%%PLOTS Fourier APPROX OF CHI_{Pi/4} ON [-PI,PI] and computes Gibbs
%% and so answeres problems A2 and A3
hold on
T = linspace(-pi, pi, 512);

chi = [zeros(1,128),ones(1,256),zeros(1,128)];
plot(T,chi);
ylim([-.2 1.2]);

approx = (1/4)*ones(1, 512);
N = 20;
gibbs = zeros(1,N+1);

for k = 1:N
    
    approx = approx + 2 * sin(k* pi/4) * cos(k*T)/(k* pi);
    plot(T, approx);
    ylim([-.2 1.2]); 
    gibbs(k) = max(approx);
end  
hold off
figure
plot(gibbs, '.')
ylim([1 1.2]);