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# fourier_4pp

DisciplinaIntrodução Aos Circuitos Elétricos30 materiais191 seguidores
Pré-visualização4 páginas
ua
de
\u3c9
po
r,
X
(j
\u3c9
)
=
\u222b \u221e \u2212\u221e
x(
t)
e\u2212
j\u3c9
t
dt
,
e,
po
rt
an
to
,
C
n
=
1 T
0
X
(j
n\u3c9
0)
\ufffd
A
ss
im
,
x T
0
(t
)
=
\u221e \u2211 n=\u2212\u221e
1 T 0
X
(j
n\u3c9
0
)e
jn
\u3c9
0
t
=
1 2\u3c0
\u221e \u2211 n=\u2212\u221e
X
(j
n\u3c9
0
)e
jn
\u3c9
0
t \u3c9
0
\ufffd
C
om
o
T 0
\u2192
\u221e,
x T
0
(t
)
ap
ro
xi
m
a
x(
t)
,n
o
lim
ite
,a
eq
ua
çã
o
an
te
rio
rr
ep
re
se
nt
a
ta
m
bé
m
x(
t)
.
A
lé
m
di
ss
o,
co
m
o
\u3c9
0
\u2192
0
qu
an
do
T 0
\u2192
\u221e,
o
la
do
di
re
ito
da
eq
ua
çã
o
pa
ss
a
a
se
ru
m
a
in
te
gr
al
e
o
es
pe
ct
ro
pa
ss
a
a
se
rc
on
tín
uo
.
39
/4
7
R
ep
re
se
nt
aç
õe
s
de
Fo
ur
ie
r
A
Tr
an
sf
or
m
a
de
Fo
ur
ie
r
\ufffd
D
es
sa
fo
rm
a,
ch
eg
a-
se
na
Tr
an
sf
or
m
a
de
Fo
ur
ie
re
su
a
in
ve
rs
a:
F{
x(
t)
}=
X
(j
\u3c9
)
=
\u222b \u221e \u2212\u221e
x(
t)
e\u2212
j\u3c9
t
dt
F\u2212
1
{X
(j
\u3c9
)}
=
x(
t)
=
1 2\u3c0
\u222b \u221e \u2212\u221e
X
(j
\u3c9
)e
j\u3c9
t
d\u3c9
\ufffd
R
el
em
br
o
a
Tr
an
sf
or
m
a
bi
la
te
ra
ld
e
La
pl
ac
e:
L{
x(
t)
}=
X
(s
)
=
\u222b \u221e \u2212\u221e
x(
t)
e\u2212
s
t
dt
co
nc
lu
i-s
e
qu
e
a
tra
ns
fo
rm
a
de
Fo
ur
ie
ré
um
ca
so
es
pe
ci
al
da
tra
ns
fo
rm
a
de
La
pl
ac
e
qu
an
do
s
=
j\u3c9
,o
u
se
ja
,\u3c3
=
0
(s
=
\u3c3
+
j\u3c9
)\u2013
no
ca
so
em
qu
e
o
ei
xo
im
ag
in
ár
io
do
pl
an
o
s
es
tá
in
se
rid
o
na
re
gi
ão
de
co
nv
er
gê
nc
ia
da
tra
ns
fo
rm
a
de
La
pl
ac
e.
40
/4
7
R
ep
re
se
nt
aç
õe
s
de
Fo
ur
ie
r
A
Tr
an
sf
or
m
a
de
Fo
ur
ie
r
\ufffd
D
et
er
m
in
e
a
tra
ns
fo
rm
a
de
Fo
ur
ie
rd
e
x(
t)
=
e\u2212
at
.
F{
x(
t)
}=
X
(j
\u3c9
)
=
\u222b \u221e \u2212\u221e
x(
t)
e\u2212
j\u3c9
t
dt
=
\u222b \u221e \u2212\u221e
e\u2212
at
e\u2212
j\u3c9
t
dt
X
(j
\u3c9
)
=
\u222b \u221e 0
e\u2212
(a
+
j\u3c9
)t
dt
=
\u22121
a
+
j\u3c9
e\u2212
(a
+
j\u3c9
)t
\u2223 \u2223 \u2223 \u2223 \u2223 \u2223 \u2223\u221e 0
X
(j
\u3c9
)
=
1
a
+
j\u3c9
,
a
>
0
\ufffd
E
xp
re
ss
an
do
a
+
j\u3c9
na
fo
rm
a
po
la
rc
om
o
\u221a a2
+
\u3c9
2
ej
ta
n\u2212
1 (
\u3c9
/a
) ,
X
(j
\u3c9
)
=
1
\u221a a2
+
\u3c9
2
e\u2212
jta
n\u2212
1 (
\u3c9
/a
)
Po
rt
an
to
,
|X
(j
\u3c9
)|=
1
\u221a a2
+
\u3c9
2
,
e
\u2220X
(j
\u3c9
)
=
\u2212t
an
\u22121
\u3c9 a
41
/4
7
R
ep
re
se
nt
aç
õe
s
de
Fo
ur
ie
r
A
Tr
an
sf
or
m
a
de
Fo
ur
ie
r
\ufffd
A
fo
rm
a
gr
á\ufb01
ca
de |X
(j
\u3c9
)|=
1
\u221a a2
+
\u3c9
2
,
e
\u2220X
(j
\u3c9
)
=
\u2212t
an
\u22121
\u3c9 a
é
m
os
tra
da
ab
ai
xo
.
