Signals and Systems - Electrical Engineering

382 C H A P T E R 6: Application to Control and Communications

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

− 1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

(a)

t (sec)

y(

t)

−2.5 − 2 −1.5 − 1 −0.5 0 0.5 1 1.5 22.5

× 104

0

50

100

150

(b) (c)

f (Hz)

−2.5 − 2 −1.5− 1 −0.5 0 0.5 1 1.5 2 2.5

f (Hz) × 104

|Z

(Ω

)|

|Y

(Ω

)|

0

100

200

300

400

500

0 0.005 0.010.015 0.02 0.0250.03 0.035 0.04

− 1

−0.5

0

0.5

1

y(

t)

t (sec)

− 2

− 1

0

1

2

z(

t)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

t (sec)

FIGURE 6.15

Commercial AM modulation: (a) original signal, (b) part of original signal and corresponding AM-modulated

signal, and (c) spectrum of the original signal, and of the modulated signal.

version. Notice that the envelope resembles the original signal. Also from the spectrum of the

segment of the train signal its bandwidth is about 5 Khz, while the spectrum of the modulated

segment displays the frequency-shifted spectrum plus the large spectrum atfccorresponding to the

carrier. n

6.4.3 AM Single Sideband

The messagem(t)is typically a real-valued signal that, as indicated before, has a symmetric

spectrum—that is, the magnitude and the phase of the Fourier transformM()are even and odd