Fit: line + power law + line
Free parameters: 2x boundary points between lines
Algorithm: Nelder-Mead, 10 iterations. (centroid correct)

Attach 1 - height (difference between intercepts)

Attach 2-8 - Signals with H~110, different t values (see filenames). 
Note t=370 and t=870 show discontinuities in the middle of the rising front. Pick-up?

Attach 9 - Comparison of the above. Note t=370-570 look visually similar in spite of very different fit results. 
Pulser *not* shown

Attach 10 - Heat map

Attach 11 - rise times (x-diff between boundary points), for H>20 (no noise)