The production of direct photons, not coming from hadron decays, at large transverse momentum p T > 2 GeV/c in proton-proton collisions at the LHC, is an interesting process to test the predictions of perturbative Quantum Chromodynamics at the highest energies ever and to put constraints on the gluon density in the proton. Furthermore, they provide a baseline reference for quark-gluon-plasma studies in Pb– Pb collisions. We will present the experimental capabilities of the ALICE electromagnetic calorimeter EMCal to reconstruct the direct and isolated photon spectra in p– p and Pb– Pb collisions.