Improving the Resolution in FFT

I need to get an output like below.

But this is the output I get as a result of the code I wrote.

clc
clear all
close all

N = 5;
n = -N-2: 1 : N+2;
u = unit(n+N/2)-unit(n-N/2);

subplot(2,1,1);
stem(n,u);
grid
title('x(t)');

X = fftshift(fft(u));

subplot(2,1,2)
plot(n,abs(X))
grid
title('|X(w)|')

How can I do this, thank you very much for your help.

Answer 1

[dpb]

Look at documentation for nextpow2

[Kutlu Yigitturk]

How can I ımplement it

[dpb]

Follow the last example there, although you'll have to use at least nextpow2(5) in order to have enough resolution so smooth out the plot -- experiment to see what can get by with.

[dpb]

subplot(2,1,1)
stem(-7:7,u)
subplot(2,1,2)
Y=abs(fft(u));
hL=plot(fftshift((Y)));
xlim([1 numel(Y)])
hold on
Y=abs(fft(u,2^nextpow2(u)));
hL(2)=plot(linspace(0,15,numel(Y)),fftshift((Y)));
Y=abs(fft(u,32));
hL(3)=plot(linspace(0.5,15,numel(Y)),fftshift((Y)));
ylim([0 5])
legend('N=15','N=16','N=32','location','northeast')

gives

You'll want to fix up legends to make the points match your above; I just normalized to the range of the first set of points; whether is exactly symmetric in indices in output vector depends on whether is even/odd number of points, of course.

[Paul]

Keep in mind that the output of fft() will need to be adjusted if desired to have the phase of the end result approximate the phase of the DTFT of u.