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EE2023 Signals & Systems Quiz
Semester 1 AY2011/12
Date: 6 October 2011
Time Allowed: 1.5 hours
Q.1 Consider the periodic signal
( )
x t
given by the expression
( )
(
)
(
)
3
2
2
3
2
2
3
5
3
2
2
j t
j t
j t
j t
x t
j e
je
je
j e
−
−
=
+
−
+
+
+
−
(a)
What is the fundamental period and fundamental frequency of
( )
x t
?
(b)
Sketch the amplitude and phase spectra of
( )
x t
.
(c)
Is
( )
x t
a real signal ? Justify your answer.
(d)
What is the power of
( )
x t
?
Q.2 Derive the Fourier transform of the signal
( )
x t
shown in Figure Q2-1.
Derive the Fourier transform of the periodic signal
( )
y t
shown in Figure Q2-2.
Q.3 A signal is modeled by
( )
(
)
(
)
2rect
rect
2
2
t
t
x t
=
where
denotes convolution. Determine the
spectrum,
(
)
X
f
, of
( )

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