Digital Signal Processing Reference
In-Depth Information
as shown in Figure 6.34(c). The effect of the filter is to double the magnitude of the
frequency components of the input signal that are within the passband of the filter,
and to eliminate all frequency components outside the passband.
The output signal from the filter is, theoretically, an exact reproduction of the infor-
mation signal, This can be seen by comparing the frequency spectrum of the de-
modulated signal, shown in Figure 6.34(d) with shown in Figure 6.33(a).
Another, more commonly encountered type of amplitude modulation is double-
sideband modulation with a carrier component in the frequency spectrum of the
modulated signal (DSB/WC). Commercial AM radio broadcasts use this method.
Figure 6.35 illustrates a technique for DSB/WC-AM modulation. In this method,
the modulated signal is described mathematically as
-v
B
F
v
F
v
B
,
m(t).
M
N
(v),
M(v)
s(t) = [1 + k
a
m(t)]c(t),
(6.21)
where
m(t)
is the message signal and
c(t)
is the carrier signal
c(t) = A
c
cos(v
c
t).
The
amplitude sensitivity,
k
a
,
is chosen such that
1 + k
a
m(t) 7 0
at all times. The modulated signal can be rewritten as
s(t) = A
c
cos(v
c
t) + k
a
A
c
m(t) cos(v
c
t),
and its frequency spectrum is given by
S(v) = A
c
p[d(v - v
c
) + d(v + v
c
)]
k
a
A
c
2
+
[M(v - v
c
) + M(v + v
c
)].
(6.22)
From Figure 6.36 it is seen that the modulated signal is a sinusoidal signal with
an amplitude that varies in time according to the amplitude of the message signal
m(t).
From (6.22) and Figure 6.36(d), we see that the frequency spectrum of the
modulated signal contains the carrier-signal frequency component in addition to the
frequency-shifted message signal. Hence, the nomenclature of this modulation
technique is
double-sideband, with-carrier, amplitude modulation
(DSB/WC-AM).
s
(
t
)
A
c
[1
k
a
m
(
t
)] cos
c
t
m
(
t
)
k
a
Figure 6.35
A system for amplitude
c
(
t
)
A
c
cos
c
t
modulation.
