PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 395

ANALYTICAL Solution

The coeffi cients of the exponential FS for f(t) are given by

F

T

n

n n








sin( / )

(/)

2

2

where T = 2 and

wn 0

2

2

 0



 for 

MATLAB Solution

% Script file: square _ time _ frq

echo off;

n =-10*pi:pi:10*pi;

tau1 =1;T=2;Tx1=tau1/T;

Fn1 = Tx1*sin(n*pi*Tx1)./(n*pi*Tx1+eps);

Fn1(11)=Tx1;

subplot(2,2,1);stem(n,Fn1);

title(‘ spectrum of square wave with tau=1’);axis([-30 30 -.6 .6]);

ylabel(‘Amplitude’); xlabel(‘w= n*wo (rad per sec)’);

tau2=0.5;T=2;Tx2=tau2/T;

Fn2=Tx2*sin(n*pi*Tx2)./(n*pi*Tx2+eps);

Fn2(11)=Tx2;

subplot(2,2,2);stem(n,Fn2);axis([-30 30 -.3 .3]);

title(‘ spectrum of square wave with tau=0.5’);

ylabel(‘Amplitude’); xlabel(‘w= n*wo (rad per sec)’);

tau3 = 0.25;T=2;Tx3=tau3/T; Fn3=Tx3*sin(n*pi*Tx3)./(n*pi*Tx3+eps);

Fn3(11) = Tx3;

subplot(2,2,3);stem(n,Fn3);axis([-30 30 -.15 .15]);

title(‘ spectrum of square wave with tau=0.25’);

xlabel(‘w= n*wo (rad per sec)’);ylabel(‘Amplitude’);

tau4 = 0.125;T = 2;Tx4 = tau4/T; Fn4 =Tx4*sin(n*pi*Tx4)./(n*pi*Tx4+eps);

Fn4(11) = Tx4;

subplot(2,2,4);stem(n,Fn4);axis([-30 30 -.1 .1]);

title(‘ spectrum of square wave with tau=0.125’);

xlabel(‘w= n*wo (rad per sec)’);ylabel(‘Amplitude’);

− 1 1

0.5

f(t)

t

1.0

T

−τ/2 0 −τ/2

FIGURE 4.44

Plots of f(t) of Example 4.6.