That's a good question. All DSP correction software I know about uses proprietary filtered response prior to inversion. So it's the way the software filters the original impulse which separates the shitty sounding DSP softwares you normally hear in cheapy AVRs from the most advanced softwares like Acourate. Acourate uses what Uli calls frequency dependent windowing (FDW). IOW, the "aggressiveness" is designed to avoid doing any overcorrection. Also, the FDW can be tailored based on the group delay plot and listening. It's important to not cause any audible pre-ringing.
I only showed a 1/12 per octave plot due to its common usage to help identify basic trends and the corresponding number of notes per octave. However, Acourate gets its inversion from what's called a "psychoacoustic" smoothed result. You'd have to ask Uli how he came up with this smoothed result prior to inversion.
Sounds like very sophisticated and slick SW. Reading Bob Katz testimonial sounds like great SW. Thanks.