Signals and Systems - Electrical Engineering

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

(b)

(a)

0

0.5

−0.5

1

Impulse Response

h(

t)

0 102030405060708090100

t

0 102030405060708090100

t

0 102030405060708090100

t

0

1

2

Unit−Step Response

s(

t)

0

20

40

Ramp Response

q(

t)

Pole−Zero Map

Real Axis

Imaginary Axis

− 1 −0.8 −0.6 −0.4 −0.2 0

− 1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

(^1) 0.72
0 86
0.96
0.72 0.58 0.44 0 32 0.22 0.1
0.86
0.96
1 0.8 0.6 0.4 0.2
0.58 0.44 0.32 0.22 0.1
0 102030405060708090100
t
0 102030405060708090100
t
0 102030405060708090100
t
− 1
0
1
Impulse Response
h(
t)
− 1
0
1
Unit−Step Response
s(
t)
0
1
2
Ramp Response
q(t)
−1.2
− 1 −0.8 −0.6 −0.4 −0.2 00.2
− 1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
0.95
0.7 0.56 0.44 0.32 0 2 0 1
0.84
0.95
11.2 0.8 0.6 0.4 0.2
0.7 0.56 0.44 0.32 0.10.2
0 84
Pole−Zero Map
Real Axis
Imaginary Axis
System: sys
Pole : −0.5 − 0.866i
Damping: 0.5
Overshoot (%): 16.3
Frequency (rad/sec): 1
FIGURE 6.13
Impulse, unit-step, and ramp responses and poles and zeros for system with transfer function (a)H 1 (s)and
(b)H 2 (s).
WhenA(t)is proportional to the message, for constant phase, we have amplitude modulation (AM).
On the other hand, if we letθ(t)change with the message, keeping the amplitude constant, we then
have frequency modulation (FM) or phase modulation (PM), which are calledangle modulations.