Not sure what you mean by a pulse welder. TIG is the way to go, and can be smooth DC or pulsed. Most TIG welders offer a pulse option. Titanium can be welded using TIG, either pulsed or non-pulsed, but it can be a very difficult metal to weld. The parts to be welded have to be very, very clean, the welding rod has to be titanium and, if the parts are thin, both sides of the weld will need shielding gas.
All the major equipment manufacturers make pulsed mig/mag machines, some are better than others, personally don't think you can do much better than Fronius, most synergic pulsed sets can be programmed for titanium, did a lot of titanium with pulsed MIG about 20 years ago