Signals and Systems - Electrical Engineering

6.4 Application to Communications 377

figure(2)

if t == 1,

subplot(311)

y = impulse(sys,20);

plot(y);title(’ Impulse response’);ylabel(’h(t)’);xlabel(’t’); grid

elseif t == 2,

subplot(312)

y = step(sys, 20);

plot(y);title(’ Unit-step response’);ylabel(’s(t)’);xlabe(’t’);grid

else

subplot(313)

sys = tf(N, D1); % ramp response

y = step(sys, 40);

plot(y); title(’ Ramp response’); ylabel(’q(t)’); xlabel(’t’);grid

end

The results forH 2 (s)are as follows.

Transfer function:

s

-----------------------

sˆ3 + sˆ2 + s + 1

poles =

−1.0000

−0.0000 + 1.0000i

−0.0000−1.0000i

zeros =

0

As you can see, two of the poles are on thejaxis, and so the system corresponding toH 2 (s)is

unstable. The other system is stable. Results for both systems are shown in Figure 6.13. n

6.4 Application to Communications

The application of the Fourier transform in communications is clear. The representation of signals in
the frequency domain and the concept of modulation are basic in communications. In this section we
show examples of linear (amplitude modulation or AM) as well as nonlinear (frequency modulation
or FM, and phase modulation or PM) modulation methods. We also consider important extensions
such as frequency-division multiplexing (FDM) and quadrature amplitude modulation (QAM).

Given the low-pass nature of most message signals, it is necessary to shift in frequency the spectrum
of the message to avoid using a very large antenna. This can be attained by means of modulation,
which is done by changing either the magnitude or the phase of a carrier:

A(t)cos( 2 πfc+θ(t)) (6.12)