Signals and Systems (EENG 320)
Assignment (5)
1.
Use either the Fourier transform analysis and synthesis equations or the
Fourier transform properties to:
a.
Compute the Fourier transform of each of the following signals:
i.
0
),
(
)]
cos(
[
>
−
α
ω
t
u
t
e
o
t
ii.
as shown in figure (1).
)
(
t
x
t
x(t)
b.
Determine the continuoustime signal corresponding to each of the
following transforms:
i.
[]
)
2
(
)
2
(
3
sin
2
)
(
πω
π
−
−
=
j
X
ii.
)
3
/
4
cos(
)
(
+
=
j
X
2.
Determine which, if any, of the real signals depicted in Figures (24) have
Fourier transforms that satisfy each of the following conditions:
i.
{}
0
)
(
=
ℜ
j
X
e
ii.
0
)
(
=
ℑ
j
X
m
Figure 1
1
2
2
3
4
2
1
5
3
4
5
6
7
1
6
0
….
….
t
x(t)
2
1
2
1
Figure (2)
1
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2
/2
()
t
xt
e
−
=
Figure (3)
t
2
t
x
tt
e
−
=
Figure (4)
3.
If
)
(
ω
j
X
denotes the Fourier transform of the signal
depicted in figure (5),
)
(
t
x
t
x(t)
2
1
0
1
3
2
1
Figure (5)
i.
Find
)
(
j
X
∠
ii.
Find
)
0
(
j
X
iii.
Find
∫
+∞
∞
−
ωω
d
j
X
)
(
iv.
Evaluate
∫
+∞
∞
−
d
j
X
2
)
(
v.
Sketch the inverse Fourier transform of
{ }
)
(
j
X
e
ℜ
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 Spring '10
 SherifAbdelaseem
 Fourier Series

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