Signals and Systems - Electrical Engineering

6.4 Application to Communications 381

that is needed. Thus, the commercial AM signal is of the form

s(t)=[K+m(t)]cos(ct)

where the AM modulation indexKis chosen so thatK+m(t) >0 for all values oftso that the
envelope ofs(t)is proportional to the messagem(t). The Fourier transform is given by

S()=Kπ[δ(−c)+δ(+c)]+

1

2

[M(−c)+M(+c)]

The receiver for this type of AM is anenvelope receiver, which basically detects the message by finding
the envelope of the received signal.

Remarks

n The advantage of adding the carrier to the message, which allows the use of a simple envelope detector,
comes at the expense of increasing the power in the transmitted signal.
n The demodulation in commercial AM is called noncoherent.Coherent demodulation consists in
multiplying—or mixing—the received signal with a sinusoid of the same frequency and phase of the
carrier. Alocal oscillatorgenerates this sinusoid.
n A disadvantage of commercial as well as suppressed-carrier AM is the doubling of the bandwidth of the
transmitted signal compared to the bandwidth of the message. Given the symmetry of the spectrum, in
magnitude as well as in phase, it becomes clear that it is not necessary to send the upper and the lower
sidebands of the spectrum to get back the signal in the demodulation. It is thus possible to have upper- and
lower-sideband AM modulations, which are more efficient in spectrum utilization.
n Most AM receivers use thesuperheterodyne receiver techniquedeveloped by Armstrong and Fessenden.^2

nExample 6.5: Simulation of AM modulation with MATLAB

For simulations, MATLAB provides different data files, such as “train.mat” (the extension mat indi-

cates it is a data file) used here. Suppose the analog signaly(t)is a recording of a “choo-choo” train,

and we wish to use it to modulate a cosine cos(ct)to create an amplitude modulated signalz(t).

Because thetrain y(t)signal is given in a sampled form, the simulation requires discrete-time pro-

cessing, and so we will comment on the results here and leave the discussion of the issues related

to the code for the next chapters.

The carrier frequency is chosen to befc=20.48 KHz. For the envelope detector to work at the

transmitter we add a constantKto the message to ensure this sum is positive. The envelope of the

AM-modulated signal should resemble the message. Thus, the AM signal is

z(t)=[K+y(t)] cos(ct) c= 2 πfc

In Figure 6.15 we show the train signal, a segment of the signal, and the corresponding modulated

signal displaying the envelope, as well as the Fourier transform of the segment and of its modulated

(^2) Reginald Fessenden was the first to suggest the heterodyne principle: mixing the radio-frequency signal using a local oscillator of
different frequency, resulting in a signal that could drive the diaphragm of an earpiece at an audio frequency. Fessenden could not
make a practical success of the heterodyne receiver, which was accomplished by Edwin H. Armstrong in the 1920s using electron tubes.