Greetings weltersys - I didn't know you before this thread, but you come across as thoroughly knowledgeable and no doubt a professional in the field. I doubly appreciate your input and others like you here, given my lack of experience with horns.
There's a lot in that last post - I need time to digest. (Sadly those zip files don't open for me (Win10).) Again, no problem dealing with LTI issues. Fixing them is a default starting point for me.
About the ultimate barrier being non-linear acoustics: exactly my suspicion. But beyond what can be corrected, I still care when I might be able to get better results from direct radiators since I have no mandate to use a horn. (A low DI tends to be the first casualty, however, since radiating area wins.)
There's a lot in that last post - I need time to digest. (Sadly those zip files don't open for me (Win10).) Again, no problem dealing with LTI issues. Fixing them is a default starting point for me.
About the ultimate barrier being non-linear acoustics: exactly my suspicion. But beyond what can be corrected, I still care when I might be able to get better results from direct radiators since I have no mandate to use a horn. (A low DI tends to be the first casualty, however, since radiating area wins.)
Correcting "linear, time-invariant" (LTI) mechanisms are now possible with relatively inexpensive FIR (Finite Impulse Response) processors, and many "DIY" approaches have been done that emulate what David Gunness has done.
I'd suggest working on what can be corrected, and not worrying about what can't .
The nonlinear component of the distortion can be (largely) cancelled because it is well behaved without instabilities, large delayed contributions, etc... which would cause complications. It also is straightforward to predict to reasonable accuracy leading to fairly efficient implementations though this will have to be done for particular horns rather than generally. Whether efficient enough to work with live sound would need to be determined (or looked up because this sort of thing will almost certainly have been done plenty of times before at least academically) but comfortably DIYable for recorded music in the home where, of course, it likely won't be needed due to modest SPLs.
PS Thought about expanding a distortion related task on my to-do list to include it but a brief google revealed several publications on the topic (from abstracts not reading) so a DIYer could follow others rather than working it out from first principles. Rather takes the fun out of it since it is not needed for my home speaker projects.