  In this paper, we develop the method of analyzing the velocity field of
cosmic matter with a multiresolution decomposition. This is necessary in
calculating the redshift distortion of power spectrum in the discrete wavelet
transform (DWT) representation. We show that, in the DWT analysis, the velocity
field can be described by discrete variables, which are given by assignment of
the number density and velocity into the DWT modes. These DWT variables are
complete and not redundant. In this scheme, the peculiar velocity and pairwise
velocity of galaxies or particles are given by field variables. As a
consequence, the velocity dispersion (VD) and pairwise velocity dispersion
(PVD) are no longer measured by number-counting or pair-counting statistic, but
with the ensemble of the field variables, and therefore, they are free from the
bias due to the number-counting and pair-counting. We analyzed the VD and PVD
of the velocity fields given by the N-body simulation for models of the SCDM,
$\tau$CDM and $\Lambda$CDM. The spectrum (scale-dependence) of the VD and PVD
show that the length scale of the two-point correlation of the velocity field
is as large as few tens h$^{-1}$ Mpc. Although the VD and PVD show similar
behavior in some aspects, they are substantially different from each other. The
VD-to-PVD ratio shows the difference between the scale-dependencies of the VD
and PVD. More prominent difference between the VD and PVD is shown by
probability distribution function. The one-point distribution of peculiar
velocity is approximately exponential, while the pairwise velocity's is
lognormal, i.e. of long tail. This difference indicates that the cosmic
velocity field is typically intermittent.
