Hi there. I don’t claim to be an expert on this branch of math and will believe you here. I would be curious to hear from someone like Oratory on the topic who has made similar arguments.

I’m only offering my subjective experience since I often find it hard to reconcile the subjective and objective side of things in audio. In the case of electronics and certainly cables, I’d rather largely ignore my subjective experience (also given the tons of failed ABT with speakers, which make it hard to believe electronics make any audible difference if not faulty). As you’ve stated, there have not been any time domain AB tests to my knowledge so the answer is ??? and people are trying to reason from the math rather than trials.

• also soundstage (partially not driven by FR) and FR smoothness (important in Harman’s experiments) are two reasons to consider higher end headphones.

The reason why is that headphones are nearly entirely minimum phase. This means that phase domain and time domain are directly related, and the above impulse response is implied by the frequency response. (This isn’t true of room issues with speakers by the way.) This is not entirely the case at low frequencies and with certain weird designs. There is a Crinacle video and some Oratory1990 posts explaining this better that I can’t find right now. Fwiw I subjectively sometimes think impulse response corresponds with my sense of speed and decay (stats sound dry/ fast decay), but don’t claim that is objectively the case.