Page 1 of 2
EE2023 Signals & Systems Midterm Quiz
Semester 2 AY2012/13
Date: 7 March 2013
Time Allowed: 1.5 hours
Q.1 The signal
( )
x t
has an amplitude spectrum given in Figure Q.1 below.
(a) What is the minimum sampling frequency that will allow
( )
x t
to be recovered from its
samples?
(b) Suppose that
( )
x t
is sampled at a rate of
38 kHz
s
f
=
. What part of
(
)
X
f
can be recovered
without error from the samples?
Explain your answer with an illustration of the appropriate
spectrum.
(c) Is
( )
x t
a power or energy signal? Explain your answer.
Q.2 Consider the complex signal
( )
( )
( )
sinc
sinc
=
+
x t
t
j
t
.
(a)
Find the energy spectral density of
( )
x t
. Hence, or otherwise, determine the total energy of
( )
x t
.
(b)
Suppose
( )
( )
2
=
y t
x t
. Find the 3dB bandwidth of
( )
y t
.
Q.3 The complex exponential Fourier Series representation of a periodic signal,
( )
x t
, is
jkt
k
k
c e
∞
=−∞
∑
where the Fourier Series coefficients are
0.1
0.1
0.49
0.1
:
2
1.5
:
1
2
:
0
1.5
:
1
0.49
0.1
:
2
0
:
j
k
j
j
k
j e
k

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*