In my experience step like impulse response are just an inconvenient method to show the complex frequency response and usually lead to questionable optical shape based interpretations which usually don't hold blind testing and the theory behind.
Personally I prefer other representations like the group delay to which known psychoacoustic audiblity limits have been studied.
I agree that group delay (and phase for that matter down low) is worth looking at, but I respectfully disagree about the step response leading to questionable interpretations. If the speaker system does not follow the the "ideal" step response, we can certainly draw conclusions. It is helpful to know who to read a step response in the first place:
There is a concept of preringing with linear phase filters, so we want to watch for this type of distortion, even though in listening tests I have conducted, large amounts are hard to audibly detect. I have some charts of preringing here on ASR. The tell-tale sign is a ramp up or oscillation of the signal before the actual signal. Most noticeable on sparse music transients, like a kick drum for example, where it sounds “reversed” in the extreme case. Most modern DSP correction software have preringing compensation as it is well understood mathematically, so this is no longer an issue.
See the vertical step itself starting at time 0 milliseconds? One can think of the vertical amplitude as the frequency scale with 20 Hz starting at the bottom and 20 kHz at the top, as this is what we specified in our ideal loudspeaker design. If I designed for flat to 30 kHz, then the vertical spike would be higher. If the drivers were not time aligned, then we would see horizontal offsets away from 0 ms of the straight vertical line representing parts of the frequency spectrum arriving at our ears at different times, and different between channels too. This is very important to keep in mind, the point being our ideal loudspeaker has all direct sound frequencies arriving at the same time for both channels, i.e. at 0 ms.
The slope of the roll off, or shape of the tail, after the initial vertical step and to where it crosses the 0 ms horizontal time axis, is based on the loudspeakers low frequency roll off and cabinet alignment (i.e. slope of roll off). A roll off at a higher frequency would push the “cross the 0 time” threshold towards the left and a lower than 10 Hz roll off will push the 0 crossing point to the right, say at 15ms or even 20ms, depending on loudspeaker design (e.g. subs or no subs) and size of room.
Finally, what I don't show on this chart is beyond 20 ms are the low frequency room reflections. This goes a bit beyond the ideal loudspeaker and mainly a concern with room correction. But excessive reflections or room build up or maximum phase peaks that are greater than the direct sound are easily detected with a step response chart.
So knowing how to interpret a step response can tell us many things, is there preringing, is there time domain distortion between the drivers, is there too much/too little high frequencies based on how well the speaker tracks to the target, is there lagging bass response or too much or too little bass looking at where the bass crosses the the horizontal axis. Here is an example of a speaker tracking just about perfectly to the target step response:
The ideal step is in black and the measures are in blue and red. From my article on
accurate sound. Note that the step response is but one of many views of the transfer function we want to look at. But it is useful as it can tell use many things and to my ears, certainly audible.
Happy New Year!