time domain reflectometry pulse shape
In TDR, the two main parameters are pulse length (or rather shortness), to get bandwidth, and pulse power, to get signal to noise ratio. Once you've struggled to produce those, the pulse shape is whatever the mechanism you've used happens to give you.
It's rather like the dog that says 'sausages'. The wonder is that the dog can talk at all, not that its pronunciation is poor.
TDRs tend to use a step recovery diode into a pulse shaping network, for instance a shorted transmission line. All pulses tend to come out looking a bit Gaussian (if you're lucky). Square pulses tend to have their edges rounded off, delta pulses tend to be spread out a bit. As long as the pulse doesn't have a long tail, or ringing, or a double peak, then most users are generally happy with what they get.