  We present a pilot study of extragalactic HI 21-cm absorption lines using the
Five-hundred-meter Aperture Spherical radio Telescope (FAST). We observed 5
continuum sources with HI absorption features firstly identified in the 40%
data release of the Arecibo Legacy Fast Arecibo L-Band Feed Array (ALFA) Survey
(ALFALFA), including two systems later detected by the Westerbork Synthesis
Radio Telescope (WSRT). Most of our observations were carried out during the
FAST commissioning phase, and we have tested different observing modes, as well
as data reduction methods, to produce the best spectra. Our observations
successfully confirmed the existence of HI absorption lines in all these
systems, including two sources that were marginally detected by ALFALFA. We
fitted the HI profiles with single or double of Gaussian functions, and
calculated the HI column densities of each source. The HI absorption profiles
obtained by FAST show much higher spectral resolution and higher S/N ratio than
the existing data in the literature, thus demonstrating the power of FAST in
revealing detailed structures of HI absorption lines. Our pilot observations
and tests have enabled us to develop a strategy to search for HI absorption
sources using the data from the FAST extragalactic HI survey, which is one of
the key projects undertaken at FAST. We expect that over 1,500 extragalactic HI
absorbing systems could be detected with survey data, based on sensitivity
level we achieved in pilot observations.
