1
EE102
Systems and Signals
Fall Quarter 2011
Jin Hyung Lee
Course Project
Amplitude Modulation (AM) is a technique widely used in communication area. One exam
ple you can see in your everyday life is the AM radio. The basic principle of the AM technique
is modulating a high frequency sinusoidal carrier signal’s amplitude by a low frequency signal
(e.g. your voice or music). (See
figure 1
)
Figure. 1
This modulation process can be expressed mathematically by:
x
(
t
) =
a
(
t
)
cos
(
ω
0
t
)
where the frequency of
ω
0
is in the range of MHz/Ghz (The AM spectrum in the US goes from
520 kHz to 1610 kHz, with channels separated by 10 kHz. ), however, the bandwidth of A(t) is
usually less than 10kHz. (e.g. Human voice band ranges from approximately
300
Hz
to
3400
Hz
).
According to the Fourier Transform properties we learned in the lecture, AM signal is the
convolution of
A
(
jω
)
and
π
[
δ
(
ω

ω
0
) +
δ
(
ω
+
ω
0
)]
in the frequency domain. Where
A
(
jω
)
and
π
[
δ
(
ω

ω
0
) +
δ
(
ω
+
ω
0
)]
are Fourier Transform of
a
(
t
)
and
cos
(
ω
0
t
)
. Thus in this process the low
frequency signal is modulated to a high frequency (See
figure 2
)
A(jw)
π[δ(ww
0
)+δ(ww
0
)]
A(jw)*π[δ(ww
0
)+δ(ww
0
)]
Figure. 2
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To demodulate this signal, ideally you can multiply
e

jω
0
t
with
x
(
t
)
. This is very easy to
program on softwares like Matlab which supports complex number calculations. However, in
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 Fall '11
 lee
 Digital Signal Processing, kHz, Fourier series coefficients

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