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Improving the Resolution in FFT

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Kutlu Yigitturk
Kutlu Yigitturk 2021-6-2
评论： Paul 2021-6-3
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.

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dpb
dpb 2021-6-2
Look at documentation for nextpow2
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dpb
dpb 2021-6-2
编辑：dpb 2021-6-3
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
Paul 2021-6-3
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.

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