I was able to find some old picture left over in my photobucket.com account:
Shows the reverse function's FR and impulse, as I tried to describe above. Sorry, my quick writing was not very good, this picture should be better explaining. The correction filter's impulse keeps decreasing and decreasing but it won't end, but there is always noise floor after that it can be considered to have ended. But in theory, you don't have noise.
Shows the reverse function's FR and impulse, as I tried to describe above. Sorry, my quick writing was not very good, this picture should be better explaining. The correction filter's impulse keeps decreasing and decreasing but it won't end, but there is always noise floor after that it can be considered to have ended. But in theory, you don't have noise.
By the way, I wrote all drivers are "stable" being passive elements. I didn't write they are all minimum phase.
I reread your reply, I think you misunderstood what I wrote; I just wrote being passive systems they are stable. Being passive, they consume energy, so eventually their impulse goes to zero.
Most of the drivers by measurement results are minimum phase, or can be safely approximated to taken as minimum phase.
I had seen measurements of some drivers with whizzer cones showing non-minimum phase behavior.
I reread your reply, I think you misunderstood what I wrote; I just wrote being passive systems they are stable. Being passive, they consume energy, so eventually their impulse goes to zero.
Most of the drivers by measurement results are minimum phase, or can be safely approximated to taken as minimum phase.
I had seen measurements of some drivers with whizzer cones showing non-minimum phase behavior.
In terms of the math side of it, for the simple case of circular baffle, the diffraction transfer function becomes
1 - A e ^ (-d s)
where 1 is the amplitude of the original impulse, A is the amplitude of the echo, d is the time delay of the echo, and s is the s variable of the transfer function, ^ is power symbol and e is the natural logarithm's e number
The above has zeros at (just did quickly on paper now, so could have mistake but it is something like this):
s = ln (A) /d + j k pi/d, where k is an integer, pi is the pi number
So if A is greater than 1, the real part ln(A)/d becomes positive making it non-minimum phase, and vice versa.
This is also given in this way in some older AES artice on speaker cabinet reflections.
What I had done was to show that for diffraction any baffle shape (flat baffle with some shape of cut) the result gives zero's that are on left side of s-plane. I can try to find my writing if I had it somewhere, it was long and a few computer harddrives ago.
1 - A e ^ (-d s)
where 1 is the amplitude of the original impulse, A is the amplitude of the echo, d is the time delay of the echo, and s is the s variable of the transfer function, ^ is power symbol and e is the natural logarithm's e number
The above has zeros at (just did quickly on paper now, so could have mistake but it is something like this):
s = ln (A) /d + j k pi/d, where k is an integer, pi is the pi number
So if A is greater than 1, the real part ln(A)/d becomes positive making it non-minimum phase, and vice versa.
This is also given in this way in some older AES artice on speaker cabinet reflections.
What I had done was to show that for diffraction any baffle shape (flat baffle with some shape of cut) the result gives zero's that are on left side of s-plane. I can try to find my writing if I had it somewhere, it was long and a few computer harddrives ago.
Beating the dead horse probably, but wanted to point out something important in the above equation. The minimum phaseness of echo system (or diffraction which is echo with negative amplitude) has NOTHING to do with how much delay is involved.
The amplitude of the echo determines it.
I think there may be some conception that short delay would be minimum phase, long won't be, that is just not that way.
One other thought example: If you think about the case where echo had higher amplitude from the original. Assume we reverse the time completely and look at the impulse response now. Now the echo became the original and original became echo, and echo is smaller than original. The Fourier of these two impulses will give same FR amplitude. The latter will be the minimum phase one, because it releases its energy in time domain quicker than the former. (High impulse peak followed by smaller, vs smaller peak followe by higher)
The amplitude of the echo determines it.
I think there may be some conception that short delay would be minimum phase, long won't be, that is just not that way.
One other thought example: If you think about the case where echo had higher amplitude from the original. Assume we reverse the time completely and look at the impulse response now. Now the echo became the original and original became echo, and echo is smaller than original. The Fourier of these two impulses will give same FR amplitude. The latter will be the minimum phase one, because it releases its energy in time domain quicker than the former. (High impulse peak followed by smaller, vs smaller peak followe by higher)
Agreed, but this makes the use of the MP concept in acoustics rather meaningless. There are very strict relationships between points in space in acoustics, these can be quite useful, but I have not found any meaningful use of MP in acoustics once the system is no longer SISO.
