Signals and Systems - Electrical Engineering

6.4 Application to Communications 389

0 0.02 0.04 0.06 0.08 0.1

− 50

0

50

m

(t

)

− 200 − 150 − 100 − (^50050100150200)
0
5
10
|M
(Ω
)|
− 5000 0 5000
0
0.005
0.01
0.015
f
|X
(Ω
)|
Time
Frequency
0.020.040.060.080.100.120.140.160.18
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 0.02 0.04 0.06 0.08 0.1
− 1
−0.5
0
0.5
1
x(
t)
m
(t
)
x(
t)
t (sec)
0 0.02 0.04 0.06 0.08 0.1
0
50
100
150
200
− 1000 − (^50005001000)
0
5
10
|M
(Ω
)|
− 5000 0 5000
1
1.5
2
2.5
3
f
|X
(Ω
)|
× 10 −^3
Time
Frequency
0.010.020.030.040.050.060.070.080.09
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
t (sec)
0 0.02 0.04 0.06 0.08 0.1
− 1
−0.5
0
0.5
1
(a) (b)
FIGURE 6.20
Wideband frequency modulation, from top to bottom, for (a) the sinusoidal message and for (b) the ramp
message: messages, FM-modulated signals, spectra of messages, spectrum of FM signals, and spectrogram of
FM signals.