  Context. The interstellar medium is affected by turbulence and observed H i
structures in channel maps are shaped by turbulent motions. It is taken for
granted by a few theoreticians that observed H i structures do not represent
real density enhancement but velocity caustics, caused by velocity crowding.
This interpretation was questioned and objections by Clark et al. led to
violent debates. Aims. To settle the discussion we verify theoretical key
parameters by using Effelsberg Bonn H i Survey (EBHIS) observations. Methods.
We apply unsharp masking to determine filamentary H i structures at high
spatial frequencies. In addition we use Gaussian parameters to distinguish the
cold neutral medium (CNM) from observed H i column densities. We compare power
spectra and spatial distributions of dust and H i column densities,
distinguishing CNM and multiphase column densities at various velocity widths.
Results. Observations contradict the Velocity Channel Analysis (VCA) postulate
that the spectral index should steepen with the width of the velocity window.
We rather find that the thin slice spectral index depends strongly on the H i
phase composition. Multiphase power spectra are steeper for regions with cold
gas. VCA denies such H i phase dependencies on the power distribution.
Separating the CNM we find that the power spectra are significantly flatter
than those for the multiphase H i composite. We observe excess CNM power for
small scale structures originating from cold dust bearing filaments that are
embedded in the CNM. Spectral indices for narrow channel widths depend on the
Doppler temperature of the H i gas. In presence of enhanced small scale H i
structure the far infrared emission from dust is also enhanced. Conclusions.
Small scale cold filamentary H i structures are predominantly caused by density
enhancements due to phase transitions rather than by velocity caustics.
