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o
d
d
ec
o
m
p
o
s
itio
n
.
Mu
lt
i
-
co
m
p
o
n
en
t
s
i
g
n
a
l
an
al
y
s
is
i
s
n
ee
d
ed
ex
p
licit
l
y
to
an
al
y
s
i
s
th
e
s
y
s
te
m
s
a
f
f
ec
ted
b
y
elec
tr
o
m
a
g
n
et
ic
i
n
ter
f
er
e
n
ce
.
I
n
t
h
e
ca
s
e
o
f
s
u
c
h
s
i
g
n
al
s
,
i
n
s
tead
o
f
a
s
in
g
le
s
i
g
n
a
l
w
it
h
a
s
p
ec
if
ic
a
m
p
l
itu
d
e
an
d
p
h
ase
,
m
u
ltip
le
s
i
g
n
als
w
it
h
r
an
d
o
m
a
m
p
lit
u
d
es
an
d
p
h
ase
s
en
t
er
th
e
s
y
s
te
m
an
d
af
f
ec
t
it
s
b
eh
a
v
io
r
.
I
n
p
r
ac
tice,
in
m
o
s
t
s
t
u
d
ies
an
d
s
i
m
u
l
atio
n
s
a
v
ailab
le
in
th
e
liter
a
t
u
r
e,
th
e
an
a
l
y
s
is
i
s
co
n
d
u
cted
f
o
r
a
s
i
n
g
le
s
ig
n
al,
an
d
t
h
e
r
es
u
lts
ar
e
t
h
en
e
x
ten
d
ed
to
th
e
ac
t
u
al
ca
lcu
la
tio
n
s
[
1
-
3
]
.
T
h
e
an
al
y
s
is
o
f
t
h
e
m
o
n
o
-
co
m
p
o
n
e
n
t
e
m
p
ir
ical
s
i
g
n
al
is
p
r
o
p
o
s
ed
in
th
e
liter
at
u
r
e
to
s
o
lv
e
in
ter
f
er
en
ce
p
r
o
b
lem
s
.
Ho
w
e
v
er
,
th
e
co
m
p
le
x
i
t
y
o
f
s
ig
n
al
es
ti
m
atio
n
w
i
ll
b
e
in
c
r
ea
s
ed
.
Ob
v
io
u
s
l
y
,
th
e
d
e
f
i
n
i
tio
n
o
f
t
h
e
m
o
n
o
-
co
m
p
o
n
e
n
t
s
i
g
n
al
p
r
o
v
id
es
a
p
ar
tial
p
o
r
tio
n
o
f
i
n
f
o
r
m
atio
n
.
Ho
w
e
v
er
,
w
e
n
ee
d
all
th
e
i
n
f
o
r
m
atio
n
an
d
f
o
r
th
at
m
atter
u
s
e
m
u
l
ti
-
co
m
p
o
n
en
t
s
i
g
n
als.
I
f
w
e
h
a
v
e
a
m
o
n
o
-
co
m
p
o
n
e
n
t
s
i
g
n
al,
it
p
r
o
v
id
es
a
m
et
h
o
d
f
o
r
q
u
an
tita
tiv
e
d
e
f
in
itio
n
s
an
d
ch
ar
ac
ter
izatio
n
s
.
W
h
en
e
v
er
th
e
co
m
p
o
n
e
n
ts
ar
e
ex
tr
ac
ted
,
q
u
an
titati
v
e
m
ea
s
u
r
e
m
e
n
ts
k
ee
p
th
e
co
m
p
o
n
e
n
t
s
in
o
r
d
er
,
w
h
ic
h
i
s
co
n
s
id
er
ed
in
t
h
e
s
i
m
u
latio
n
o
f
co
m
p
o
n
en
t
d
ec
o
m
p
o
s
itio
n
m
eth
o
d
.
T
h
e
p
r
o
p
o
s
ed
id
ea
cr
ea
tes
a
n
i
m
p
o
r
tan
t
p
h
ase
d
u
e
to
m
u
l
t
i
-
co
m
p
o
n
e
n
t
s
i
g
n
al
s
.
An
o
b
j
ec
tiv
e
o
f
t
h
is
p
ap
er
is
to
p
r
o
v
id
e
a
m
e
th
o
d
f
o
r
m
ea
s
u
r
in
g
co
m
p
o
n
e
n
ts
b
y
i
m
p
le
m
en
t
in
g
a
d
ec
o
m
p
o
s
itio
n
alg
o
r
ith
m
.
Her
e
v
ar
io
u
s
m
eth
o
d
s
ab
o
u
t
co
m
p
o
n
e
n
t
s
ep
ar
atio
n
ar
e
d
escr
ib
ed
,
s
u
c
h
as
e
m
p
ir
ical
a
n
al
y
s
i
s
d
ec
o
m
p
o
s
itio
n
an
d
lo
ca
l
d
ec
o
m
p
o
s
itio
n
al
g
o
r
ith
m
.
Fo
r
th
e
a
n
al
y
s
i
s
o
f
m
o
n
o
-
co
m
p
o
n
en
t
s
ig
n
al
b
y
a
d
ec
o
m
p
o
s
itio
n
al
g
o
r
ith
m
,
t
h
e
in
ter
f
er
en
ce
is
ac
h
iev
ed
th
r
o
u
g
h
m
u
lti
-
co
m
p
o
n
e
n
t s
ig
n
als [
4
-
7
]
.
T
h
e
o
th
er
m
et
h
o
d
s
ar
e
b
ased
o
n
Gab
o
r
f
ilter
in
g
an
d
en
er
g
y
s
ep
ar
atio
n
,
b
u
t
th
e
i
n
ter
f
er
e
n
ce
w
ill
b
e
e
m
b
ed
d
ed
in
th
e
s
ep
ar
ated
co
m
p
o
n
en
ts
.
