  Superconducting transition-edge sensors (TESs) carried by X-ray telescopes
are powerful tools for the study of neutron stars and black holes. Several
methods, such as optimal filtering or principal component analysis, have
already been developed to analyse X-ray data from these sensors. However, these
techniques may be hard to implement in space. Our goal is to develop a
lower-computational-cost technique that optimizes energy and time resolution
when X-ray photons are detected by a TES. TESs exhibit a non-linear response
with photon energy. Therefore, at low energies we focus on the current-pulse
height whereas at high energies we consider the current-pulse width, to
retrieve energy and arrival time of X-ray photons. For energies between 0.1 keV
and 30 keV and with a sampling rate of 195 kHz, we obtain an energy resolution
(full width at half the maximum) between 1.32 eV and 2.98 eV. We also get an
arrival-time resolution (full duration at half the maximum) between 163 ns and
3.85 ns. To improve the accuracy of these results it will be essential to get a
thorough description of non-stationary noise in a TES, and to develop a robust
on-board identification method of pile-up events.