I couldn't find my original write up on any baffle shape minimum phaseness, I wrote another one today . I give proof (if not proof solid enough arguments 🙂 ) that the baffle diffraction even off axis is minimum phase in front of baffle, if anyone is interested:
http://skydrive.live.com/?cid=1a09e8277e286a06&id=1A09E8277E286A06!177
I think, it depends on how much importance you give to the listening axis speaker sound (inlcuding diffractions from speaker) vs room input. The former is a SISO (the anechoic response). And if it is important than MP concept has some meaning, in that for same FR amplitude response systems, a minimum phase will be the best because it will give the more accurate time domain response. Obviously something meaningful for xovers used, if they give minimum phase then their time domain is good.
There were and probably still some arguments that baffle diffraction containing delayed impulse makes the system minimum phase, and since it is minimum phase it sounds bad. Diffraction may sound bad, but it is not because it is none minimum phase, because it actually is minimum phase. May point is on this. Also on the point that not being able to correct a none minimum phase is a very different thing than not being able to correct a speaker system in all points in space. The former is because the required correction filter is an unstable one, the latter has nothing to do with this.
http://skydrive.live.com/?cid=1a09e8277e286a06&id=1A09E8277E286A06!177
I think, it depends on how much importance you give to the listening axis speaker sound (inlcuding diffractions from speaker) vs room input. The former is a SISO (the anechoic response). And if it is important than MP concept has some meaning, in that for same FR amplitude response systems, a minimum phase will be the best because it will give the more accurate time domain response. Obviously something meaningful for xovers used, if they give minimum phase then their time domain is good.
There were and probably still some arguments that baffle diffraction containing delayed impulse makes the system minimum phase, and since it is minimum phase it sounds bad. Diffraction may sound bad, but it is not because it is none minimum phase, because it actually is minimum phase. May point is on this. Also on the point that not being able to correct a none minimum phase is a very different thing than not being able to correct a speaker system in all points in space. The former is because the required correction filter is an unstable one, the latter has nothing to do with this.
Correction to typo and some clearer sentences:
There were and probably still some arguments that baffle diffraction containing delayed impulse makes the system non-minimum phase, and since it is non-minimum phase it sounds bad. Diffraction may sound bad, but it is not because it is non-minimum phase, because that is a false assumption. It actually is minimum phase.
My opinion on this is well known. I give very little importance to any single axis especially an axis of symmetry (because of acoustic features of such axes).
Diffraction has high levels of group delay for the obvious reason that the diffraction is delayed from the initial impulse and group delay is well known to be audible with a sensivity that lowers with higher SPLs. If this is MP or not is really not the issue in my mind.
Understood that your focus is different due to your preference for OS waveguides. Let me ask a question with the caveat that you set aside waveguides entirely in considering this.
To preface the question, a couple of comments. I don't think that Feyz is limiting his comments to an axis of symmetry. Those of use who listen to non-waveguide systems, be they monopoles, dipoles, whatever, usually do not listen on an axis of symmetry just as you do not with your OS waveguides. I don't, plus the driver most susceptible to diffraction influence, the tweeter, is very often placed specifically to try to avoid symmetry that does fairly effectively reduce the influence in and around the design axis (not to be confused with the axis orthogonal to the baffle). Of course power response is considered important, while the first arrival importance is not zero or so I believe.
The question: given the non-waveguide caveat, what importance and influence would you place on diffraction in the context described?
Dave
Well.... that depends... because when the system is minimum phase, the question of what is exactly audible comes to picture: is it the FR amplitude variations from flatness or is it the group delay, or can you even separate the two since one drives the other and the other drives one.
As far as I know group delay audibility tests are usually made on all-pass systems which have flat FR amplitude but non flat group delay which are of course non-minimum phase. In these systems since FR amplitude is flat, you can test only for group delay audibility.
So here again, minimum phase vs non-minimum phase comes to play.
Just curious, do you have any reference to studies to audibility thresholds group delay of minimum phase systems? (Actually even the question sounds strange, because as I wrote just here, amplitude and phase of minimum phase systems are derived from each other..)
I am not arguing it is audiable or not or something to ignore or not. Anything detrimental is better removed if possible.