T
h
e
tech
n
iq
u
e
s
ep
ar
ates
a
m
u
lti
-
co
m
p
o
n
en
t
s
ig
n
a
l
as
n
o
n
-
s
tatio
n
ar
y
in
to
n
ar
r
o
w
-
b
a
n
d
co
m
p
o
n
e
n
ts
.
T
h
e
g
en
er
al
p
r
e
m
is
e
in
t
h
e
p
ast
w
a
s
t
h
at
t
h
e
Fo
u
r
ier
tr
an
s
f
o
r
m
is
i
n
e
f
f
ic
ien
t
f
o
r
th
e
n
o
n
-
s
tatio
n
ar
y
an
d
n
o
n
li
n
ea
r
an
al
y
s
i
s
,
w
h
ic
h
is
r
i
g
h
t
in
m
o
s
t
p
ap
er
s
.
A
n
ad
ap
tiv
e
tech
n
iq
u
e
m
a
y
b
e
u
s
ed
i
n
a
m
o
n
o
-
co
m
p
o
n
e
n
t
s
i
g
n
al
ap
p
licatio
n
ac
co
r
d
in
g
to
th
e
f
u
n
d
a
m
e
n
tal
s
o
l
u
tio
n
an
a
l
y
s
i
s
to
in
c
lu
d
e
its
ef
f
ec
ts
f
o
r
n
o
n
li
n
ea
r
a
n
d
n
o
n
-
s
tatio
n
ar
y
ti
m
e
s
eq
u
e
n
ce
s
.
T
h
e
Fo
u
r
ier
s
ep
ar
atio
n
m
eth
o
d
is
a
p
ar
tic
u
lar
t
y
p
e
o
f
m
o
n
o
-
co
m
p
o
n
e
n
t
s
ig
n
al
s
e
p
ar
atio
n
.
I
t
m
a
n
y
p
ap
er
s
an
a
d
ap
tiv
e
Fo
u
r
ier
s
ep
ar
atio
n
m
eth
o
d
is
p
r
esen
ted
b
ased
o
n
an
en
er
g
y
cr
iter
io
n
.
A
d
ap
tiv
e
Fo
u
r
ier
s
ep
ar
atio
n
m
et
h
o
d
an
d
it
s
v
ar
iatio
n
s
lead
to
f
a
s
t
s
ep
ar
atio
n
o
f
f
u
n
ctio
n
s
i
n
to
m
o
n
o
-
co
m
p
o
n
en
ts
,
w
h
ic
h
ca
n
e
x
tr
ac
t
a
s
o
l
u
tio
n
to
t
h
e
f
o
r
m
u
latio
n
p
r
o
b
le
m
o
f
a
n
o
p
ti
m
al
esti
m
atio
n
[
8
]
.
T
h
e
m
et
h
o
d
s
u
s
ed
in
t
h
e
ti
m
e
-
f
r
eq
u
en
c
y
d
o
m
ai
n
ar
e
ex
p
r
ess
ed
b
y
t
w
o
v
ie
w
p
o
in
ts
:
p
ar
a
m
etr
i
c
an
d
n
o
n
-
p
ar
a
m
etr
ic
ti
m
e
-
f
r
eq
u
en
c
y
a
n
al
y
s
is
;
th
e
f
ir
s
t
f
o
r
m
h
as
s
i
g
n
al
-
d
ep
en
d
en
t
p
ar
a
m
e
ter
s
an
d
th
e
s
ec
o
n
d
f
o
r
m
i
s
d
ef
i
n
ed
w
it
h
o
u
t
s
i
g
n
al
-
d
ep
en
d
e
n
t
p
ar
a
m
eter
s
.
P
ar
am
eter
ized
m
e
th
o
d
s
co
n
s
id
er
an
ad
d
itio
n
al
p
ar
am
eter
ized
s
ig
n
al
w
i
th
th
e
f
r
eq
u
e
n
c
y
m
o
d
u
la
ted
in
f
o
r
m
atio
n
.
A
n
o
i
s
y
m
u
lti
-
co
m
p
o
n
en
t
s
i
g
n
al
ca
n
b
e
s
h
o
w
n
a
s
t
h
e
s
u
m
o
f
n
o
is
e
a
n
d
s
in
u
s
o
id
al
f
u
n
c
tio
n
s
,
w
h
ich
i
s
d
ef
in
ed
as [
9
]
,
1
(
)
(
)
(
)
N
lw
l
S
t
S
t
n
t
(
1
)
w
h
er
e
n
w
(
t)
is
th
e
Ga
u
s
s
ian
n
o
is
e
w
i
th
m
ea
n
=0
,
v
ar
ian
ce
=σ
2
an
d
N
i
s
t
h
e
n
u
m
b
er
o
f
co
m
p
o
n
e
n
t
s
.
I
n
th
e
an
al
y
tic
th
e
s
ig
n
al
f
o
r
m
,
S
l
(
t)
is
th
e
L
-
th
co
m
p
o
n
en
t
o
f
th
e
s
ig
n
al,
S
l
(
t)
∈
L
2
(
R
)
an
d
ca
n
b
e
p
r
esen
ted
th
r
o
u
g
h
th
e
Hilb
er
t tr
an
s
f
o
r
m
th
eo
r
y
:
()
1
(
)
(
)
(
)
l
N
jt
ln
l
Z
t
Y
t
e
Z
t
(
2
)
w
h
er
e
ev
er
y
i
n
s
ta
n
ta
n
eo
u
s
f
r
eq
u
en
c
y
i
s
f
l
=(
β
'
l
(
t)
)
/2
π.
As
Y
l
(
t)
is
v
ar
iab
le
an
d
v
ar
ies
w
it
h
th
e
in
s
ta
n
ta
n
eo
u
s
f
r
eq
u
en
c
y
a
n
d
i
s
co
n
s
id
er
ed
to
h
av
e
a
co
n
s
tan
t
a
m
p
lit
u
d
e.
