  Based on the theoretical description of Position-Position-Velocity(PPV)
statistics in Lazarian & Pogosyan(2000), we introduce a new technique called
the Velocity Decomposition Algorithm(VDA) in separating the PPV fluctuations
arising from velocity and density fluctuations. Using MHD turbulence
simulations, we demonstrate its promise in retrieving the velocity fluctuations
from PPV cube in various physical conditions and its prospects in accurately
tracing the magnetic field. We find that for localized clouds, the velocity
fluctuations are most prominent at the wing part of the spectral line, and they
dominate the density fluctuations. The same velocity dominance applies to
extended HI regions undergoing galactic rotation. Our numerical experiment
demonstrates that velocity channels arising from the cold phase of atomic
hydrogen (HI) are still affected by velocity fluctuations at small scales. We
apply the VDA to HI GALFA-DR2 data corresponding to the high-velocity cloud
HVC186+19-114 and high latitude galactic diffuse HI data. Our study confirms
the crucial role of velocity fluctuations in explaining why linear structures
are observed within PPV cubes. We discuss the implications of VDA for both
magnetic field studies and predicting polarized galactic emission that acts as
the foreground for the Cosmic Microwave Background studies. Additionally, we
address the controversy related to the filamentary nature of the HI channel
maps and explain the importance of velocity fluctuations in the formation of
structures in PPV data cubes. VDA will allow astronomers to obtain velocity
fluctuations from almost every piece of spectroscopic PPV data and allow direct
investigations of the turbulent velocity field in observations.
