I didn't see how you could take a swept sine wave and figure out where the "edges" would be.
So an experiement:
Create a transient of the worst (and for digital, illegal) case - a single full scale sample. Play that trough the speakers and record it. IIt sounds like a "click".
Then do a swept sine frequency response measurement, and display the imoulse response. It wounds like a "woooooooooooop" from low to high frequency.
The analysis of the impulse resonse derived from the frequency response looks all but exactly like the recorded "click" (transient).
Single Full Scale Sample sent through speakers, audio playback recorded in Audacity via UMIK-1:
Impulse response calculated from a ten second 10-24kHz sweep tone in REW:
A recorded and calculated Step response are equally similar.
There obviously is some math beyond my pay scale going on there.