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Sec. 5–5 Asymmetric Sideband Signals 325
Figure 5–4 illustrates this theorem. Assume that m(t) has a magnitude spectrum that is of
triangular shape, as shown in Fig. 5–4a. Then, for the case of USSB (upper signs), the spectrum
of g(t) is zero for negative frequencies, as illustrated in Fig. 5–4b, and s(t) has the USSB
spectrum shown in Fig. 5–4c. This result is proved as follows:
PROOF. We need to show that the spectrum of s(t) is zero on the appropriate sideband
(depending on the sign chosen). Taking the Fourier transform of Eq. (5–15), we get
G(f) = A c {M(f) ; j[mN (t)]}
and, using Eq. (5–17), we find that the equation becomes
G(f) = A c M(f)[1 ; jH(f)]
(5–20)
(5–21)
|M(f)|
1
(a) Baseband Magnitude Spectrum
– B B
f
|G(f)|
2A c
B
f
(b) Magnitude of Corresponding Spectrum of the Complex Envelope for USSB
|S(f)|
A c
–f c -B –f c f c f c +B
(c) Magnitude of Corresponding Spectrum of the USSB Signal
Figure 5–4
Spectrum for a USSB signal.
f