PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 449

x5 = k5*sin(w5*k);x7 = k7*sin(w7*k);

subplot(2,2,1);plot(k,x1)

subplot(2,2,2);plot(k,x1+x3)

subplot(2,2,3);plot(k,x1+x3+x5)

subplot(2,2,4)

plot (k,x1+x3+x5+x7) 11

Obtain the following:

a. An expression of f(t)

b. The fundamental frequency w 0 and the period T

c. Properly label the axis

d. Estimate the values of the Fourier coeffi cients F 0 and F 1

e. Estimate the 9th and 10th harmonic

f. A neat fl ow chart of the program

g. Estimate the discontinuity and the magnitude of f(t) at the discontinuities (Gibbs)

P.4.8 Let the FS of the functions f 1 (t) and f 2 (t) be given by

ft

n

nt

n

n

1

1

1

1

()

()

sin

  

∑ ()

and

ft

n

nt

n

n

2

3

2

1

1

3

4

1

()




()

cos

 

∑ ()

Determine or obtain

a. The fundamental frequency, w 0 , for each of the given functions

b. The plots of f 1 (t) versus t and f 2 (t) versus t

c. The plots of F 1 (w) versus w and F 2 (w) versus w

0 2 4 6 8

− 2

− 1

0

1

2

0 2 4 6 8

− 2

− 1

0

1

2

0 2 4 6 8

− 2

− 1

0

1

2

0 2 4 6 8

− 2

− 1

0

1

2

FIGURE 4.90

Plots of P.4.7.