function [cb p] = aufg2a(i)

 N = 20; m =5;
 f1 = sin(4*linspace(0,2*pi,N));
 f2 = max(pi/2 - abs(linspace(0,2*pi,N)-pi/2),pi/2-abs(linspace(0,2*pi,N)-3*pi/2));
 f3 = round((sin(2*linspace(0,2*pi,N))+1)/2);

 f =[f1 ; f2 ; f3];

 fk = f(i,:);

N = length(fk);
M = N*2^m;
x = 2*pi/N*[0:N-1]';
fig = plot(x,fk,'or');

c = fft(fk)/N;
cb = c;
c = [c(1:N/2) zeros(1,M-N) c(N/2+1:N)];
p = real( M*ifft(c) );
hold on;
plot(linspace(0,2*pi,M),p);
hold off;
saveas(fig,'aufg2a.pdf');