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AM, FM, and Digital Modulated Systems Chap. 5
However, if m(t) is a polar data signal, binary 1’s might come out as binary 0’s after the
circuit is energized, or vice versa. As we found in Chapter 3, there are two ways of abrogating
this 180 phase ambiguity: (1) A known test signal can be sent over the system after the
loop is turned on, so that the sense of the polarity can be determined, and (2) differential
coding and decoding may be used.
5–5 ASYMMETRIC SIDEBAND SIGNALS
Single Sideband
DEFINITION. An upper single sideband (USSB) signal has a zero-valued spectrum for
| f | 6 f c , where f c is the carrier frequency.
A lower single sideband (LSSB) signal has a zero-valued spectrum for | f | 7 f c ,
where f c is the carrier frequency.
There are numerous ways in which the modulation m(t) may be mapped into the complex
envelope g[m] such that an SSB signal will be obtained. Table 4–1 lists some of these methods.
SSB-AM is by far the most popular type. It is widely used by the military and by radio amateurs
in high-frequency (HF) communication systems. It is popular because the bandwidth is the same
as that of the modulating signal (which is half the bandwidth of an AM or DSB-SC signal). For
these reasons, we will concentrate on this type of SSB signal. In the usual application, the term
SSB refers to the SSB-AM type of signal, unless otherwise denoted.
THEOREM.
envelope
An SSB signal (i.e., SSB-AM type) is obtained by using the complex
which results in the SSB signal waveform
g(t) = A c [m(t) ; jmN (t)]
(5–15)
s(t) = A c [m(t) cos v c t < mN (t) sin v c t]
(5–16)
where the upper (-) sign is used for USSB and the lower (+) sign is used for LSSB. mN (t)
denotes the Hilbert transform of m(t), which is given by †
mN (t) ! m(t) * h(t)
(5–17)
where
h(t) = 1 pt
(5–18)
and H(f) = [h(t)] corresponds to a - 90 phase-shift network:
H(f) = e -j, f 7 0
j, f 6 0 f
(5–19)
† A table of Hilbert transform pairs is given in Sec. A–7 (Appendix A).