W
e
can
u
s
e
t
h
e
p
r
o
p
er
ties
o
f
(
1
)
,
w
h
er
e
N=
1
,
th
e
n
th
e
s
ig
n
al
r
ep
r
o
d
u
ce
s
to
a
m
o
n
o
-
co
m
p
o
n
e
n
t s
ig
n
al,
t
h
u
s
S(t)
=S
l
(
t)
+n
w
(
t)
.
T
h
e
m
o
d
el
o
f
s
i
g
n
al
ap
p
lies
to
n
o
i
s
y
m
u
lti
-
co
m
p
o
n
e
n
t
s
ig
n
als
[
1
0
]
.
B
etw
ee
n
t
h
e
s
i
g
n
al
d
ec
o
m
p
o
s
itio
n
m
et
h
o
d
s
,
th
e
Hilb
er
t
tr
an
s
f
o
r
m
p
la
y
s
e
m
p
ir
ical
m
o
d
e
d
ec
o
m
p
o
s
it
io
n
to
p
r
esen
t
th
e
m
u
lt
i
-
co
m
p
o
n
en
t
s
i
g
n
a
l
w
ith
a
g
r
o
u
p
o
f
f
u
n
ctio
n
s
.
T
h
e
Hilb
er
t
tr
an
s
f
o
r
m
i
s
u
s
ed
to
co
n
v
er
t
th
e
ti
m
e
d
o
m
ai
n
s
ig
n
al
i
n
to
an
an
al
y
tic
s
i
g
n
a
l.
Si
g
n
al
s
ar
e
o
f
ten
v
ec
to
r
s
o
f
co
m
p
le
x
n
u
m
b
er
s
.
T
h
e
v
ec
to
r
o
f
a
s
i
m
p
le
s
i
n
e
w
a
v
e
i
n
t
h
e
ti
m
e
d
o
m
a
in
co
n
s
i
s
ts
o
f
co
m
p
lex
n
u
m
b
er
s
,
o
f
w
h
ic
h
th
e
p
h
a
s
e
is
ch
a
n
g
in
g
in
ti
m
e
s
er
ie
s
co
n
ce
r
n
i
n
g
th
e
m
ai
n
s
i
n
e
w
av
e
w
i
th
a
c
o
n
s
ta
n
t
m
a
g
n
it
u
d
e.
T
h
is
m
et
h
o
d
is
ap
p
lied
to
g
et
th
e
i
n
s
tan
ta
n
eo
u
s
p
h
a
s
e
la
g
b
e
t
w
ee
n
t
w
o
s
i
g
n
als.
I
t
s
m
ai
n
li
m
itatio
n
i
s
t
h
at
t
h
e
in
p
u
t
s
i
g
n
al
n
ee
d
s
to
b
e
m
o
n
o
-
co
m
p
o
n
en
t
[
1
1
]
.
T
h
er
ef
o
r
e,
y
o
u
m
a
y
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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5
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Octo
b
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ch
an
g
es
i
n
s
i
g
n
al
co
n
ce
p
ts
.
T
h
e
s
p
ec
if
icatio
n
o
f
m
o
n
o
-
co
m
p
o
n
en
t
s
i
g
n
a
ls
i
n
clu
d
es
s
in
g
le
s
in
e
w
a
v
es
u
s
i
n
g
th
e
f
ast
Fo
u
r
ier
tr
an
s
f
o
r
m
.
Fo
r
th
e
e
s
ti
m
atio
n
o
f
f
r
e
q
u
en
cie
s
as
f
u
n
ctio
n
s
o
f
t
i
m
e,
w
e
ca
n
u
s
e
s
p
ec
tr
o
g
r
a
m
[
1
2
]
.
I
n
s
e
v
er
al
p
ap
er
s
,
it
is
r
ef
er
r
ed
to
T
h
e
Hilb
er
t
-
H
u
a
n
g
tr
an
s
f
o
r
m
t
h
at
i
s
an
e
m
p
ir
ical
ap
p
r
o
ac
h
an
d
h
a
s
b
ee
n
test
ed
an
d
v
alid
ated
.
I
n
al
m
o
s
t
all
th
e
ca
s
es
s
t
u
d
ied
,
th
e
Hilb
er
t
-
H
u
an
g
tr
a
n
s
f
o
r
m
g
iv
e
s
r
es
u
lts
m
u
ch
s
h
ar
p
er
th
an
a
n
y
o
f
t
h
e
th
eo
r
etica
l
an
al
y
s
is
m
et
h
o
d
s
in
a
ti
m
e
-
f
r
eq
u
en
c
y
-
en
er
g
y
d
em
o
n
s
tr
atio
n
.
I
n
[
1
3
]
,
to
d
ef
i
n
e
p
h
ase
d
er
i
v
ati
v
es o
f
an
al
y
ti
c
s
ig
n
al
s
an
d
a
n
e
w
t
y
p
e
o
f
p
ar
tial d
er
iv
ativ
e
s
f
o
r
p
h
ase
co
m
p
u
tatio
n
(
ca
lled
Ha
r
d
y
-
So
b
o
lev
d
er
i
v
ati
v
es)
f
o
r
i
n
p
u
t
s
i
g
n
als
in
t
h
e
r
elate
d
So
b
o
lev
s
p
ac
es.
B
ased
o
n
th
e
s
t
u
d
y
o
f
s
e
v
er
al
t
y
p
e
s
o
f
p
h
a
s
e
d
er
iv
ati
v
es
an
d
t
h
eir
c
h
ar
ac
ter
izatio
n
,
[
1
3
]
g
en
er
all
y
w
o
r
k
s
o
n
th
e
th
r
ee
s
u
b
j
ec
ts
:
-
E
x
ten
d
t
h
e
s
tate
b
et
w
ee
n
th
e
in
s
ta
n
ta
n
eo
u
s
f
r
eq
u
e
n
c
y
a
n
d
th
e
Fo
u
r
ier
tr
an
s
f
o
r
m
o
f
f
r
eq
u
en
c
y
r
esp
o
n
s
e
an
d
th
e
r
elate
d
o
n
es
f
o
r
in
p
u
t
s
ig
n
al
s
to
th
o
s
e
i
n
th
e
So
b
o
lev
s
p
ac
es.
