Karma points to you Arnauld! Thanks for bringing all this up! Indeed CSD plots are not typical in my field.

You are correct in regards to CSD and impulse response ringing. I actually visualized this in the past, but I guess I forgot. What threw me off was the visualization of a linear phase window filter which should have pristine FR and CSD in the passband, yet crazy ringing in the IR. However, this ringing will correspond to severe CSD ringing at the corner frequency which could be outside the audio band... Thank you very much for bringing this up.

I also understood your comment regarding IR ringing at lower and higher frequencies. Also, removing the propagation delay will definitively help in visualizing the effects of phase (removes crazy slopes.)

In regards to minimum phase, by definition if the poles and zeros of a system's transfer function lie inside the unit circle, by definition the system is minimum phase. In some cases, removing the propagation delay is sufficient to make a system minimum phase. Sometimes, this is not possible AFAIK.

Regarding minimum phase and stability. In the digital domain, one could use the pole and zero cancellation approach to invert a channel (headphone coloration.) However, if the headphone's zeros lie outside the unit circle (non-minimum phase) then an equalizer would have to have poles outside the unit circle as well to cancel the zeros. Systems with poles outside the unit circle are unstable by definition. That said, one could put together an all zeros (FIR) equalizer and do a very decent job... I've done this when reversing a communication channel.

As far as how good of a job one will do in equalizing a headphone, what one could do is to derive an equalizer to reverse a particular headphone measured IR. Then apply said equalizer to different measurements as a function of positional variation and such... I'll see what I can do as well.

BTW, as far as old goes, I remember dealing with minimum phase and rceps when dealing with a design 10 years ago  (playing with a channel model)

If the poles lie outside the unit circle, the filter will go through the roof (oscillate) if excited at the pole frequency.

As far as causal filters, it just means that the impulse response has taps in t >= 0. Implementation-wize, such a filter requires a delay line, multipliers per delay element, and then adders to add all the scaled delay line elements (FIR case.) A non-causal filter cannot be implemented, because the filter buffer will no longer be just a delay line... It would have to have knowledge of samples in the future, and that is "non-realizable", just a fancy word for impossible.

What is done is to effectively delay the signal and move t = 0 to the past, and sort of cheat. This off course results in a non-minimum phase filter because what has been done introduces propagation delay...

EDIT: Dunno if this helps (regarding the notion of stability), but when we talk about poles we start getting away from FIR, and into the domain of IIR filters. Unlike FIR, IIR filters have feedback (and therefore poles.) This feedback yields the possibility of having an unstable system.

LOL! There are many ways to tackle a problem. z-transform is only one.

I visualize it this way: Suppose one could decompose an IIR filter into multiple single feedback cascaded mini IIR filters (by finding the roots of the TF denominator.) Each mini IIR filter would have a single pole. The magnitude of the pole represents the feedback gain, while the phase of the pole represents the frequency (0 degrees = DC / 180 degrees = fs/2.) If the gain is equal to one, the whole thing becomes marginally stable. If any of the gains is greater than one (pole outside the unit circle) the whole thing blows up if the pole frequency gets excited.

Way above my hat all this theoretical talk

Can I ask a question about the IR plot post 34.
The only difference I can spot is a difference in delay, the signal itself only seems to arrive about 175micro seconds 'earlier' but the ringing is unchanged.

What is the goal of having the delay altered ?
In speakers where they are physically inline but not soundwavefront wise I can understand why a signal might have to come earlier.
In a headphone there is only one speaker and one origin (not for K340  ) what would altering a delay bring or am I misinterpreting the plot and missing something ?