Problem Set
5
1
ECSE304 Signals and Systems 2
Winter
Semester 20
11
McGill University
Department of Electrical and Computer Engineering
Problem Set
5
Distributed:
Tuesday
,
March
1, 20
11
Due
:
Thursday,
March
10
, 20
11
Assignments can be worked in Groups of 2. A cover sheet, which is found at the bottom
of the Assignments page in the ECSE304 webCT site, should be handed in with each
assignment.
MatLab Exercises
In all MatLab Exercises, you are to show all your work and hand in both your MatLab
code and the plots that you generate.
An Introduction to Amplitude Modulation and Demodulation
:
Amplitude modulation
is often used to transmit a signal with lowfrequency content
using a high frequency transmission channel. A common example is AM radio. In AM
radio a relatively low frequency signal such as a speech signal (which has frequencies
between 50 Hz and 4 kHz) is transmitted by radio waves at frequencies around 1 MHz.
Amplitude modulation is performed by multiplying a high frequency signal (called the
carrier
) by a the lowfrequency
message
signal
m
(
t
):
() (1
()
)cos
(2
)
xt
mt
ft
c
π
φ
=+
+
(1)
where the carrier signal corresponds to the cos(2
)
c
+
term. Although the message
signal
m
(
t
) may be very complicated, a good understanding of AM can be obtained by
analyzing AM signals of the form:
cos2
)
x
tA
f
t
f
t
mc
ππ
(2)
i.e., the message signal is a cosine, ()
co
s2
A
f t
m
=
. A straightforward expansion of
(2) shows that:
( )
cos(2
)
cos 2 (
)
cos 2 (
)
22
AA
x
tf
t
f
f
t
f
f
t
cm
c
+
+
−
(3)
In communications terminology, the signal components at
f
ff
=
±
are called the
sidebands
and the signal component with a frequency of
f
c
is called the carrier. When
f
f
>>
the spectrum of the AM signal looks like that shown in the following figure:
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 Spring '09
 JANBAJCSY
 Digital Signal Processing, Signal Processing, message signal, ωnot

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