Discrete Cosine Transform 2D Serial Processing

This function does a serial processing to obtain the 2D Discrete Cosine Transform. It could be used for Real Time processing by modifying the input parameters.

function [S] = dct_2d(P)    %where P is the matrix to apply the dct
N=length(P);
Cu=[1/sqrt(2),ones(1,N-1)];   %Constant coeficients d1
Cv=[1/sqrt(2),ones(1,N-1)];   %Constant coeficients d2
S=zeros(N,N);
for v=0: N-1;
    for y=0: N-1;
        for u=0: N-1;
            for x=0: N-1;    %serial processing
                S(u+1,v+1)=S(u+1,v+1)+Cu(u+1)*Cv(v+1)*P(x+1,y+1)*cos((2*x+1)*pi*u/(2*N))*cos((2*y+1)*pi*v/(2*N));
            end;
        end;
    end;
end;
S=(2/N)*S;  %final result