6.4 Application to Communications 379
6.4.1 AM with Suppressed Carrier
Consider a message signalm(t)(e.g., voice or music, or a combination of the two) modulating a
cosine carrier cos(ct)to give an amplitude modulated signal
s(t)=m(t)cos(ct) (6.13)
The carrier frequencyc>> 2 πf 0 wheref 0 (Hz) is the maximum frequency in the message (for music
f 0 is about 22 KHz). The signals(t)is called anamplitude modulated with suppressed carrier(AM-SC)
signal (the last part of this denomination will become clear later). According to the modulation
property of the Fourier transform, the transform ofs(t)is
S()=
1
2
[M(−c)+M(+c)] (6.14)
whereM()is the spectrum of the message. The frequency content of the message is now shifted to
a much larger frequencyc(rad/sec) than that of the baseband signalm(t). Accordingly, the antenna
needed to transmit the amplitude modulated signal is of reasonable length. An AM-SC system is
shown in Figure 6.14.
At the receiver, we need to first detect the desired signal among the many signals transmitted by
several sources. This is possible with a tunable band-pass filter that selects the desired signal and
rejects the others. Suppose that the signal obtained by the receiver, after the band-pass filtering, is
exactlys(t)—we then need to demodulate this signal to get the original message signalm(t). This is
done by multiplyings(t)by a cosine of exactly the same frequency of the carrier in the transmitter
(i.e.,c), which will giver(t)= 2 s(t)cos(ct), which again according to the modulation property has
a Fourier transform
R()=S(−c)+S(+c)=M()+
1
2
[M(− 2 c)+M(+ 2 c)] (6.15)
The spectrum of the message,M(), is obtained by passing the received signalr(t)through a low-pass
filter that rejects the other termsM(± 2 c). The obtained signal is the desired messagem(t).
The above is a simplification of the actual processing of the received signal. Besides the many other
transmitted signals that the receiver encounters, there is channel noise caused by interferences from
× ×
m(t) m(t)
cos(Ωct) 2cos(Ωct)
Channel
Band-pass
filter
Low-pass
filter
ˆ
Transmitter Receiver
FIGURE 6.14
AM-SC transmitter, channel, and receiver.
