I'd think the track/hold amp is where the solution lies. But it's
really the "suitable" that's the question.
Do you need to catch each pulse and criticize in turn, in real
time? Or only capture the crest value as a running average or
a "sampled" value with a don't-care time of capture? These
would point you to very different implementations. Is it
acceptable to steal some pulse energy (as a diode & cap
peak detector) or must it present a "light touch", maybe
even add no distortion (like for example a RF / frequency
domain application, downstream)?
If you can make a delayed image of the waveform then
you could "hold" that, self-clocked by a comparator whose
delay is tuned to the delay element and track/hold ideal
lag, input risetimes and flat-top width, etc.. But getting
high amplifier fidelity at these pulse widths is another
challenge. What does "suitable" have to say about the
required accuracy (amplitude and waveshape) at the end
of it all?