Fourier Transform of Rectangular Pulse

clear all
close all
clc

%fs = 500;
T = 1;

t = -2.5 : 0.001 : 2.5;
x = rectpuls(t,T);

subplot(2,1,1)
plot(t,x,'r','Linewidth',3);
axis([-2.5 2.5 0 1.2])
title({'Rectangular Pulse'})
xlabel({'Time(s)'});
ylabel('Ampltude');
grid

How can I get Fourier Transform of this Rectangular Pulse. Thank you.

It should look like this

Answer 1

[Star Strider]

A symbolic approach —

syms t omega 
F(omega) = int(1*exp(1j*omega*t), t, -0.25, 0.25)

F(omega) = 

figure
fplot(F, [-1 1]*16*pi)
grid

.

For a numeric calculation use the fft function.

[Kutlu Yigitturk]

If I changing the T value, this output is not changing.

[Star Strider]

In my code ‘T’ corresponds to the integration limits in the posted image. The pulse you coded goes from (-0.5,0.5), not the same as the posted image. To create the posted image, ‘T’ would be 0.5 instead. My code follows the posted image.

Your code —

T = 1;
t = -2.5 : 0.001 : 2.5;
x = rectpuls(t,T);
% subplot(2,1,1)
plot(t,x,'r','Linewidth',3);
axis([-2.5 2.5 0 1.2])
title({'Rectangular Pulse'})
xlabel({'Time(s)'});
ylabel('Ampltude');
grid

My code for any ‘T’ —

syms t omega 
T = 0.5;
F(omega) = int(1*exp(1j*omega*t), t, -T/2, T/2)

F(omega) = 

figure
fplot(F, [-1 1]*16*pi)
grid

Change ‘T’ to be whatever you want (obviously within computational limits), and my code will produce the coreect result.

.

[Kutlu Yigitturk]

I am an engineering student studying in Turkey. Throughout my university life, I have never received as much help from anyone as you did. Really thank you so much. God bless you.

[Star Strider]

I very much appreciate your compliment!

As always, my pleasure!