Basis functions of DCT-II

The code below, plots with Matlab (for Octave one has to do some modifications) the functions fk(x)fl(x) with fk(x)=cos(pi k (x+1/2)/N). these are, up to a normalization, the basis functions of DCT-II. In the code one can choose legoh=1 and legov = N to produce the actual step functions. With large value we have approximations of the continuous versions.

For instance, for N=8, that corresponds to JPEG, we have
k=0, l=5
 k=2, l=2
 k=3, l=5
fig05d
 fig22d fig35d

k=0, l=5
 k=2, l=2
 k=3, l=5
fig05c
 fig22c fig35c

The code


% DCT-II
N = 8

legoh = 1*1000;
legov = N*1000;

% meshgrid for Z
npoints = 400;
x = linspace(0,N, npoints);
y = linspace(0,N, npoints);
[X,Y] = meshgrid(x,y);


for l=0:N-1
    for k=0:N-1
        Z = cos(pi*k/2/N*(2*floor(legoh*X)/legoh+1)).*cos(pi*l/2/N*(2*floor(legoh*Y)/legoh+1));
        Z = floor(legov*Z)/legov;

        % plot
        figure(1)
        surf(X,Y,Z,'EdgeColor','none')
        colormap gray
        camlight right; lighting phong
        view([78,40])
        axis off

        namefig = './images/fig%d%d.png';
        namefig = sprintf(namefig,k,l);
        saveas(gcf,namefig)
    end
end



Other interesting values for the azimuth and elevation in view are
view([-30,40])
view([80,60])
view([66,40])
view([58,36])
view([78,28])