B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

4.4 Bandwidth-Efficient Amplitude Modulations 161
Figure 4.15
Expressing SSB
spectra in terms
af M + (f) and
M- (J) .
-B 0 B
f-
(a)
(b)
0 B
1-
(c)
0
(d)
0 fc -
(e)
Time Domain Representation of SSB Signals
Because the building blocks of an SSB signal are the sidebands, we shall first obtain a time
domain expression for each sideband.
Figure 4.15a shows the message spectrum M (f) . Figure 4.15b shows its right half M+ (f),
and Fig. 4.15c shows its left half Af _ (f). From Fig. 4.15b and c, we observe that
1 1
M + (f) = M (f) · u(f) = M (!) 2 [ l + sgn(f)] = 2
[M (f) + }Mh (f)]
1 1
M_ (f) = M (f)u(-f) = M(f) 2 [ l - sgn(f)] = 2
[M (f) - }Mh(f)]
(4.19a)
(4.19b)
We can now express the SSB signal in terms of m(t) and mh(t) . From Fig. 4.15d it is clear
that the USB spectrum <l>usB (f) can be expressed as
<l>usB (f) = M + (f - Jc ) + M - (f + Jc)
1 1
= 2
[M (f -Jc) + M (f + Jc)] - 2 / M U - Jc ) - M (f + Jc)]