PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

448 Practical MATLAB® Applications for Engineers

t

t

t t

− 2 0 1 2

− 1

− 1

+1

1

f 7 (t)

f 4 (t)

f 6 (t)

f 5 (t)

f 1 (t) f 2 (t) f 3 (t)

2

0 1

1

0 2 − 2 0 2

t

t

t

1

− 1 0 3 − 1

3

0 2 3

3

2

1

1.5

FIGURE 4.89
Plots of P.4.1.

P.4.5 Let

ft

n

nt

n

2

1

1

2

11

()
 sin( 2 )



 





∑




Sketch by hand

a. f 2 (t) versus t

b. [f 3 (t) = 1 − f 2 (t)] versus t

c. mag[F 3 (w)] versus w

d. phase[F 3 (w)] versus w

P.4.6 Repeat P.4.5 using MATLAB.

P.4.7 The script fi le drill returns the FS expansion of the function f(t), as shown in the
following, as well as its fi rst four partial FS approximations shown in Figure 4.90.

% Script file: drill

w1=1; w3 =3; w5 =5; w7=7;

k1= 4/pi;k3 = 4/(pi*3);

k5 = 4/(pi*5);k7= 4/(pi*7);

k = 0:pi/30:2*pi;

x1 =k1*sin(w1*k);x3 = k3*sin(w3*k);