-
B
ased
o
n
th
e
p
h
ase
d
er
iv
at
i
v
e
th
eo
r
y
an
d
t
h
e
r
ec
en
t r
es
u
lt
s
o
f
p
h
ase
d
er
iv
a
tiv
e
s
,
th
e
t
h
eo
r
et
ical
s
tr
u
ct
u
r
e
o
f
th
e
m
i
n
i
m
u
m
p
h
a
s
e
an
d
all
-
p
ass
f
il
ter
s
ar
e
estab
lis
h
ed
.
B
o
th
th
e
co
n
ti
n
u
o
u
s
a
n
d
d
is
cr
ete
s
ig
n
al
s
t
y
p
es
ar
e
co
n
s
id
er
ed
.
-
T
o
s
tu
d
y
a
p
ar
tial
t
y
p
e
o
f
ti
m
e
-
f
r
eq
u
e
n
c
y
f
u
n
ctio
n
s
u
itab
l
e
f
o
r
m
o
n
o
-
co
m
p
o
n
e
n
t,
ca
lle
d
tr
an
s
ie
n
t
t
i
m
e
-
f
r
eq
u
en
c
y
d
is
tr
ib
u
tio
n
.
Fo
r
m
u
lti
-
co
m
p
o
n
en
ts
,
w
e
n
ee
d
s
o
m
e
s
u
p
p
le
m
e
n
tar
y
s
t
u
d
y
[
1
4
]
.
T
h
e
p
r
esen
t
s
tu
d
y
atte
m
p
ted
t
o
d
ev
elo
p
a
m
et
h
o
d
f
o
r
s
i
m
u
l
t
an
eo
u
s
a
s
s
e
s
s
m
e
n
t
o
f
m
u
ltip
le
s
ig
n
als
s
o
th
at
to
in
cr
ea
s
e
t
h
e
e
f
f
icien
c
y
th
r
o
u
g
h
m
u
lt
i
-
co
m
p
o
n
en
t
s
ig
n
als
a
n
d
u
s
i
n
g
s
i
g
n
al
m
o
d
elin
g
.
Ne
w
co
m
p
o
n
en
t
s
m
a
y
b
e
ad
d
ed
to
th
e
s
ig
n
al
wh
en
e
x
p
o
s
ed
to
an
y
i
n
ter
f
er
e
n
ce
.
T
h
e
m
o
n
o
-
co
m
p
o
n
en
t
s
i
g
n
al
an
al
y
s
i
s
is
n
o
t
a
n
o
p
tio
n
an
d
th
e
c
u
r
r
en
tl
y
co
m
m
o
n
m
et
h
o
d
s
,
s
u
ch
a
s
an
al
y
tic
s
ig
n
al
m
o
d
elin
g
,
s
h
o
u
ld
b
e
u
s
ed
f
o
r
th
e
en
v
elo
p
e,
p
h
ase,
an
d
in
s
ta
n
tan
eo
u
s
f
r
eq
u
en
c
y
ca
lc
u
latio
n
s
.
Mo
r
eo
v
er
,
en
v
elo
p
e
d
etec
to
r
s
an
d
i
m
p
le
m
en
tatio
n
s
o
f
p
h
ase
d
etec
to
r
s
w
er
e
u
s
ed
to
d
eter
m
i
n
e
t
h
e
u
n
k
n
o
w
n
s
ig
n
al
p
a
r
a
m
eter
s
a
n
d
s
ep
ar
ate
an
d
d
eter
m
i
n
e
t
h
e
s
ig
n
al
p
h
ase
s
ar
e
e
n
ter
i
n
g
t
h
e
s
y
s
te
m
[
1
5
,
1
6
]
.
W
e
s
tu
d
y
m
u
lti
-
c
o
m
p
o
n
en
t
s
i
g
n
als
f
o
r
a
n
al
y
t
ic
s
i
g
n
al
s
m
o
d
elin
g
.
Un
li
k
e
th
e
S
in
,
C
o
s
,
an
d
s
in
g
l
e
-
p
u
l
s
e
f
u
n
c
tio
n
s
,
w
h
ic
h
ar
e
b
o
u
n
d
ed
in
o
n
e
d
o
m
ai
n
an
d
u
n
b
o
u
n
d
ed
in
an
o
th
er
(
f
r
o
m
a
d
u
r
atio
n
p
er
s
p
ec
tiv
e)
,
th
e
Gau
s
s
ian
f
u
n
cti
o
n
is
lo
ca
li
ze
d
in
b
o
th
ti
m
e
a
n
d
f
r
eq
u
e
n
c
y
d
o
m
ain
s
.
A
d
d
itio
n
al
l
y
,
d
u
e
to
it
s
in
f
i
n
ite
d
if
f
er
e
n
tiab
ilit
y
,
t
h
e
Gau
s
s
ian
f
u
n
ctio
n
an
d
it
s
Fo
u
r
ier
tr
an
s
f
o
r
m
w
er
e
u
s
ed
i
n
th
e
ca
lcu
la
tio
n
s
g
i
v
e
n
th
e
ir
m
o
r
e
s
tr
ai
g
h
tf
o
r
w
ar
d
an
al
y
tical
ap
p
licatio
n
s
co
m
p
ar
ed
to
o
th
e
r
p
u
r
p
o
s
es.
