  We test a new technique of studying magnetohydrodynamic (MHD) turbulence
suggested by Lazarian \& Pogosyan, using synthetic synchrotron polarization
observations. This paper focuses on a one-point statistics, which is termed the
polarization frequency analysis, that is characterized by the variance of
polarized emission as a function of the square of wavelengths along a single
line of sight. We adopt a ratio $\eta$ of the standard deviation of the
line-of-sight turbulent magnetic field to the line-of-sight mean magnetic field
to depict the level of turbulence. When this ratio is either large
($\eta\gg1$), which characterizes a turbulent field dominated region, or small
($\eta\lesssim0.2$), which characterizes a mean field dominated region, we
obtain the polarization variance $\left<P^2\right>\propto\lambda^{-2}$ and
$\left<P^2\right>\propto\lambda^{-2-2m}$, respectively. At small $\eta$, i.e.,
the mean field dominated region, we successfully recover the turbulent spectral
index by the polarization variance. We find that our simulations agree well
with the theoretical prediction of Lazarian \& Pogosyan. With existing and
upcoming data cubes from the Low-Frequency Array for Radio astronomy (LOFAR)
and Square Kilometer Array (SKA), this new technique can be applied to study
the magnetic turbulence in the Milky Way and other galaxies.
