Looking at the shape of the pulse,it looks a lot like the sin^2 pulses we used to test TV system video response.
Back in the day,they used rectangular pulses,but problems with ringing made them less than perfect for the job.
The sin^2 pulse provides a much more repeatable test result.
There was a fair bit written up about this by J.E.Weaver,& others.
The relationships are different to simple rise time,but that's about all I can remember about the niceties of it all,at this remove.