I
n
s
p
ec
tr
al
co
m
p
u
ta
tio
n
s
,
|
S(
w
)
|
2
d
e
n
o
tes
t
h
e
p
o
w
er
s
p
ec
tr
u
m
,
w
h
ic
h
d
ef
i
n
es
th
e
s
i
g
n
al
p
o
w
er
at
d
if
f
er
e
n
t
f
r
eq
u
e
n
cies
an
d
is
ex
ten
s
i
v
el
y
e
m
p
lo
y
ed
i
n
a
n
al
y
tic
s
i
g
n
al
ca
lc
u
latio
n
s
.
I
n
o
t
h
er
w
o
r
d
s
,
|
S(
w
)
|
2
r
ep
r
esen
ts
th
e
d
i
s
tr
ib
u
tio
n
o
f
s
ig
n
a
l
en
e
r
g
y
i
n
th
e
f
r
eq
u
e
n
c
y
d
o
m
ai
n
.
Fo
r
s
ec
u
r
e
co
m
p
u
tati
o
n
in
t
h
e
f
r
eq
u
e
n
c
y
d
o
m
ai
n
,
w
e
u
s
e
t
h
e
Fo
u
r
ier
tr
an
s
f
o
r
m
.
Dete
cti
n
g
s
ig
n
al
s
th
a
t
af
f
ec
t
d
i
f
f
er
e
n
t
s
u
b
s
y
s
te
m
s
a
t
d
if
f
er
en
t
an
g
les
is
o
f
s
p
ec
ial
i
m
p
o
r
tan
ce
in
th
e
d
esig
n
o
f
h
i
g
h
-
f
r
eq
u
e
n
c
y
s
y
s
te
m
s
,
w
h
ic
h
is
w
h
y
s
i
g
n
al
d
etec
tio
n
h
as
b
ee
n
ex
ten
s
i
v
el
y
d
is
c
u
s
s
ed
in
th
e
liter
atu
r
e.
Sig
n
al
d
etec
tio
n
is
a
d
ata
an
al
y
s
i
s
m
et
h
o
d
f
o
r
d
ec
is
io
n
-
m
a
k
i
n
g
p
r
o
b
lem
s
i
n
v
o
lv
i
n
g
u
n
ce
r
tai
n
t
y
(
n
o
is
e)
[
2
,
6
,
1
2
]
.
T
h
e
s
w
itch
m
atr
ix
co
n
tai
n
i
n
g
all
in
f
o
r
m
at
io
n
ab
o
u
t
t
h
e
s
ig
n
al
w
a
s
u
s
ed
i
n
t
h
is
s
t
u
d
y
to
p
r
esen
t
a
n
e
w
s
o
l
u
tio
n
.
W
e
e
m
p
lo
y
ed
th
is
m
atr
i
x
w
i
th
a
p
r
o
p
er
w
ei
g
h
t
p
er
ce
n
tag
e
i
n
n
tes
ts
to
an
al
y
z
e
d
if
f
er
e
n
t sce
n
ar
io
s
.
2.
SI
M
UL
AT
I
O
N
O
F
S
I
G
NAL
Giv
e
n
th
at
t
h
e
Fo
u
r
ier
tr
an
s
f
o
r
m
is
a
n
i
m
p
r
o
p
er
i
n
teg
r
al
an
d
b
ased
o
n
th
e
W
ien
er
-
Kh
i
n
tch
in
e
th
eo
r
e
m
,
t
h
e
s
i
g
n
al
p
o
w
er
is
o
b
tain
ed
u
s
i
n
g
th
e
a
u
to
co
r
r
elatio
n
f
u
n
ct
io
n
:
2
(
)
(
)
jw
s
S
w
r
e
d
(
3
)
w
h
er
e
r
s
(
ζ
)
is
t
h
e
s
ig
n
al
a
u
to
c
o
r
r
elatio
n
f
u
n
ctio
n
.
Si
m
u
latio
n
o
f
t
h
e
s
ig
n
al
s
in
p
u
t
to
t
h
e
s
u
b
s
y
s
te
m
i
n
t
h
e
ti
m
e
an
d
f
r
eq
u
e
n
c
y
d
o
m
ai
n
s
ar
e
d
em
o
n
s
tr
ated
in
Fi
g
u
r
es 1
,
2
,
an
d
3
.
Fro
m
a
m
at
h
e
m
atica
l
p
er
s
p
ec
tiv
e,
a
u
n
iq
u
e
s
i
g
n
al
ca
n
b
e
ex
p
an
d
ed
in
a
n
in
f
i
n
ite
n
u
m
b
e
r
o
f
w
a
y
s
,
w
h
ic
h
is
a
m
o
n
g
th
e
a
m
b
i
g
u
iti
es
f
ac
ed
i
n
t
h
e
f
ield
o
f
s
i
g
n
al
an
al
y
s
i
s
.
T
h
e
s
i
g
n
al
s
c
h
ec
k
-
i
n
ti
m
e
d
o
m
ai
n
a
n
d
u
s
e
r
es
u
lt
s
in
t
h
e
f
r
eq
u
e
n
c
y
d
o
m
ai
n
[
1
6
]
.
(
)
(
)
c
o
s
(
(
)
)
s
t
y
t
P
t
(
4
)
w
h
er
e
y
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lex
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Evaluation Warning : The document was created with Spire.PDF for Python.
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N:
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Desig
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jt
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5
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(
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r
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t
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Fig
u
r
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1
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R
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d
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ai
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u
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tical
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ain
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u
r
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t Fo
u
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s
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h
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tical
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g
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ar
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p
lex
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g
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l
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n
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id
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ed
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ig
n
al
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y
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t)
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s
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t)
)
)
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th
e
r
ea
l
a
m
p
lit
u
d
e
an
d
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h
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s
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ar
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t n
ec
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ain
[
1
8
,
1
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el
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p
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o
llo
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s
:
()
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S
w
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(
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)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8708
I
n
t J
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lec
&
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m
p
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n
g
,
Vo
l.
9
,
No
.
