Very impressive work to be sure. I do wonder about the subjective sound though. In my experience when I have really gone to the limit to make a speaker extremely linear with DSP, the sound is subjectively less enjoyable than a less corrected version.
It is very difficult to quantify or to use words to express the effect, but allowing most of the naturally occurring minor peaks and dips above the Schroeder frequency to remain uncorrected has generally sounded more pleasing when I toggled between the corrected version and the less corrected version.
Have you experimented with anything along these lines?
Yes indeed. I wonder greatly about the amount of correction, its measurement improvements vs its sonic effect. And have run near countless experiments comparing degrees of correction, trying to assess subjective sonic results.
I've found tunings having what folks would consider identical transfer functions and impulse responses, to have not so identical sound.
Tunings where nothing changed other than the degree of correction, in terms of how finely the PEQs/ filters were applied. Tunings where on-axis and spins, all look identical at 1/12th smoothing, and sometimes even at 1/24th. And still sound different....(frankly it is quite frustrating.)
It's one of those imponderables for me.....
We know in theory any minimum-phase correction of a minimum phase device is a valid correction, correcting both magnitude (frequency) and phase at the same time. And that drivers are predominantly minimum-phase devices. So I make all my corrections at the driver level, using a DSP/amp channel for each driver section.
I figure if a minimum-phase correction of a driver holds up spatially, it is a valid correction that is likely to have audible (and certainly measurable benefits.)
I also figure the quality of the measurements has a ton to do with the quality of the corrections. (I use dual channel FFT coherence to assess measurement quality)
Using that logic, I've tested different degrees smoothing of applied filters. With FIR, using min-phase EQs embedded into the filter for driver correction, it's very easy to change filter resolution simply by varying the number of taps (coefficients) used. With IIR , I vary the restriction on Q/bandwidth being applied.
In both cases, I'm strongly led to believe higher Q filters, no matter how well they seem to correct drivers, are best avoided.
(Worth noting, avoiding high Q/bandwidth PEQs does not mean avoiding high order crossovers. Their rate of change continuity is such even a LR 96 dB/oct lpf or hpf does not have a high Q property. IIR high order imparts too much phase rotation/ freq dependent group delay, but complementary linear-phase FIR high order crossovers do not. If we can live with the fixed latency of lin-phase FIR crossovers, it's all win ime/imo).
Anyway, I've rambled and digressed enough i guess.. I could go on for along time about all this lol
fwiw, here's the same response for the big white 5-way i posted, but now at 1/48th measurement resolution.
You can see a bunch of good sounding whiskers/stubble