GW Instek GRF-1300A - Manual (Page 64)

GRF-1300A User Manual and Teaching Materials
(unmodulated state) to an AM wave (modulated state).
Figure 5-1. A
diagram showing
how an
unmodulated
carrier signal
undergoes the
process of
modulation.
Figure 5-2. AM
waveform in the
time domain and
the frequency
domain
m
U
Ω
t
t
t
cm
U
( )
AM
U t
cm
U
c −
ω
ω ω Ω
c
ω + Ω
2
a
m
Ucm
2
a
m
Ucm
2. AM Wave Spectrum
Expand formula (4.3) to get the following formula:
1 1
( ) cos cos( ) cos( )
2 2
AM cm c a cm c a cm c
u t U t m U t m U t
−
= ω + ω + Ω + ω Ω
As can be seen here, a
single modulated audio signal consists of three high frequency
components. In addition to the carrier, two new frequency
components (ω
c
+Ω) and (ω
c
- Ω) are included. One is higher than
ω
c
, known as the upper sideband, and the other is lower than ω
c
,
known as the lower sideband. Its spectrum is shown in Figure 5-
3.
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