Signals and Systems - Electrical Engineering

316 CHAPTER 5: Frequency Analysis: The Fourier Transform

(a)

(b)

− 5 05

−0.5

0

0.5

1

t(sec)

y^1

(t

)

− 20 0 20

0

0.2

0.4

0.6

0.8

1

Ω

− 20 0 20

− 1

0

1

Ω

|Y

( 1

Ω

)|

<Y

( 1

Ω

)

− 5 0 5

0

0.5

1

t

− 5 0 5

− 1

−0.5

0

0.5

1

t

y^2

(t

)=

x^2

(t

)cos(10

t)

− 5 0 5

0

1

2

3

4

5

Ω

− 20 − 10 0 10 20

0

1

2

3

4

5

Ω

|Y

( 2

Ω

)|

|X

( 2

Ω

)|

x^2

(t

)

FIGURE 5.5

(a) The modulated signaly 1 (t)=e−|t|cos( 10 t)and its magnitude and phase spectra. Notice that the phase is

zero. (b) The triangular signal, its modulated version, and their magnitude spectra.