I don’t understand your comment that there is no need to get into the math. Do you realize the original comment was misunderstanding the exact math I was talking about?

To make sure you’ve read my post… I’m not saying the math tells us anything. I replied to a comment that claims that impulse response is exactly the same as frequency response, and therefore we could safely ignore impulse response graphs. The math says that isn’t true. Therefore I claim we need controlled studies to understand what an impulse response can or cannot tell us before anyone knows what to interpret from them.