  Turbulent motions induce Doppler shifts of observable emission and absorption
lines motivating studies of turbulence using precision spectroscopy. We provide
the numerical testing of the two most promising techniques, Velocity Channel
Analysis (VCA) and Velocity Coordinate Spectrum (VCS). We obtain an expression
for the shot noise that the discretization of the numerical data entails and
successfully test it. We show that the numerical resolution required for
recovering the underlying turbulent spectrum from observations depend on the
spectral index of velocity fluctuations, which makes low resolution testing
misleading. We demonstrate numerically that, dealing with absorption lines,
sampling of turbulence along just a dozen directions provides a high quality
spectrum with the VCS technique.