5
,
Octo
b
er
2
0
1
9
:
4
2
0
4
-
4216
4208
w
h
er
e
C
(
w
)
is
s
p
ec
tr
al
a
m
p
lit
u
d
e,
an
d
ψ(
w
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i
s
th
e
s
p
ec
tr
al
p
h
ase.
A
s
i
g
n
al
n
o
r
m
a
lized
in
th
e
ti
m
e
d
o
m
ai
n
i
s
also
n
o
r
m
al
ized
in
t
h
e
f
r
eq
u
e
n
c
y
d
o
m
ai
n
.
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n
ce
,
w
e
m
a
y
ca
lcu
late
t
h
e
m
ea
n
f
r
eq
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en
c
y
<
w
>
a
n
d
t
h
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v
ar
ia
n
ce
2
()
w
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th
e
f
r
eq
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e
n
c
y
d
o
m
ai
n
.
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t
e
th
at
in
t
h
e
f
r
eq
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en
c
y
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o
m
ai
n
,
v
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ce
r
ep
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t
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an
d
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h
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2
()
w
Q
w
s
w
d
w
(
1
0
)
2
2
2
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wQ
(
1
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W
e
m
a
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t
b
e
ab
le
to
ca
lcu
late
th
e
Fo
u
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ier
tr
an
s
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o
r
m
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all
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ig
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s
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d
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tr
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t
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s
tatis
t
ical
s
p
ec
if
icatio
n
s
.
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h
is
m
ea
n
s
t
h
at
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is
i
n
itiall
y
r
eq
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ir
ed
to
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eter
m
i
n
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n
d
2
w
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t
h
e
v
ar
ia
n
ce
o
f
t
h
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r
eq
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en
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o
m
ai
n
.
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h
e
Fo
u
r
ie
r
tr
an
s
f
o
r
m
d
o
es n
o
t a
p
p
l
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to
all
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ig
n
al
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;
w
e
d
ef
i
n
ed
o
u
r
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b
j
e
ctiv
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to
ex
tr
ac
t t
h
e
s
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t
ical
s
p
ec
i
f
icatio
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s
f
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m
th
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m
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s
i
g
n
al
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a
n
d
s
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g
n
al
co
m
p
o
n
en
ts
.
s
r
d
en
o
tes
a
r
ea
l
k
n
o
w
n
s
i
g
n
al,
a
n
d
w
e
ai
m
to
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eter
m
i
n
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s
i
.
()
2
(
)
(
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()
(
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(
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jt
ri
i
r
r
i
i
Z
t
s
js
Y
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e
s
s
s
s
t
w
t
Y
(
1
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h
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e
φ
'
(
t)
is
i
n
s
tan
ta
n
eo
u
s
f
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eq
u
en
c
y
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t
h
e
i
m
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g
i
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ar
y
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ar
t
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s
i
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n
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e
d
eter
m
i
n
ed
w
it
h
An
al
y
tic
m
et
h
o
d
.
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n
th
is
m
eth
o
d
,
an
an
a
l
y
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ic
f
o
r
m
is
co
n
s
id
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ed
f
o
r
t
h
e
s
ig
n
al.
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h
e
m
eth
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ased
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t
h
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ce
s
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th
e
s
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al
f
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en
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co
m
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lex
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s
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o
m
es
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ith
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th
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m
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t
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f
o
r
p
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s
iti
v
e
an
d
n
eg
at
iv
e
f
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eq
u
en
c
ies,
r
esp
ec
tiv
el
y
.
I
n
th
e
s
i
m
u
latio
n
f
o
r
s
p
ec
tr
u
m
p
o
w
er
an
al
y
s
is
,
we
u
s
e
th
e
an
a
l
y
t
ic
m
et
h
o
d
[
2
0
,
2
1
]
.
I
n
F
ig
u
r
e
4
s
h
o
w
s
th
e
co
m
p
r
i
s
io
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o
f
p
o
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e
r
s
p
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tr
al
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en
s
it
y
s
i
m
u
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n
f
o
r
tw
o
o
r
ig
i
n
al
an
d
Hilb
er
t t
y
p
es.
Fig
u
r
e
4
.
P
o
w
er
s
p
ec
tr
al
d
en
s
i
t
y
Giv
e
n
Q
=
∘
,
s
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ce
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w
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|
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i
s
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o
n
d
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o
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er
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a
ls
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|
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|
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)
.
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w
e
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er
,
w
is
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d
d
,
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ield
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g
t
h
at
th
e
e
x
p
r
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io
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2
|
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|
w
S
w
d
w
is
ze
r
o
.
T
h
er
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o
r
e,
n
o
in
f
o
r
m
atio
n
is
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ai
lab
le
o
n
t
h
e
m
ea
n
f
r
eq
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en
c
y
,
an
d
t
h
is
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elatio
n
al
w
a
y
s
p
r
o
d
u
ce
s
ze
r
o
f
o
r
r
ea
l sig
n
al
s
,
w
h
ich
i
s
also
tr
u
e
f
o
r
all
o
d
d
m
o
m
e
n
t
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m
s
:
1
0
:
1
:
,
,
,
.
.
.
w
o
d
d
F
i
r
s
t
T
h
i
r
d
F
i
f
t
h
m
o
m
e
n
t
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m
s
(
1
3
)
T
h
e
an
al
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tic
s
ig
n
al
is
t
h
e
n
e
m
p
lo
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ed
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s
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i
f
y
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e
r
ea
l
s
ig
n
al.
I
n
o
th
er
w
o
r
d
s
,
b
y
d
eter
m
i
n
in
g
Z
(
t)
,
th
e
en
v
elo
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e
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d
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h
ase
c
h
ar
ac
ter
is
tics
ar
e
o
b
tain
ed
w
ith
n
o
a
m
b
ig
u
itie
s
(
d
eter
m
i
n
in
g
th
e
in
s
tan
tan
eo
u
s
f
r
eq
u
en
c
y
)
.
