zad2

N=20;
for k=1:1
    for n=1:N
        A(1,n)=sqrt(1/N)*cos((pi*k/N)*(n+0.5));
    end
end
for k=2:N
    for n=1:N
        A(k,n)=sqrt(2/N)*cos(pi*k/N*(n+0.5));
    end
end

S=inv(A);
S*A
x=randn(1,N);
X=A*x';
xs=S*X;
hold on;
plot(xs,'r');
plot(x','g');
plot(xs-x','b');