  We study the unphysical recurrence phenomenon arising in the numerical
simulation of the transport equations using Hermite-spectral method. From a
mathematical point of view, the suppression of this numerical artifact with
filters is theoretically analyzed for two types of transport equations. It is
rigorously proven that all the non-constant modes are damped exponentially by
the filters in both models, and formally shown that the filter does not affect
the damping rate of the electric energy in the linear Landau damping problem.
Numerical tests are performed to show the effect of the filters.
