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 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 \pm 0.14 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 .