clear
clc
close all

% DATOS
y1=[-1,1,2,3];
y2=[0 1 2 3];
pp=0:0.13:2*pi;
y3=sin(pp)+cos(3*pp);
for m=1:3
    if m==1
        y=y1;T=length(y);
    elseif m==2
        y=y2;T=length(y);
    elseif m==3
        y=y3;T=2*pi;
    end
    n=length(y);
    w=exp(-2*pi/n*i);
    W=ones(n,n);
    W(2,:)=w.^(0:n-1);
    for k=3:n
        for j=2:n
            W(k,:)=W(k-1,:).*W(2,:);
        end
    end
    Y=W*y';
    xx=linspace(-2*T,3*T,5000);
    s=zeros(1,length(xx));
    for k=1:ceil(n/2)
        s=s+Y(k)*exp(2*pi*(k-1)*xx*i/T);
    end
    for k=ceil(n/2)+1:n
        s=s+Y(k)*exp(2*pi*(k-n-1)*xx*i/T);
    end
    s=real(s)/n;
    figure(m)
    if m==1 || m==2
        plot(0:n-1,y,'.','Markersize',20)
    elseif m==3
        plot(pp,y,'.','Markersize',20)
    end
    hold on
    plot(xx,s)
    axis([min(xx) max(xx) min(s) max(s)])
    if m==1
        title('Con cuatro puntos','Fontsize',16)
    elseif m==2
        title('Con otros cuatro puntos','Fontsize',16)
    elseif m==3
        title(['Con ',num2str(length(pp)),' puntos'],'Fontsize',16)
    end
    if m==3
        ss=linspace(-2*T,6*T,5000);
        plot(ss,sin(ss)+cos(3*ss),'r');
        pp=0:2*pi/25:2*pi;
        y3=sin(pp)+cos(3*pp);
        legend('nodos','Reconstruida','Verdadera')
    end
    pause
end