Page 196 - Fundamentals of Communications Systems

6.18 Chapter Six

1.5 2
Message Spectrum
1 VSB-AM Spectrum
1.5
0.5
1
0
−f v f v
0.5
−0.5
Message Spectrum
Quadrature Filter 0
−1

−1.5 −0.5
−3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3
Frequency, f, Hz Frequency, f, Hz
(a) (b)
Figure 6.20 An example to show how quadrature modulation can be used to reduce the bandwidth of the trans-
mitted signal. Upper sideband modulation.

some part of f ∈ [−W, W]. The remainder of the discussion will examine the
conditions which must hold to produce

X z (f ) = 0 − W ≤ f ≤− f v ≤ 0

where f v is commonly called the vestigial frequency. In other words, what condi-
tions on H z (f ) must hold so that a portion of the lower sideband of the bandpass
signal is eliminated to achieve

W
E B = > 50%
W + f v
Note that VSB-AM is always more bandwidth efficient than either DSB-
AM or LC-AM and the improvement in bandwidth efficiency is a function of
f v . Since the lower portion of the signal spectrum is eliminated, this type of
transmission is often termed upper sideband VSB-AM (the upper sideband is
transmitted). Similar results as the sequel can be obtained to produce lower
sideband VSB-AM transmissions. A set of example spectra for upper sideband
VSB-AM is shown in Figure 6.20 to illustrate the idea of quadrature modulation.
The figure uses the energy spectrum of the baseband transmitted signal since
it is simple to represent the energy spectrum with a two dimensional graph.
Note that the remains of the lower sideband in this example illustrates the
2
reason for the name VSB-AM and that the resulting transmission bandwidth
is clearly B T = W + f v .

2 A dictionary definition of vestigial is pertaining to a mark, trace, or visible evidence of something
that is no longer present or in existence.