Toward a direct measurement of the cosmic acceleration: the first
  attempt with FAST
  Damped Lyman-$\alpha$ Absorber(DLA) of H {\sevensize I} 21cm system is an
ideal probe to directly measure cosmic acceleration in real-time cosmology via
Sandage-Loeb(SL) test. During short observations toward two DLAs in the
commissioning progress of FAST, we manage to exhibit an H {\sevensize I} 21cm
absorption feature from PKS1413+135 spectrum with our highest resolution up to
100 Hz, preliminarily validating the frequency consistency under different
resolutions and bandwidths. We make a Gaussian fitting to extract the spectral
features, introduce two indicators to describe the fitted velocity uncertainty,
and ultimately give a mean redshift and its constraint of
$z_\mathrm{M}=0.24670047\pm0.00000019$ in accord with most literature. But our
redshift error is still three magnitudes larger than theoretical cosmic
acceleration over a decade. Though our first attempt has some flaws in time
recording and diode settings, it still proves the correctness of our data
process. For a higher-resolution radio observation, we propose four main
challenges: (1) an accurate barycentric radial velocity correction; (2) a
precise timing standard in data recording; (3) a statistical sample set of DLAs
with prominent absorptions; (4) a widely accepted standard of velocity
uncertainty in the DLA approach. Only with close corporation among the
community, our understanding for cosmic acceleration could advance firmly.