I
t sh
o
u
ld
b
e
n
o
ted
th
at
an
a
n
al
y
tic
s
i
g
n
al
is
r
elate
d
to
th
e
Hilb
er
t tr
an
s
f
o
r
m
as
f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Desig
n
a
n
d
imp
leme
n
ta
tio
n
o
f
th
e
s
u
b
s
ystem
s
u
b
ject
to
emis
s
io
n
o
f m
u
ltico
m
p
o
n
e
n
t
.
.
.
(
M
ila
d
Da
n
esh
va
r
)
4209
0
2
(
)
(
)
2
j
w
t
Z
t
S
w
e
d
w
(
1
4
)
I
n
th
e
ca
s
e
o
f
an
a
n
al
y
tic
s
i
g
n
al,
th
e
in
v
er
s
e
Fo
u
r
ier
tr
an
s
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o
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u
r
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s
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ai
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
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m
p
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n
g
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9
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No
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er
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0
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4
2
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-
4216
4210
Fig
u
r
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ates
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e
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(
MT
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t
w
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h
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T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Desig
n
a
n
d
imp
leme
n
ta
tio
n
o
f
th
e
s
u
b
s
ystem
s
u
b
ject
to
emis
s
io
n
o
f m
u
ltico
m
p
o
n
e
n
t
.
.
.
(
M
ila
d
Da
n
esh
va
r
)
4211
I
n
th
e
tab
le
2
s
h
o
w
s
t
h
e
R
elia
b
ilit
y
ca
lc
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latio
n
s
i
n
a
s
u
b
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y
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t
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n
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3
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ce
i
n
c
r
ea
s
es,
t
h
e
co
n
tr
o
l
m
ec
h
a
n
i
s
m
m
a
n
ip
u
lates
th
e
o
s
cillato
r
s
u
c
h
t
h
at
t
h
e
e
r
r
o
r
is
m
in
i
m
ized
.
I
n
th
is
p
h
a
s
e
c
o
n
tr
o
l
m
ec
h
an
i
s
m
,
th
e
o
u
tp
u
t
s
ig
n
al
is
lo
c
k
ed
o
n
t
h
e
r
ef
er
e
n
ce
s
ig
n
al
p
h
ase.
I
n
s
o
m
e
o
f
th
e
p
h
ase
lo
ck
l
o
o
p
(
P
L
L
)
,
v
o
ltag
e
co
n
tr
o
lled
o
s
cillato
r
(
VC
O)
is
u
s
ed
i
n
s
tead
o
f
t
h
e
cu
r
r
en
t
co
n
tr
o
lled
o
s
cillato
r
(
C
C
O)
,
in
w
h
ic
h
c
ase
t
h
e
p
h
ase
d
etec
to
r
o
u
tp
u
t
is
a
co
n
tr
o
lled
cu
r
r
en
t
s
o
u
r
ce
.
Ho
w
ev
er
,
a
s
i
m
ilar
p
er
f
o
r
m
a
n
ce
o
b
tain
ed
in
b
o
th
ca
s
es.
P
r
o
p
o
r
tio
n
al
d
er
iv
ativ
e
(
P
D)
i
s
r
esp
o
n
s
ib
le
f
o
r
co
m
p
ar
i
n
g
t
h
e
p
h
ases
o
f
t
h
e
o
u
tp
u
t
a
n
d
th
e
r
ef
er
en
ce
s
ig
n
al
s
.
T
h
e
P
D
r
elatio
n
is
p
r
o
p
o
r
ti
o
n
al
to
th
e
p
h
ase
d
i
f
f
er
e
n
ce
w
it
h
i
n
a
s
p
ec
if
ied
i
n
ter
v
al.
T
h
e
o
u
tp
u
t
s
ig
n
al
p
r
o
d
u
ce
d
b
y
t
h
e
P
D
is
co
m
p
o
s
ed
o
f
a
d
c
co
m
p
o
n
e
n
t
a
n
d
an
u
n
d
e
s
ir
ab
le
ac
co
m
p
o
n
en
t
th
at
is
eli
m
i
n
ated
u
s
i
n
g
a
u
s
u
a
ll
y
f
ir
s
t
-
d
e
g
r
ee
lo
w
-
p
ass
f
i
lter
.
T
h
e
7
4
HC
4
0
4
6
I
C
is
o
f
P
L
L
t
y
p
e,
t
h
e
XO
R
g
ate
o
f
w
h
ic
h
w
a
s
u
s
ed
i
n
o
u
r
ca
s
e.
I
n
t
h
e
p
h
a
s
e
s
h
i
f
ter
b
lo
ck
,
t
h
e
p
h
ase
d
i
f
f
er
en
ce
b
et
w
ee
n
t
h
e
t
w
o
s
i
g
n
a
ls
is
g
e
n
er
ated
an
d
ap
p
lied
to
th
e
I
C
.
T
h
e
f
u
n
ct
io
n
o
f
an
XO
R
g
ate
i
s
v
er
y
s
i
m
i
lar
to
a
li
n
ea
r
m
u
lt
ip
lier
.
I
n
t
h
i
s
m
eth
o
d
,
t
h
e
p
h
a
s
e
d
if
f
er
e
n
ce
b
e
t
w
ee
n
t
w
o
o
r
m
o
r
e
s
ig
n
al
s
is
tr
an
s
f
o
r
m
ed
i
n
to
a
s
q
u
ar
e
w
a
v
e
u
s
i
n
g
XO
R
,
a
n
d
th
e
ar
ea
u
n
d
er
t
h
e
s
ig
n
al
c
u
r
v
e
i
s
ca
lcu
la
ted
u
s
i
n
g
a
n
i
n
teg
r
ato
r
.
