I mean this diagram and i have add the lines of the 2.8 ms i mean.
This is due to the high-pass filter at 15Hz (so similar to e.g. a good subwoofer's low frequency limit). If you put the high-pass filter at a higher frequency, this 'decay time' will decrease, as also illustrated here:
We see from all this that e.g.
1) without high-pass (so frequency response flat down to 0 Hz / DC) the step function never returns to 0% - i.e. we have an ideal step function,
2) with high-pass at 15Hz it takes 2,8ms to return to 0%, and
3) with high-pass at 100Hz it takes ~0,45ms to return to 0%.
Note from this that the lower the high-pass frequency, the longer the "decay" is, and consequently the closer the resulting filtered function will look to the ideal step response. This basically means that the 'longer it takes' for a loudspeaker's step response to go from 100% to 0%, the lower in frequency the loudspeaker plays. This is all perfectly predicted from Fourier transform and linear systems theory.
Since no real loudspeakers can play down to 0 Hz (DC) we will always see this 'decay' and oscillation in measured step responses, as
@KSTR explained.
and thanks for posting the JBL 305 step response. the without DRC left measure is without any EQ ?. it look slower but in compare to kali the time the level have around 90% look much fewer on your step response. maybe this is bad when the step response is much curved as from the Kali and have no sharp edge.
The black line is without any EQ, correct. Also no smoothing/gating applied there.
Your measurements look like some kind of smoothing is applied somewhere - maybe it is worth checking that - and as if they may also possibly contain very early reflections (due to your measurement methodology), which will make the measurement non-time-invariant (so not LTI) and therefore unfortunately make it invalid for this kind of analysis.
but it is still strange wy i get such a much smaller step response with the headphone correctet and LP 1.2 khz. the FR look very linear from bass until crossover freq come.
As explained by
@ctrl, unfortunately the way you are measuring headphones is also causing attenuation of low frequencies, which of course affects how the corresponding step response looks. If you measured the same pair of headphones with e.g. a dummy head you would definitely get a very different (and more correct) frequency and step responses. Unfortunately this alone makes it difficult to compare the measured responses and draw conclusions from them.
Let me give you another example how well the theory explains the step response shapes from the frequency response, I did the following test:
- I have an in-room on-axis measurement of the LSR305 taken at 50cm from tweeter, first significant reflection was 4,8ms after initial pulse so the first few ms are reasonably representative of the loudspeaker's anechoic on-axis impulse or step response
- Checked the JBL LSR305 datasheet to find that the crossover is implemented as a LR4 filter at 1725Hz and that 41Hz is the -10dB point (48Hz at -3dB).
- The woofer therefore plays from 41Hz (-10dB) to 1725Hz
- The tweeter play from 1725Hz onward
- Based on this I took the ideal step response (0-96kHz bandwidth) and applied an BU8@48Hz high-pass filter and LR4@1725Hz low-pass filter to create an idealized representation of the woofer in LSR305.
- Then I applied an LR4@1725Hz high-pass filter and BU8@22kHz low-pass filter to the ideal step response to create the idealized representation of the LSR305 tweeter response
- Lastly I used the REW 'trace arithmetic' A+B function to sum the simulated ideal 'woofer' and 'tweeter' responses to get a representation of the complete simulated ideal LSR305-like loudspeaker
Here's how that looks in the frequency domain:
Similar but also quite different in some ways, at least at first glance - note that in the 'real' LSR305 measurement there are room reflections and modes, especially affecting the LF. If you look at the
LSR305 quasi-anechoic measurement you will see that the actual LF extension is really close to the above simulation:
Now let's look at the same in-room measurement vs simulation in the time domain (step response):
Amazingly similar in many ways, right?

As you can see, even this grossly over-simplified simulation of a loudspeaker (just band-limiting an ideal step function) vs a real measurement of the loudspeaker shows a lot of similarities, and reinforces the principles that I (and others) were trying to explain before.
Related - notice that in REW you can import a pure impulse response, and based on that REW will display the corresponding frequency (magnitude+phase) response, as well as the step response.
This is another clue that they all show the same data, just presented differently (and the mathematical process that converts between them is called the Fourier transform)

