  We study the observable properties of compressible MHD turbulence covering
different turbulence regimes, based on synthetic synchrotron observations
arising from 3D MHD numerical simulations. Using the synchrotron emissivity and
intensity, we first explore how the cosmic ray spectral indices affect the
measurements of turbulence properties by employing normalized correlation
functions. We then study how the anisotropy of synchrotron total and
polarization intensities arising from three fundamental MHD modes vary with the
viewing angle, i.e., the angle between the mean magnetic field and the line of
sight. We employ the ratio of quadrupole moment to the monopole one (QM) for
this purpose. Our numerical results demonstrate that: (1) the two-point
correlation function of synchrotron statistics for the arbitrary cosmic ray
spectral index is related to the special case of magnetic field index
$\gamma=2$ in agreement with the analytical formulae provided by Lazarian \&
Pogosyan (2012); (2) the anisotropy of synchrotron total and polarization
intensities arising from Alfv\'en and slow modes increases with the increase of
the viewing angle, while that of fast mode remains almost unchanged with the
viewing angle; (3) the analytical formulae of synchrotron intensities for
studying turbulence can be applied to describing statistics of polarization
intensities, and the QM can be successfully used to recover turbulence
anisotropy. This study validates Lazarian \& Pogosyan's analytical approach and
opens a way to study turbulence from observations.
