Computing and Ploting Fourier transform

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How can i use the fft command to transform a rectangular pulse to sinc function and plot the sinc function, i'm using a very traditional way to compute the fourier transform and plot it, but this way is too slow, when i use the fft command and try to plot, the ploting of the magnitude is only the pins or a spike, i need the plot to be a sinc function as the picture that i attached here, also i'm using the same method to compute the inverse fourier transform so i also need to use the ifft command, can anyone help?
if true
p = heaviside(t+1)-heaviside(t-1);
k = 0;
for f= -4:0.001:4
F(k) = trapz(t,p.*exp(-1i*2*pi*f*t));
f = -4:0.001:4;

Accepted Answer

Rick Rosson
Rick Rosson on 21 Feb 2016
Edited: Rick Rosson on 21 Feb 2016
Fs = 8;
dt = 1/Fs;
N = 8000;
t = dt*(-N/2:N/2-1)';
dF = Fs/N;
f = -Fs/2:dF:Fs/2-dF;
p = heaviside(t+1)-heaviside(t-1);
P = dt*fftshift(fft(ifftshift(p)));
grid on;
  1 Comment
omarahmed.m on 21 Feb 2016
Thank you for your response, Could you just specify this command "P = dt*fftshift(fft(ifftshift(p)));", why it consist of fftshift of fft of ifftshift, and why multiplying by "dt". thank you very much.

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