%   Call: tdft_5x5.m.m
%   Demo code for calculating the 5x5-point DFT by
%   the tensor transform: six 5-point DFTs are used
%
%   Dr. Artyom M. Grigoryan,         11/12/1997

        N=5;
        f=[ 1   2   1   3   1 
            2   4   1   1   2 
            1   3   2   2   1 
            4   2   1   1   3 
            2   4   1   2   1];
        F2D=fft2(f);
        
        % illustration of the method for one generator:
        p=2; s=1;
        Image_signal=zeros(1,N); 
        Image_signal=ft_pst(f,p,s);      
        % 7    14     6    12     9
        TDFFT_signal=fft(Image_signal);
        % 48,-0.4549-1.2286i,-6.0451-8.6453i,-6.0451+8.6453i,-0.4549+1.2286i
        T_ps=cyclic_group(p,s,N);
        % 0     0
        % 2     1
        % 4     2
        % 1     3
        % 3     4
        FT=zeros(N);
        for k=1:N
            p1=T_ps(k,1)+1;
            s1=T_ps(k,2)+1;
            FT(s1,p1)=TDFFT_signal(k);
        end;        
      
        % The whole 2-D DFT by the tensor transform
        FT=zeros(N);
        s=1;
        for p=0:N-1
            Image_signal=zeros(1,N); 
            Image_signal=ft_pst(f,p,s);      
            TDFFT_signal=fft(Image_signal);
            T_ps=cyclic_group(p,s,N)+1;
            for k=1:N
                p1=T_ps(k,1);
                s1=T_ps(k,2);
                FT(s1,p1)=TDFFT_signal(k);
            end;                    
        end;
        p=1; s=0;
        Image_signal=zeros(1,N); 
        Image_signal=ft_pst(f,p,s);      
        TDFFT_signal=fft(Image_signal);
        T_ps=cyclic_group(p,s,N)+1;
        for k=1:N
            p1=T_ps(k,1);
            s1=T_ps(k,2);
            FT(s1,p1)=TDFFT_signal(k);
        end;                    
%  48.0000             4.9721 - 4.8940i  -3.9721 - 6.9677i  -3.9721 + 6.9677i   4.9721 + 4.8940i
%  -2.0000 + 1.1756i  -3.9721 + 1.5388i  -0.4549 - 1.2286i  -1.3090 + 5.2043i  -1.3090 + 2.1266i
%  -2.0000 - 1.9021i  -0.1910 - 2.0409i   4.9721 - 0.3633i  -0.1910 - 1.3143i  -6.0451 - 8.6453i
%  -2.0000 + 1.9021i  -6.0451 + 8.6453i  -0.1910 + 1.3143i   4.9721 + 0.3633i  -0.1910 + 2.0409i
%  -2.0000 - 1.1756i  -1.3090 - 2.1266i  -1.3090 - 5.2043i  -0.4549 + 1.2286i  -3.9721 - 1.5388i        
        
        % to check if the 2-D DFT has been calculated correctly:
        Inv_image=real(ifft2(FT));
        % Inv_image=correct_image(Inv_image);        
        % Inv_image=Inv_image.*(Inv_image>=0);
        Inv_image=round(Inv_image);
        fprintf('    %3d %3d %3d  %3d %3d \n',Inv_image');