6.4 Application to Communications 383
FIGURE 6.16
Upper sideband AM transmitter.cis
the carrier frequency andBis the
bandwidth in rad/sec of the message.
× BPF
m(t)
cos(Ωct)
Ωc Ωc+B
Ω
1
s(t)
H(jΩ)
functions of frequency. When using AM modulation the resulting spectrum has redundant informa-
tion by providing the upper and the lower sidebands. To reduce the bandwidth of the transmitted
signal, we could get rid of either the upper or the lower sideband of the AM signal. The resulting
modulation is calledAM single sideband(AM-SSB) (upper or lower sideband depending on which
of the two sidebands is kept). This type of modulation is used whenever the quality of the received
signal is not as important as the advantages of a narrowband and having less noise in the frequency
band of the received signal. AM-SSB is used by amateur radio operators.
As shown in Figure 6.16, the upper sideband modulated signal is obtained by band-pass filtering the
upper sideband in the modulated signal. At the receiver, band-pass filtering the received signal the
output is then demodulated like in an AM-SC system, and the result is then low-pass filtered using
the bandwidth of the message.
6.4.4 Quadrature AM and Frequency-Division Multiplexing
Quadrature amplitude modulation (QAM) and frequency division multiplexing (FDM) are the pre-
cursors of many of the new communication systems. QAM and FDM are of great interest for their
efficient use of the radio spectrum.
Quadrature Amplitude Modulation
QAM enables two AM-SC signals to be transmitted over the same frequency band, conserving band-
width. The messages can be separated at the receiver. This is accomplished by using two orthogonal
carriers, such as a cosine and a sine (see Figure 6.17). The QAM-modulated signal is given by
s(t)=m 1 (t)cos(ct)+m 2 (t)sin(ct) (6.16)
wherem 1 (t)andm 2 (t)are the messages. You can think ofs(t)as having a phasor representation that
is the sum of two phasors perpendicular to each other (the cosine leading the sine byπ/2); indeed,
s(t)=Re[(m 1 (t)ej^0 +m 2 (t)e−jπ/^2 )ejct].
Since
m 1 (t)ej^0 +m 2 (t)e−jπ/^2 =m 1 (t)−jm 2 (t)
we could interpret the QAM signal as the result of amplitude modulating the real and the imaginary
parts of a complex messagem(t)=m 1 (t)−jm 2 (t).