Thinking about it more, one thing to look is audibility of comb filtering, since basicly addition of echo gives the comb filter. There are some study results in AES, I may have e-copies of them if they are from the times I had subsciption.
But baffle diffraction signature, unless centeral on axis off a circular, is less severe than comb filtering, because the echo gets distributed from the different paths that the sound waves takes until reaching ear. This is also visible on the FR amplitude of diffraction signature of say a rectangular baffle, which smoother than a comb filter. So comb filter audibililty may give the worse case scenario on baffle diffraction audibility.
Just a disclaimer again, I am not arguing baffle diffraction is something to ignore and doesn't matter. At least for myself, I am trying to put it in its place as what it is, and how it behaves.
But baffle diffraction signature, unless centeral on axis off a circular, is less severe than comb filtering, because the echo gets distributed from the different paths that the sound waves takes until reaching ear. This is also visible on the FR amplitude of diffraction signature of say a rectangular baffle, which smoother than a comb filter. So comb filter audibililty may give the worse case scenario on baffle diffraction audibility.
Just a disclaimer again, I am not arguing baffle diffraction is something to ignore and doesn't matter. At least for myself, I am trying to put it in its place as what it is, and how it behaves.
Hi Dave
I don't see where the context makes any difference. Everything that I have done in my systems and in my rooms that lowers the diffraction (and VER) has had a positive audible effect. Diffraction is not a good thing, that's what all the data says. It doesn't matter if its in a waveguide, from a baffle, or off of an object next to the speakers. None of it is positive.
Of "minimum phase systems"? I don't know of anyone who has framed the question like that. Lidia and I did a study of group delay audibility several years ago where we showed that it becomes much more audible at higher SPLs. This means that "thresholds" aren't meaningful because they differ with SPL level. Moore showed this as well in his AES papers on the audibility of group delay - that it was audible in some contexts and not in others. The fact that its audibility is SPL dependent makes the whole thing rather complex to talk about - things like "thresholds" don't have much meaning in this context.
This seems to be a bit of a contradiction. Earlier you said:
But in the context of drivers with baffle diffraction that is probably much more related to axis than is HOM diffraction in waveguides (my interpretation) as you have described them, the diffraction influence is evident on all axes, but most influential on the listening (first arrival )axis because all other axes (that of course also exhibit influence) are essentially the off-axis and therefore contribute to the in-room (power) response. But the power response is not M-P (whether that matters or not) nor is it subject to variations according to any specific axes.
In other words, the only axis on which diffraction should have an audible impact is the listening axis, essentially a single axis. The rest is room response. How could diffraction in the off-axis response be an issue at the listening position?
Dave
Sometimes it helps to be empirical.
What is known from observation:
When things get loud diffraction products from the speaker sound really nasty and the louder it gets the nastier it gets.
Diffraction products help in locating the speaker.
So it's a Good Thing to diminish or eliminate them.
It's my experience from sitting in bad seats in concert halls, comb filtering has same negative effects with increasing SPLs.
I don't follow most of your discussion, but the statement above is clearly incorrect. The listening axis is the axis that we listen along, but that could be any axis, implying that diffraction is audible everywhere.
This question is either not well phrased or I don't understand it. In fact I'm kind of lost on your whole discussion.
"Is diffraction an issue where there isn't anyone to hear it?" sounds like what you are asking, which is a little like asking "If a tree falls and there ... "
Maybe not well phrased. One listens on one axis. My point is that the audible diffraction influence would be the diffraction that one hears from the direct (listening) axis response variation, whichever axis that happened to be. Of course the diffraction affects all individual axes, but all non-listening axes are those that affect the power response, not the on-axis response and are those that are in the reverberant field, meaning it is unlikely that there would be an audible impact from the diffraction from the off-axis.
In the end, I see it counter to your position. That is, the most important area to consider with respect to diffraction is the listening axis. The rest is room response. If I take a small baffle with a lot of diffraction, the difference on the listening axis with and without felt can be large, at times as much as 3db reduction, measured. However, the in-room (power) response will exhibit little change, not enough that I would expect it to be audible.
I am definitely on the side of minimizing diffraction as well, but my difference is in where its influence comes into play, at least in the home environment with well-placed speakers.
Dave
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