T
h
en
,
b
y
c
o
n
v
er
ti
n
g
t
h
e
o
b
tain
ed
a
n
alo
g
v
al
u
e
to
a
d
ig
ita
l
v
alu
e,
t
h
e
m
icr
o
co
n
tr
o
ller
u
n
it
ca
r
r
ies
o
n
th
e
p
r
o
ce
s
s
i
n
g
o
p
er
atio
n
s
an
d
ca
lcu
lates
th
e
p
h
ase
d
if
f
er
e
n
ce
.
I
n
F
ig
u
r
e
1
2
s
h
o
w
s
t
h
e
C
alc
u
l
atio
n
o
f
p
h
ase
d
i
f
f
er
en
ce
u
s
i
n
g
XOR
g
ate
f
o
r
t
w
o
s
i
g
n
als
[
2
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Desig
n
a
n
d
imp
leme
n
ta
tio
n
o
f
th
e
s
u
b
s
ystem
s
u
b
ject
to
emis
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io
n
o
f m
u
ltico
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p
o
n
e
n
t
.
.
.
(
M
ila
d
Da
n
esh
va
r
)
421
3
Fig
u
r
e
1
2
.
C
alcu
latio
n
o
f
p
h
as
e
d
if
f
er
e
n
ce
u
s
in
g
XO
R
g
ate
[
2
1
]
I
n
F
ig
u
r
e
1
3
s
h
o
w
s
th
e
b
lo
ck
d
iag
r
a
m
o
f
t
h
e
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y
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te
m
u
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ed
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o
r
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r
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h
ase
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if
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ce
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et
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t
w
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g
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al
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in
p
u
t to
t
h
e
s
u
b
s
y
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te
m
.
Fig
u
r
e
1
3
.
T
h
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v
er
all
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lo
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iag
r
a
m
o
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th
e
s
y
s
te
m
u
s
ed
f
o
r
m
ea
s
u
r
in
g
t
h
e
p
h
ase
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i
f
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er
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c
e
b
et
w
ee
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t
w
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ig
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p
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t to
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e
s
u
b
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m
(
ex
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to
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s
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g
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3
.
4
.
P
ro
po
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Alg
o
rit
h
m
Her
e,
an
alg
o
r
ith
m
w
as
p
r
o
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o
s
ed
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ased
o
n
th
e
s
w
i
tch
m
atr
i
x
to
r
elate
th
e
d
if
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er
e
n
t
co
m
p
o
n
en
t
s
an
d
p
ar
am
eter
s
.
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h
e
s
w
itc
h
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at
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m
et
h
o
d
ac
tu
all
y
,
is
u
s
e
d
in
a
co
m
m
u
n
icatio
n
s
y
s
t
e
m
f
o
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ar
a
m
eter
m
ea
s
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r
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e
n
t
co
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n
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t
s
a
d
ev
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ce
o
n
a
ce
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tain
r
o
w
to
a
s
ig
n
a
l
o
n
a
p
ar
ticu
lar
co
lu
m
n
.
T
h
e
r
e
ar
e
m
o
r
e
s
i
g
n
a
ls
th
an
d
ev
ice
s
.
T
h
e
n
u
m
b
er
o
f
r
o
w
s
M
a
n
d
co
lu
m
n
s
N
d
ef
i
n
e
s
t
h
e
s
ize
o
f
t
h
e
m
atr
i
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as
M
*
N.
B
y
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n
v
en
tio
n
,
r
o
w
s
ar
e
lis
ted
b
ef
o
r
e
co
lu
m
n
s
.
T
h
is
m
eth
o
d
is
u
s
ed
f
o
u
r
d
if
f
er
e
n
t
s
it
u
atio
n
s
f
o
r
ex
a
m
p
le
s
ig
n
al,
s
u
p
p
l
y
,
co
n
n
ec
tio
n
,
an
d
B
N
C
co
n
n
ec
t
io
n
f
ield
Ma
tr
ices
th
a
t
is
s
h
o
w
n
i
n
Fig
u
r
e
1
4
an
d
b
y
r
elati
o
n
o
f
d
i
f
f
er
en
t
p
ar
ts
,
w
e
ca
n
co
m
p
u
te
m
o
r
e
in
f
o
r
m
a
tio
n
ab
o
u
t
p
ar
a
m
eter
s
r
es
u
lt
s
.
A
m
atr
i
x
th
at
a
llo
w
s
e
v
er
y
i
n
p
u
t
to
b
e
co
n
n
ec
te
d
to
a
s
ep
ar
ate
o
u
tp
u
t
i
s
d
esc
r
ib
ed
as
n
o
n
-
b
lo
ck
i
n
g
a
n
d
c
an
b
e
v
er
y
h
e
lp
f
u
l
i
n
co
m
p
l
ex
co
m
m
u
n
icatio
n
s
y
s
te
m
s
.
I
n
Fi
g
u
r
e
1
5
s
h
o
w
s
th
e
s
w
itc
h
m
atr
i
x
d
e
m
o
n
s
t
r
atio
n
f
o
r
m
u
ltip
le
m
o
d
es
u
s
in
g
f
o
u
r
d
if
f
er
en
t
s
itu
a
tio
n
s
f
o
r
e
x
a
m
p
le
s
i
g
n
al,
s
u
p
p
l
y
,
co
n
n
ec
tio
n
,
a
n
d
B
NC
co
n
n
ec
tio
n
f
ie
ld
Ma
tr
ices
[
2
0
]
.
I
n
th
e
s
o
f
t
w
ar
e
d
esig
n
,
w
e
u
s
e
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if
f
er
en
t
m
o
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es
f
o
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s
t
h
at
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e
r
y
r
elatio
n
s
h
ip
b
et
w
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n
s
it
u
atio
n
s
ca
lled
R
ela
y
.
s
T
o
r
elate
th
e
d
if
f
er
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t c
o
m
p
o
n
en
t
s
an
d
p
ar
a
m
eter
s
i
s
cr
ea
te
d
b
y
3
5
m
o
d
es th
at
ar
e
s
h
o
w
n
in
Fi
g
u
r
e
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.