I have numerically computed phonon dispersion using small displacement method by solving dynamical matrix along high symmetry direction ,  and  for f.c.c lattice. Now I want to calculate density of state i.e $D(\omega)$ and plot $D(\omega)$ vs. $\omega$ in a graph. I have managed to do that by generating random $q$ vectors then computed phonon frequencies using my code and constructed a histogram using bin_size = 150 (though not sure what should be the range of $q$ vectors and the normalization of count). There exist a direct method to compute density of state for 1D phonon dispersion but don't know any existing method for 3D lattice. Can anyone please enlighten me in this matter, any reference or detail explanation will be very helpful.