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>> Is it correct to assume that this loudspeaker is displaying non-minimum phase behavior
>> around the crossover region when one looks at the 2-nd order all-pass response of its
>> phase response?
>> Can the phase adjustments being done around the crossover region, to flatten the phase
>> response, be deemed to be “maximum phase” corrections seeing that we are inverting an
>> all-pass response?
Yes. But remember this is just one loudspeaker. Each loudspeaker is different.
>> Is the flattening of both the magnitude (EQ boosting) and phase response around the
>> crossover region not going to introduce audible artifacts like pre-ringing?
Maybe. Linear-phase brick-wall crossovers also have pre-ringing but it’s rare that people say they think they can hear it.
>> Can the same EQ concepts be readily applied in correcting the room transfer function
>> displaying non-minimum phase characteristics at the listening/measurement position?
Yes but I’d suggest doing a literature search on the topics of room impulse response correction and inverting room impulse responses; maybe in the Audio Engineering Society resource library.