Signals and Systems - Electrical Engineering

326 CHAPTER 5: Frequency Analysis: The Fourier Transform

0 2 4

−0.2

0

0.2

0.4

0.6

0.8

1

t(sec)

x^1

(t

)

− 20

− 2

020

0

0.2

0.4

0.6

0.8

1

Ω

− 20 0 20

Ω

|X

( 1

Ω

)|

∠

X

( 1

Ω

)

−3

−2

−1

0

1

2

3

(a)

x^2

(t

)

0 2 4

0

0.5

1

t(sec)

− (^20020)
Ω
− 20 0 20
Ω
|X
( 2
Ω
)|
<X
( 2
Ω
)
0
0.5
1
− 1
0
1
(b)
FIGURE 5.7
Fourier transforms of (a) pulsex 1 (t)and of (b) decaying exponentialx 2 (t).