I had a hunch. Could a headphone's square wave and impulse response be a direct consequence of its frequency response? And so I tested, and here are my results. Here are my synthesized results. No headphones were used to create these images.
First off, tried to get the EQ to match the headphone's uncompensated response as closely as possible. Here it is along with the 30Hz square wave response for comparison.
Things get more interesting with the 300Hz square wave response.
And finally, impulse response.
My conclusion would be the following points:
- The exact square wave alone is irrelevant to sound quality.
- The overshoot in square wave response is normal, and is caused naturally by the concha of the ear. Any attempt to correct it would result in an unnatural response.
- The headphone's frequency response should closely match a target HRTF.
- The closer the headphones are to a perfect IIR filter representing the HRTF, the better.
- Any deviations from a perfect IIR filter are thus caused by imperfections in driver physics or other causes, and will impact the objective perfect response of the headphone. This doesn't necessarily imply that the headphone will sound bad, but it does mean that the waveform that it produces will be imperfect. This appears to be the case with multi-driver IEMs with crossover networks.