Dwarf Galaxies in the Coma Cluster: I. Velocity Dispersion Measurements
  We present the study of a large sample of early-type dwarf galaxies in the
Coma cluster observed with DEIMOS on the Keck II to determine their internal
velocity dispersion. We focus on a subsample of 41 member dwarf elliptical
galaxies for which the velocity dispersion can be reliably measured, 26 of
which were studied for the first time. The magnitude range of our sample is
$-21<M_R<-15$ mag.
  This paper (paper I) focuses on the measurement of the velocity dispersion
and their error estimates. The measurements were performed using {\it pPXF
(penalised PiXel Fitting)} and using the Calcium triplet absorption lines. We
use Monte Carlo bootstrapping to study various sources of uncertainty in our
measurements, namely statistical uncertainty, template mismatch and other
systematics. We find that the main source of uncertainty is the template
mismatch effect which is reduced by using templates with a range of spectral
types.
  Combining our measurements with those from the literature, we study the
Faber-Jackson relation ($L\propto\sigma^\alpha$) and find that the slope of the
relation is $\alpha=1.99\pm0.14$ for galaxies brighter than $M_R\simeq-16$ mag.
A comprehensive analysis of the results combined with the photometric
properties of these galaxies is reported in paper II.