42
/4
7
R
ep
re
se
nt
aç
õe
s
de
Fo
ur
ie
r
A
Tr
an
sf
or
m
a
de
Fo
ur
ie
r
\ufffd
D
et
er
m
in
e
a
tra
ns
fo
rm
a
de
Fo
ur
ie
rd
e
x(
t)
=
\u3b4(
t)
.
F{
x(
t)
}=
X
(j
\u3c9
)
=
\u222b \u221e \u2212\u221e
\u3b4(
t)
e\u2212
j\u3c9
t
dt
=
1
\ufffd
Q
ua
la
im
po
rt
ân
ci
a
di
ss
o?
43
/4
7
R
ep
re
se
nt
aç
õe
s
de
Fo
ur
ie
r
A
Tr
an
sf
or
m
a
de
Fo
ur
ie
r
\ufffd
D
et
er
m
in
e
a
tra
ns
fo
rm
a
de
Fo
ur
ie
rd
e
um
pu
ls
o
re
ta
ng
ul
ar
:
x(
t)
=
{ 1
se
\u2212T
<
t
<
T
0
se
|t|
>
T
\ufffd
O
pu
ls
o
re
ta
ng
ul
ar
é
ab
so
lu
ta
m
en
te
in
te
gr
áv
el
(T
<
\u221e)
:
F{
x(
t)
}=
X
(j
\u3c9
)
=
\u222b \u221e \u2212\u221e
x(
t)
e\u2212
j\u3c9
t
dt
=
\u222b T \u2212T
e\u2212
j\u3c9
t
dt
X
(j
\u3c9
)
=
\u2212
1 j\u3c9
e\u2212
j\u3c9
t\u2223 \u2223 \u2223 \u2223 \u2223 \u2223 \u2223T \u2212T
=
2 \u3c9
se
n(
\u3c9
T)
,
\u3c9
\ufffd
0
\ufffd
P
ar
a
\u3c9
=
0,
a
in
te
gr
al
se
si
m
pl
i\ufb01
ca
pa
ra
2T
.
O
es
pe
ct
ro
de
m
ag
ni
tu
de
é:
|X
(j
\u3c9
)|=
2
\u2223 \u2223 \u2223 \u2223 \u2223sen
\u3c9
T
\u3c9
\u2223 \u2223 \u2223 \u2223 \u2223
44
/4
7
R
ep
re
se
nt
aç
õe
s
de
Fo
ur
ie
r
A
Tr
an
sf
or
m
a
de
Fo
ur
ie
r
\ufffd
O
es
pe
ct
ro
de
fa
se
é
da
do
po
r:
\u2220X
(j
\u3c9
)
=
\u23a7 \u23aa \u23a8 \u23aa \u23a90
se
se
n
(\u3c9
t)
\u3c9
>
0
\u3c0
se
se
n
(\u3c9
t)
\u3c9
<
0
45
/4
7
R
ep
re
se
nt
aç
õe
s
de
Fo
ur
ie
r
A
Tr
an
sf
or
m
a
D
is
cr
et
a
de
Fo
ur
ie
r
\ufffd
A
ve
rs
ão
di
sc
re
ta
da
Tr
an
sf
or
m
a
de
Fo
ur
ie
ré
da
da
po
r:
X
(e
j\u3a9
)
=
\u221e \u2211 n=\u2212\u221e
x[
n]
e\u2212
j\u3a9
n
x[
n]
=
1 2\u3c0
\u222b \u3c0 \u2212\u3c0
X
(e
j\u3a9
)e
j\u3a9
n
d\u3a9
\ufffd
A
Tr
an
sf
or
m
a
R
áp
id
a
de
Fo
ur
ie
r(
FF
T)
re
du
z
dr
as
tic
am
en
te
o
nú
m
er
o
de
cá
lc
ul
os
ne
ce
ss
ár
io
s
pa
ra
ca
lc
ul
ar
a
tra
ns
fo
rm
a
di
sc
re
ta
de
Fo
ur
ie
r,
da
or
de
m
de
N
2
pa
ra
N
lo
g
N
46
/4
7
R
ep
re
se
nt
aç
õe
s
de
Fo
ur
ie
r
S
im
ul
aç
õe
s
C
om
pu
ta
ci
on
ai
s
\ufffd
C
on
vo
lu
çã
o
no
te
m
po
di
sc
re
to
\ufffd
C
on
vo
lu
çã
o
no
te
m
po
co
nt
ín
uo
\ufffd
S
ér
ie
s
de
Fo
ur
ie
r
\ufffd
Tr
an
sf
or
m
a
R
áp
id
a
de
Fo
ur
ie
r(
ex
.
fu
nç
ão
so
m
a
de
se
nó
id
es
e
a
sé
rie
S
un
sp
ot
s)
\ufffd
S
im
ul
aç
ão
qu
e
ilu
st
ra
a
re
la
çã
o
en
tre
en
tra
da
e
sa
íd
a
de
\ufb01l
tro
s
47
/4
7