Signals and Systems - Electrical Engineering

6.4 Application to Communications 385

+ Channel

m 1 (t)

m 2 (t)

×

×

×

cos(Ω 1 t)

cos(Ω 2 t)

cos(Ω 3 t)

cos(Ω 1 t)

cos(Ω 2 t)

cos(Ω 3 t)

m 3 (t)

BPF × LPF m∧ 1 (t)

m∧ 2 (t)

m∧ 3 (t)

BPF × LPF

BPF × LPF

FIGURE 6.18

FDM system: transmitter (left), channel, and receiver (right).

locally as an FDM sytem. In the United States, the Federal Communication Commission (FCC) is in

charge of the spectral allocation. In telephony, using a bank of filters it is possible to also get several

users in the same system—it is, however, necessary to have a similar system at the receiver to have a

two-way communication.

To illustrate an FDM system (Figure 6.18), consider we have a set of messages of known finite band-

width (we could low-pass filter the messages to satisfy this condition) that we wish to transmit. Each

of the messages modulate different carriers so that the modulated signals are in different frequency

bands without interfering with each other (if needed a frequency guard could be used to make sure

of this). These frequency-multiplexed messages can now be transmitted. At the receiver, using a bank

of band-pass filters centered at the carrier frequencies in the transmitter and followed by appropri-

ate demodulators recover the different messages (see FDM receiver in Figure 6.18). Any of the AM

modulation techniques could be used in the FDM system.

6.4.5 Angle Modulation

Amplitude modulation is said to be linear modulation, because as a system it behaves like a linear

system. Frequency and phase, or angle, modulation systems on the other hand are nonlinear. The

interest in angle modulation is due to the decreasing effect of noise or interferences on it, when

compared with AM, although at the cost of a much wider bandwidth and greater complexity in

implementation. The nonlinear behavior of angle modulation systems makes their analysis more

difficult than that for AM. The spectrum of an FM or PM signal is much harder to obtain than that

of an AM signal. In the following we consider the case of the so-callednarrowband FMwhere we are

able to find its spectrum directly.

Professor Edwin H. Armstrong developed the first successful frequency modulation system—

narrowband FM.^3 Ifm(t)is the message signal, and we modulate a carrier signal of frequency

(^3) Edwind H. Armstrong (1890–1954), professor of electrical engineering at Columbia University, and inventor of some of the basic
electronic circuits underlying all modern radio, radar, and television, was born in New York. His inventions and developments form
the backbone of radio communications as we know it.