Just be reminded that magnitude response (the amplitude of each of the frequencies) is sufficient to calculate the phase response of each frequency, given that the system is minimum-phase, via the Hilbert Transform. So you really don't need to measure separately phase information in such...

The point is that the assumption is generally harmless. IEMs usually deviate from minimum-phase systems only very slightly, in negligible amounts, the audibility of the deviations are severely in doubt.

The idea is that you can fully reconstruct the CSD from the FR, in a linear time-invariant system. And with minimum-phase systems (which by definition are linear time-invariant), you can reconstruct the CSD from magnitude response alone, without the need to know phase information at all. Both of...

The necessary assumption is simply that the IEM is minimum-phase. With this assumption in place, you can calculate the IR from the FR (not even full FR, but just the magnitude response). Once that assumption is in place, the rest is just solid maths that everyone working in signal processing...

The missing piece is that our usual frequency response graphs don't actually tell us the frequency response directly. Strictly speaking, frequency response contains time-domain information, i.e., the phase of each frequency. With that, if you line up the frequencies with the right amplitude and...

Usually, manufacturers of multi-driver IEMs make sure that the phase response of the drivers are matched with each other, any remaining mismatch will be negligible. The second point is just maths and assumptions about the system. Ignoring the negligible non-linearity and phase-mismatch...

I think the whole picture is this. The way most people measure frequency response on IEMs, i.e., with a sine wave sweep across the spectrum, should give you just the magnitude response, i.e., doesn't contain phase information. However, because IEMs are assumed to be minimum-phase, the magnitude...

When talking about IEMs as being minimum-phase, we implicitly make the assumption that they are linear and ignore the non-linearity, and we discuss the audibility of non-linearity separately, as people are doing now in this thread. In that case, FR and IR should contain exactly the same amount...

Another quote from wikipedia, on the page for Frequency Response: The frequency response characterizes systems in the frequency domain, just as the impulse response characterizes systems in the time domain. In linear systems (or as an approximation to a real system neglecting second order...

That EQ adjustment mostly targets the decay of that specific frequency; it is very narrow band. The causal relationship is clear; if you change the FR and the phase information/impulse response changes accordingly. If there is a causal relationship, science will make sure that you can calculate...

I did some more research. It seems that "the output follows the input as closely as possible in terms of impulse response" is indeed true of minimum-phase. it is in fact FALSE for linear phase. Linear phase keeps the phase relationship between the frequencies constant. But that doesn't mean that...

In theory, yes. In practice, not yet possible to reliably and accurately do so, due to difficulty of precisely measuring FR at the eardrum.

From wikipedia: A minimum-phase system, whether discrete-time or continuous-time, has an additional useful property that the natural logarithm of the magnitude of the frequency response (the "gain" measured in nepers, which is proportional to dB) is related to the phase angle of the frequency...

It could just mean that your subjective perception of detail and contrast is very coarse-grained, in relation to changes in FR.

Also try this paragraph from an ASR post: 1. Headphones/IEMs being minimum-phase systems means FR fully describes their output. Minimum-phase is a mathematical concept that applies not just to loudspeakers. In this case, it means that at any time, the loudspeaker's movement (and the resulting...