clear all;
hold off;

N=32;
F=zeros(N,N);

for m=1:N
    for n=1:N
        F(m,n)=cos(-2*pi*(m-1)*(n-1)/N)+i*sin(-2*pi*(m-1)*(n-1)/N);
        %exp(-2*pi*i*(m-1)*(n-1)/N);
    end;
end;

for k=1:N
    v_1(k)=sin(2*pi*(k-1)/N);
end;

for k=1:N
    v_2(k)=sin(4*pi*(k-1)/N);
end;

for k=1:N
    v_3(k)=cos(2*pi*(k-1)/N);
end;

subplot(3,1,1);
plot(real(1/sqrt(N)*F*v_1'));

subplot(3,1,2);
plot(real(1/sqrt(N)*F*v_2'));

subplot(3,1,3);
plot(real(1/sqrt(N)*F*v_3'));