close all
clear all 
clc

T = 0.01;
t = -2:T:2;
x = triang(t);
N = length(x);
om = (-round((N-1)/2):round(N/2)-1) *2*pi/(N*T);          
X = fftshift(T*fft(x)).*exp(-1i*om*t(1));
Xref = sinc(om/(2*pi)).^2;

figure
subplot(2,1,1)
plot(t,x)
grid
xlabel('t')
ylabel('x(t)')
title('signal')
subplot(2,2,3)
semilogy(om,abs(X),om,abs(Xref))
axis([0 max(om) ylim])
grid
xlabel('\omega')
ylabel('X(\omega)')
legend('MatLab','analytical')
title('Fourier transform')
subplot(2,2,4)
semilogy(om,abs(X-Xref))
axis([0 max(om) ylim])
grid
xlabel('\omega')
title('Difference')

% printing figure in png format
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 6 4.5])
print -dpng homework1.png -r100

function s = triang(t)
s = (1-abs(t)).*(abs(t)<1);
end