PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

402 Practical MATLAB® Applications for Engineers

% Script file: square _ FT _ sym

% This file returns the expressions and plots for the pulse

% spectrums for tau’s= 1,5, and10

syms t w

Fw1 = fourier(sym(‘Heaviside(t+1/2)’)- sym(‘Heaviside(t- 1/2)’),t,w);

Fw5 = fourier(sym(‘Heaviside(t+2.5)’)- sym(‘Heaviside(t- 2.5)’),t,w);

Fw10 = fourier(sym(‘Heaviside(t+5)’)- sym(‘Heaviside(t-5)’),t,w);

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

disp(‘ ***********R E S U L T S ************’)

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

disp(‘The FT of the rect pulse with tau =1, 5 and 10 are given by:’);

Fw1sim = simplify(Fw1)

Fw5sim = simplify(Fw5)

Fw10sim = simplify(Fw10)

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

figure(1)

subplot(3,1,1)

ezplot(Fw1sim,[-10 10])

ylabel(‘ Amplitude’)

title(‘ Spectrum of the pulse for tau=1.0’)

subplot(3,1,2)

ezplot(Fw5sim,[-10 10])

axis([-10 10 -4 6])

ylabel(‘ Amplitude’)

title(‘ Spectrum of the pulse for tau= 5’)

subplot(3,1,3)

ezplot(Fw10sim,[-10 10])

axis([-4 4 -6 11])

xlabel(‘frequency w (in rad/sec’),

ylabel(‘ Amplitude’)

title(‘ Spectrum of the pulse for tau=10’)

The script fi le square_FT_sym is executed and the results are as follows (Figure 4.51):

>> square _ FT _ sym

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

*************************R E S U L T S *************************

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

The FT of the rect pulse with tau =1, 5 and 10 are given by :

Fw1sim =

2*sin(1/2*w)/w

Fw5sim =

2.*sin(2.5000000000000000000000000000000*w)/w

Fw10sim =

2*sin(5*w)/w

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

Observe that the spectrum expressions obtained using the MATLAB symbolic toolbox

shown in Figure 4.51 fully agree with the transform of Table 4.1 and the spectrum plots

of part 2 shown in Figure 4.52.