zad2+

A=randn(20);
%zepsute DCT
N=20;
for k=1:1
    for n=1:N
        AA(1,n)=sqrt(1/N)*cos((pi*(k+0.25)/N)*(n+0.5));
    end
end
for k=2:N
    for n=1:N
        AA(k,n)=sqrt(2/N)*cos(pi*(k+0.25)/N*(n+0.5));
    end
end
%
orto=zeros(N,N);
for i=1:N
   for j=1:N
      z=A(i,:).*A(j,:);
      orto(i,j)=sum(z);
   end
end
orto
S=inv(A);
A*S
x=randn(1,20);
X=A*x';
xs=S*X;
hold on;
plot(xs,'r');
plot(x','g');
plot(xs-x','b');