PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 447

FIGURE 4.88

Time and frequency domain of parts d, e, and f of Example 4.22.

0

0

5

− 5

1 23

0123

0

0

0

2

− 2

− 10

10

0.5 1 1.5 2

time (sec)

fm(t)

am-dsb-wc(t)

am-dsb-sc(t)

− 100 − 50

− 50

0

0

50

10

15

50

− (^50050)
100
0
0
0
1
2
2
4
5
6
frequency w (rad/sec)
mag[FM(w)]
mag[AM-DSB-SC(w)]
mag[AM-DSB-SC(w)]
TIME DOMAIN FREQUENCY DOMAIN

4.5 Application Problems

P.4.1 Given the functions shown in Figure 4.89, draw the even and odd parts for each func-

tion by hand, and determine the trigonometric FS of each part using MATLAB.

P.4.2 Write a function fi le that returns the energy of a given arbitrary function f(t). Test

your fi le for each of the functions shown in Figure 4.89.

P.4.3 Let the FS for the function f 1 (t) be given by

ft

n

nt

n

1 ()
)

1

2

11

1















∑ 

sin(2

Evaluate the energy of f 1 (t) in the frequency and the time domain.

P.4.4 Using the trigonometric FS given in P.4.3, write a MATLAB program that returns

the following plots:

a. f 1 (t) vs. t

b. The FS approximation of f 1 (t) using the fi rst fi ve terms versus t

c. Repeat part b for the fi rst 15 terms versus t

d. F 1 (w) versus w (magnitude and phase)

e. Power of f 1 (t) versus t