We analyze numerically a rocking ratchet for cold atoms. The ratchet setup consists of a spatially symmetric dissipative optical lattice, and a biharmonic driving force. This setup corresponds to recent experimental realizations. We investigate the dependence of the features of the current generation on the scattering rate, which plays the role of the noise strength. Such a dependence is then used to investigate the origin of current reversals and of the rectification of fluctuations in a cold atom ratchet with broken Hamiltonian time symmetry.