PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 391

− 2 − 1 012

time (in sec)

0.2

−0.2

0

Fifth harmonic

Third harmonic

0.5

−0.5− 2 − 1

0

012

− 2 − 1 012

1

− 1

0

DC component Fundamental frequency

Second harmonic

2

1

− 1

0

Amplitude (FO)

Amplitude of F2 Amplitude of F3

Amplitude of F4 Amplitude of F5

Amplitude of F1

− 2 012

5

− 5

− 5

0

− 2

− 2 − 1

− 1

− 1

01

012

5 Fourth harmonic

0

2

time (in sec)

× 10 −^17

× 10 −^17

FIGURE 4.40

Plots of part a of Example 4.4.

disp(‘ ’);

syms x;

intft = 1/2*int(‘Heaviside(x+.5)’,-.5,.5);

Pavesym = vpa(intft);

disp(‘ ’);

disp(‘*********************************’);

disp(‘ ’);

disp(‘The average power using integration in time is:’);

vpa(intft)

disp(‘ ’);

disp(‘*********************************’);

disp(‘ ’);

disp(‘The percentage error is :’); % parts (2g)

error = (Pavesym-Pave)*100/Pavesym;disp(error)

disp(‘ ’);disp(‘**********************************’);

The script fi le Fourier_ series is executed and the results are as follows:

>> Fourier _ series

*************************************************

Verification of Parseval’s theorem

*************************************************

The average power using summation of Fn (coefficients) is:

0.4833

*************************************************

The average power using integration in time is:

ans =

.50000000000000000000000000000000

*************************************************

The percentage error is :

3.3472238873502480061006281175660

**************************************************