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Exponential Fourier Series
A periodic si...
Question
A periodic signal x (t) of period
T
o
is given by
x
(
t
)
=
{
1
,
∣
t
∣
<
T
1
0
,
T
1
<
∣
t
∣
<
T
o
2
the dc component of x(t) is
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Solution
x
d
c
=
1
T
0
∫
T
0
/
2
−
T
0
/
2
x
(
t
)
d
t
1
T
o
∫
T
1
−
T
1
1
d
t
=
1
T
o
[
t
]
T
1
−
T
1
x
d
c
=
1
T
o
[
T
1
−
(
−
T
1
)
]
=
2
T
1
T
o
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0
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Q.
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Q.
A periodic signal x(t) has a trigonometric Fourier series expansion
x
(
t
)
=
a
0
+
∑
∞
n
−
1
(
a
n
c
o
s
n
ω
0
t
+
b
n
s
i
n
n
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