1. Let's think about an ideal speaker. It would perfectly reproduce the input signal, it transfer behaviour is 1:1. A FIR representation would consist of a Dirac pulse, one single sample has the value 1, all other samples are 0. The Fourier transform leads to a straight horizontal magnitude response from DC to fs/2. The group delay is constant for all frequencies.
2. The ideal behaviour is valid for the movement of the driver coil. A battey connected to the coil will lead to a constant displacement of the coil. Thus it can transfer also DC. But we listen to sound waves in the air. The membrane oscillation causes changes in air pressure radiating into the room. With common speakers a constant displacement of the membrane does not lead to a constant change of air pressure (whereas moving the front wall in a totally sealed room would achieve this). Anyway the result is: we do not expect a transfer behaviour of a speaker down to DC.
furthermore we experience a drooping frequency response at the listening position because of a bigger distance between listener and speaker. Whereas a close-up measurement will show up the neutral behaviour of our ideal speaker.
An example of such an assumed ideal speaker is thus
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It is not important of the lowest frequency is now 40 Hz, 25 Hz or 10 Hz. This depends on the size of the bass driver/s and the speaker design. The slope may be of 2nd or 4th oder dependent on closed or vented box. It also does not matter where the high frequency droop starts and how big it is. So the picture simply shows a possible example which includes the low frequency limitations and the high frequency droop. The speaker is still ideal.
As we live in a causal world the speaker will not play before it receives a signal. It will answer by a minimumphase behaviour which means that the given frequency response is achieved by the minimum phase changes in the speakers time behaviour. The derived step response of the ideal speaker thus is
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Keeping this ideal step resonse in mind it makes sense to study published step responses of different speakers including ultra high-end speakers. A nice learing experience. Luckily our ears is quite tolerant for deviations but we are talking about the ideal case here.
Now let's take a real world step response example (a speaker in the class of about 15000 Euros), measured at the listening position:
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We can identify the common behaiour of tweeter first, then midrange driver and then the bass. It's caused by the XO design chosen for this speaker.
With an applied room correction we get now:
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Obviously the timing has improved pretty much. There are still jags in the curve caused by room reflections. The reflections are not corrected. It simply does not make sense to do this because the reflection times are not constant when you move around in the room. The reflections show up also the improved shape of the direct step response.
So what's wrong with a "room correction" here? Please note that we have not talked here about frequency response or target curve. Just about one dimension = timing.