  Dispersion relations are fundamental characteristics of the dynamics of
quantum and wave systems. In this work we introduce a simple technique to
generate arbitrary dispersion relations in a modulated tilted lattice. The
technique is illustrated by important examples: the Dirac, Bogoliubov and
Landau dispersion relations (the latter exhibiting the roton and the maxon). We
show that adding a slow chirp to the lattice modulation allows one to
reconstruct the dispersion relation from dynamical quantities. Finally, we
generalize the technique to higher dimensions, and generate graphene-like Dirac
points and flat bands in two dimensions.
