You haven't vectorised any of your code. Try this:
function [Fcc,Fcs,Fsc,Fss]=fun_cosine_series2(f,u,v)
a = pi * u / size(f, 1);
b = pi * v / size(f, 2);
rows = (1:size(f, 1)).';
cols = 1:size(f, 2);
cos1 = cos(a * (rows + 0.5));
cos2 = cos(b * (cols + 0.5));
sin1 = sin(a * (rows + 0.5));
sin2 = sin(b * (cols + 0.5));
Fcc = sum(sum(f .* cos1 .* cos2));
Fcs = sum(sum(f .* cos1 .* sin2));
Fsc = sum(sum(f .* sin1 .* cos2));
Fss = sum(sum(f .* sin1 .* sin2));
end
It requires R2016b or later for implicit expansion, if you're on an earlier version replace all the sum(sum(f .* x .* y)) by
sum(sum(f .* bsxfun(@times, x, y)))
where x and y are the respective cos an sin vectors obviously.
