Once more, you'd have to think about this problem as to include a curtain test (within reason, I mean just to make the point) where you take the optimal example tube amp, place the mic in front of it, put that on the PA or monitoring in another room (or in the same room, to let the guitar feedback work properly, certainly for high gain examples) in an analog fashion, and then put in a AD/DA insert somewhere, and see what the difference is.
If you put the digital insert before the guitar amp, probably things won't work all too good, unless it's a tuned and intended digital effect unit, and I'm sure that monitoring the mic-in-from-of-the-guitar-amp digital instead of analog makes a difference. And amping that mic with a digital conversion in between, unless the PA is tuned for it, is going to change the sound, and it should, at least there's a few milliseconds shift in phase, and IMO for sure if the sound isn't a very degenerate sound, the aliasing/reconstruction will be audible, all the more so if the analog-digital-analog signal sub-path is part of the sound feeding back to the guitar body, and therefore to the sound.
Also, applying the proper theory is cool and I find it great when people try to make nice plugins and so on, but be aware of it that even a simple filter will in most cases have significant distortion in the digital domain, even if it's a nice (natural) IIR, because of the integration not including a sinc function partial, and the not necessarily perfect curve of the power sequence (impulse response) compared with a natural e-power curve, regardless of zero-th order reconstruction, average DA convertor reconstruction filtering, or (near-)perfect signal reconstruction. I mean it sounds nice to presume perfection, but those integrals are going to be off, circuits are more natural, especially relatively high impedance circuits with non-electrolytic capacitors with tube connections: there will be some seriously accurate long-term integration in those natural poles and zeros, that simply isn't that easy to approach in the digital domain as people might think, might take more than single precision to accumulate in some cases, and most human beings are used to judging the naturalness of low order systems, and very sensitive to small signal aberrations.
It might pay to convert some of the private and various state funded thinking to making sure a decent EE designs some well-parametrized solutions, and start from those, probably cheaper...
Also, about the seemingly trivial to defend approximations in the sense of large signal amplification and clipping: most amps will do a lot of things while a part of their analog state is in clipping. For instance the pre-amp and filters will still do accurate signal tracking and integration, and the clipping doesn't take place at a sampling grid, so the PWM behavior of the guitar-amp-speaker system can be accurately driven, which brings me to the last bit: the whole system works very accurately in the feedback loop.
It's like landing a 3 ton chopper with a stick: it's perfectly possible, but takes training, and involving any of the crude simplifications some people take for granted would make the thing un-flyable and dangerous, so please think about this a bit.
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