  We investigate an atom interferometer in which large momentum differences
between the arms are obtained by using quantum resonances in the atom optics
$\delta$-kicked rotor. The interferometer can potentially measure the Talbot
time (from which $h/m$ can be deduced), the local gravitational field, or can
serve as a narrow velocity filter. We present an analytical analysis in the
short pulse limit, and a numerical investigation for finite pulse durations.
The sensitivity of the interferometer is improved by a moderate violation of
the short pulse limit. Remarkably simple relations predict the optimal pulse
duration, and the sensitivity of the interferometer.
