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AM, FM, and Digital Modulated Systems Chap. 5
To prove the result for the USSB case, choose the upper sign. Then, from Eq. (5–19), Eq.
(5–21) becomes
G(f) = e 2A cM(f), f 7 0
0, f 6 0 f
Substituting Eq. (5–22) into Eq. (4–15), yields the bandpass signal:
(5–22)
+ A c e 0, f 7 -f c
S(f) = A c e M(f - f c), j 7 f c
f
f (5–23)
0, f 6 f c M(f+f c ), f 6 -f c
This is indeed a USSB signal (see Fig. 5–4).
If the lower signs of Eq. (5–21) were chosen, an LSSB signal would have been obtained.
The normalized average power of the SSB signal is
8s 2 (t)9 = 1 2 8|g(t)|2 9 = 1 2 A c 2 8m 2 (t) + [mN (t)] 2 9
(5–24)
As shown in study-aid Example SA5–1, 8mN 1t2 2 9 = 8m 2 1t29, so that the SSB signal
power is
8s 2 (t)9 = A 2 c 8m 2 (t)9
(5–25)
which is the power of the modulating signal 8m 2 (t) 9 multiplied by the power gain factor A 2 c.
Example 5–4 USSB SIGNALING
Let m(t) = sin(2pt). Using Eq. (5–16), evaluate and plot the resulting USSB signal where the
carrier frequency is 10 Hz and A c = 1. Demonstrate that this is USSB. See Example5_04.m for the
solution.
The normalized peak envelope power (PEP) is
1
2 max {|g(t)|2 } = 1 2 A c 2 max {m 2 (t) + [mN (t)] 2 }
(5–26)
Figure 5–5 illustrates two techniques for generating the SSB signal. The phasing method
is identical to the IQ canonical form discussed earlier (Fig. 4–28) as applied to SSB signal generation.
The filtering method is a special case in which RF processing (with a sideband filter) is
used to form the equivalent g(t), instead of using baseband processing to generate g[m] directly.
The filter method is the most popular method because excellent sideband suppression can
be obtained when a crystal filter is used for the sideband filter. † Crystal filters are relatively
inexpensive when produced in quantity at standard IF frequencies. In addition to these two techniques
for generating SSB, there is a third technique, called Weaver’s method [Weaver, 1956].
† Excellent sideband suppression is possible because communications-quality audio has negligible spectral
content below 300 Hz. Thus, the sideband filter can be designed to provide the required sideband attenuation over a
2 × 300 = 600-Hz transition band.