As explained before, from knowing the frequency response (magnitude+phase) you can calculate the step or impulse response (and vice-versa). It also means that two identical frequency responses (magnitude+phase) will have an identical step response.
I understand Linear superposition and i undersand what you want say. frequency and driver have influence of the step response. I agree to this. But this is no forumula with 2 unknown parameter because the Frequency response is measure too and a software can calc step response with normalize FR to better compare. or just use a 100 hz 24 db highpass for all speakers, so the bass range is not so low. I understand that in Bass range small and large speakers are much diffrent in FR. this have a little influence of the fall time of the step response.
here you can see much diffrent FR of the JBL done with EQ in Bass Range. but the fall/rise time from 20% to 20% level increase only a little from 580 µsec to 650 µsec (this are 12%) with this much diffrent Bass frequency change. the kali step response 20% to 20% time need 1440 µsec but have not so much bass as the JBL with the EQ. so because of the kali bass there need much shorter step response, and so conclusion is the driver is very slow.
EDIT: the JBL measure in compare at 1.5 cm. because the room have very less influence it can give much bass. because its coaxial the tweeter is see too in FR and step response
View attachment 169839View attachment 169840
so i think the step response of a speaker is important to see. if you like it more, then can ignore the fall time and show only the raise time. impulse response i think not usefull when test complete speakers. because in a impulse response it is hard to see which is the raise and fall time of the mid/bass. or maybe need see the impulse response of bass/mid or mid only to see if it is good for ITD
View attachment 169838
Or can somebbody explain how i can see on the JBL and kali and headphone impulse response compare which is faster ?????. i can only see the kali look slow. but the headphone look much slower as jbl but it is not
It should hopefully be clear from the explanations and examples so far that the 'rise time' will largely depend on the high-frequency content of the measured response. This will of course be different between different woofers due to different crossover frequencies, and especially compared to headphones with their full-range drivers.
To get comparable results you'd need to make sure that the low-pass filters you are using to level the playing field really remove an equal amount of high-frequency content in all cases.
Also, you'd need to make sure that your response measurement procedure is creating comparable results in the first place. Unfortunately this will not be the case if you're measuring loudspeaker woofers in extreme nearfield and comparing that to an unsealed headphone measurement (without a headphone measurement jig/dummy head) - neither of those two methods will generate good reference measurements for either case, and especially not to compare between them.
However if you put all necessary controls in place to make sure the frequency responses are comparable, you will see that the step responses will in the end become very similar-looking as well

as I've illustrated above on the LSR305 example.
EDIT: Though I'd still be reluctant to compare headphone measurements to loudspeaker measurements. Due to the nature of headphone measurements (which will include very early reflections within the cup and ear canal) it would be easy to miss important controls and come to wrong conclusions.
I look on it, but sound stage and spacious is only a large room interaction if you sit far from the speaker. I use my JBL 104 BT 45-50 cm, in nearfield. I have measure of RT60 decay from 1 meter and 50 cm away from speaker. when measure at 50 cm it reduce alot room reflections. in my measure i have the volume of speaker same and i get then less level on microphone. to have same level on microphone i need add volume 6 db. then it get even more worse.
https://www.audiosciencereview.com/...re-coaxials-so-rare.26915/page-12#post-991037 I hear amazing wide soundstage. my 17 qm room can not produce a concert reverb. So i come to the conclusion directivity of a speaker is does not create concert hall reverbs or reverbs of large rooms that sound good. when you have a speaker with lots directivity it happen that only your room reverb is mixed more to music. but it sound not as a good reverb from the record of music. thats not real. also when make music mono upto 460 hz then the room feeling from large concert hall is lost. so this is another fact, that tweeter directivity is not so important, and speakers have all wide directivity upo 460 hz. thats the reason wy the brain use ITD the phase to recognize direction i think because on low frequency the direction can very bad hear with level diffrence because sound source are always wide on 460 hz
here is video that show how it sound in mono upto 460 hz. the room size get very small then
https://www.audiosciencereview.com/...for-itd-see-measures.28585/page-2#post-996188
EDIT: on your link this is only a preprint. preprint can everbody do. and if it since 1986 in preprint state, then other scientist do not conform to this
Learn about preprints and submitting your paper to Taylor & Francis after uploading to a non-commercial preprint server.
authorservices.taylorandfrancis.com
I can also do a preprint and upload it to the server about my theorie with the few stereo wide= slow stepresponse

maybe the journal buy 100 speakers and verify with the measured step responses if there is a connection . i know that the few speakers i have test are not enough. so more should verify it
My english is not good and i can this not translate in google so i can also not look if there is something i did not know
I see only in the headlines he write nothing about interaural delay hearing and stereo recognize. the interaural crosstalk(about thie he write) is maybe not so much relevant on low frequency when hear ITD. on real sounds in a room you too have lots intraural crosstalk and you can recognize good. for example when you stand near a wall and the soundsource is 5 meter away but the wall only 10 cm.
I have my speakers 80 cm distance left to right and the JBL have a amazing wide soundstage. wider as headphone. the kali is very small much smaller as headphones.
ITD is one of several psychoacoustic mechanisms that humans use to localize sounds around us. To my knowledge there is no direct relation between the minimum audible interaural time delay value and the required rise-time of a loudspeaker's step function for good stereo width in the way which you are proposing. If a loudspeaker reproduces a transient, the sound will almost always reach one ear a little bit later that the other ear - that is ITD. This happens in the exact same way regardless whether the source (loudspeaker or something else) reproducing the sound has a 'slow' or 'fast' step response, so it should not be relevant in this context.
Anyway, hoping this wall of text might be interesting (or even useful) to some
