T
e
c
h
n
i
q
u
e
S
u
it
a
b
le
fo
r
o
n
-
Ch
i
p
Ge
n
e
ra
ti
o
n
a
n
d
An
a
lys
is
o
f
S
in
u
s
o
id
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l
S
ig
n
a
ls”
,
In
P
r
o
c
e
e
d
in
g
s
o
f
th
e
1
8
t
h
IE
EE
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n
tern
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ti
o
n
a
l
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y
m
p
o
siu
m
o
n
De
f
e
c
t
a
n
d
F
a
u
l
t
T
o
l
e
ra
n
c
e
in
V
L
S
I
S
y
st
e
m
s,
2
0
0
3
.
[1
9
]
G
u
p
ta
S
,
G
u
p
ta
G,
“
S
i
m
u
latio
n
T
i
m
e
a
n
d
En
e
rg
y
T
e
st
f
o
r
T
o
p
o
lo
g
y
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n
stru
c
ti
o
n
P
ro
t
o
c
o
l
i
n
W
irele
ss
S
e
n
so
r
Ne
tw
o
rk
s”
,
In
d
o
n
e
sia
n
J
o
u
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ls.
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