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> The frequency response and the impulse response are correlated. You can just get one from the other through fourier transformation.

It's true. It should be added, however, that when the frequency response is complex (and it always is with transducers) and the measurement conditions are not very repeatable, it's probably beneficial to also get an impulse response.

> Phase shift can also be measured through this approach

I thought headphones are zero-phase-shift devices? This is because of the very small volume of air between the membrane and the eardrum - they both move in lockstep, hence zero phase shift.




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