Abstract
Propagation properties of a numerical semi-discretization of hyperbolic equation are analyzed, using time-Fourier Transforms. It is shown that numerical solutions are of two types, corresponding to the two roots of a characteristic equation, which is associated with the semi-discretization. The properties of those two types of solutions in terms of phase velocity, wavelength and group velocity are derived. While solutions of the first type converge to genuine solutions of the equation., solutions of the second type have group velocities opposite to the direction of flow, and are entirely spurious.