Giveaway details will be a solved issue soon.

One of them can’t take phone calls.

Maybe this helps: The impulse response in OPs post image basically does not have to be windowed at all, it’s decently close to zero at the edges. Plug it into a FT and you’ll get a decently accurate FR.

In the extreme case? Infinitesimally short time. The FT of a Dirac pulse is a flat, constant response from 0 Hz to infinity Hz (or, in the case of DFT, Nyquist frequency).

As I said, the FT of a Gaussian is a Gaussian. Really sharp in the time domain means really wide in the frequency domain. If you do not understand why that is, your intuition about FTs will be flawed.

Proper decaying/windowing is performed via element-wise multiplication with a window function. All we want is that the signal is smoothly approaching zero at the edges. Since this is approximately the case for typical impulse responses of audio systems, it won’t change the result that much if you don’t window it at all.

To help your intuition, convince yourself that the FT of a centered Gaussian bell curve is itself a Gaussian bell curve. Note that the “low frequencies” in this graph are near the center.

Of course. As in professionally, for decades. Note that for that to work, you need the full, complex-valued FR of a system. The amplitude response does not contain phase information.

That’s why people add the impulse response as supporting information: A plot of the complex-valued response (either 3D or as two real-valued graphs) is not intuitive for humans.

Here is a quick explanation of how the responses are calculated in REW.

Well, I’m allowed to have that fetish. Digital signal processing was literally my job for decades. Let me tell you that the math and the methods very much apply to the real world. That’s how they were conceived; to analyze the filter properties of physical systems.

What exactly is it you doubt? That the impulse response and the frequency response are linked? This is taught in any undergrad course on the subject. For instance, see this online textbook, last sentence on the page. (“Decayed” here is often named “windowed” in other texts.)

It’s also very easy to convince oneself of the fact. Just fire up MATLAB, Octave, Mathematica, etc. Manipulate a vector to emulate an impulse response, calculate its DFT (typically using the FFT algorithm), then calculate the element-wise magnitude — et voilà, that’s the associated frequency response. If you apply the inverse DFT on the output of the DFT (before you calculate the magnitude), you get the original impulse again.

> real systems are not of infinite bandwidth

I don’t see anyone making that assumption here. Could you elaborate?

> that response […] cannot be derived by just looking at [frequency] response.

Of course not from the magnitude response as it is typically plotted. But from the complex-valued frequency response, of course it can, no assumption of infinite bandwidth required.

> Time domain and frequency domain are only equivalent if both are infinite.

We’re talking about discrete FTs here. There is nothing infinite about those.

> One cycle at 200 hz is 0.005 seconds.

This is completely irrelevant. You can easily pack a signal that contains components below 200 Hz into a time window much shorter than 1/200 s.

If your understanding of the “myth” is based on this flawed intuition, you may want to reconsider your argument.

> I definitely want more clamp

Ditto. My main gripe with these cans is that they slide (and make a sound) when I move my head.