% Demonstration Fourier Transform of short rectangular pulse 

T=40; %Period 
T0=20;

t=linspace(-T/2, T/2, 1000);
y=zeros(1, length(t));
A=1;

for i = 1:length(t)
   if (( t(i) < 0) ) %|| ((T0<= t(i) < 2*T0) ))
       y(i) = -A;
   elseif ( (t(i)>0) )% || (2*T0 <= t(i) < 3*T0) ) 
       y(i) = A;
   end
end

N=input('Truncation of Fourier series at N=');

% b Coefficients
xn=zeros(1,length(t)); 
for k=1:N
xn = xn + 2*A/k/pi*(1-(-1).^k) * sin(2*pi/T*k*t);
end

% Plot
plot(t,xn)
hold on 
plot(t,y, ':')
grid