  In this paper we test the results of a recent analytical study by Lazarian
and Pogosyan, on the statistics of emissivity in velocity channel maps, in the
case of realistic density and velocity fields obtained from numerical
simulations of MHD turbulence in the interstellar medium (ISM). To compensate
for the lack of well-developed inertial ranges in the simulations due to the
limited resolution, we apply a procedure for modifying the spectral slopes of
the fields while preserving the spatial structures. We find that the density
and velocity are moderately correlated in space and prove that the analytical
results by Lazarian and Pogosyan hold in the case when these fields obey the
fluid conservation equations. Our results imply that the spectra of velocity
and density can be safely recovered from the position-position-velocity (PPV)
data cubes available through observations, and confirm that the relative
contributions of the velocity and density fluctuations to those of the
emissivity depend on the velocity resolution used and on the steepness of the
density spectral index. Furthermore, this paper supports previous reports that
an interpretation of the features in the PPV data cubes as simple density
enhancements (i.e., ``clouds'') can be often erroneous, as we observe that
changes in the velocity statistics substantially modify the statistics of
emissivity within the velocity data cubes.
