MartinQ said:
SFM = Sound Field Management
A multisub approach with goals and results similar to Dr. Geddes's, but involves a lot of computation in attempt to optimize sub placement and settings. Like Earl's, it works well for the not-a-shoebox room shapes** many of us have to deal with.
The computation required for SFM is out-of reach for many/most of us.
**(You probably already know, but the Harmon/JBL symmetrical placement approach and the DBA approach both require shoebox rooms).
john k... said:
John
I did not misspeak, you are incorrect here, since you can recover the direct field with more "terms" in the summation, i.e. more modes.
I also don't accept your example as proving anything.
Todd
In Morse he shows how the Greens function series solution, what everyone uses in their room simulations, can be modified by subtracting off the singularity at the source point. This term, when subtracted off represents the direct field since it is basically the free field Green's function. The summation that remains after you subtract off this direct field term is dominated by the lower order modes and converges very quickly, but the series is now different than the usual one.
john k... said:
Perhaps we misunderstand. For me, anyway, I'm not trying to "recover" the direct sound per se (i.e. separate it out). I'm just interested in whether or not it is included in my simulation (and yes it's true that that only matters when you are close to the source, but still...). And as for bandwidth, it's not really an issue. I only need to go up to order 7 or so to get the BW I need for subwoofer investigations in most rooms I work with.
I'm intested in your simulations. Are you then adding the "direct" term in? the one we seem to agree is a fudge? I did simulations where I went from order 10 to order 35 with the source and receiver 4" apart and saw no significant difference. So i conclude that you really need to go to high order to have the direct show up. Of course you are even closer to the source and going up to order 100. Is that sufficient to include the direct (which your plots show), or are you adding the "fudge"?
cap'n todd said:
Todd
By "order" do you mean total number of terms or the value of the index for each direction? 35 terms would never show up any direct field, it would take thousands. I've done simulations with more than 1000 modes considered.
But as you and I have discussed this near field thing is irrelavent, so lets not get hung up on it.
Johns simulation is unrealistic in that one can't actually do what he is simulating, so it shows nothing useful.
Hi guys!
Are you still debating this??
One corner placed sub excites all modes (all axial modes at least) but adding sources in all corners (8 in total for a rectangular room) we side step the first order mode excitation in the first place. It's not there.
Also I can' see how you strive for "big room bass" in a hifi listening room. The recording have ambient signatures which would be masked if you imposed a "big room sound" at the time of playback. The decay time in the listening room need to be short enough not to mask the signature of the recorded room or the artifically added room in the recording.
Well that's how I see it anyway!
/Peter
Are you still debating this??
gedlee said:
One corner placed sub excites all modes (all axial modes at least) but adding sources in all corners (8 in total for a rectangular room) we side step the first order mode excitation in the first place. It's not there.
Also I can' see how you strive for "big room bass" in a hifi listening room. The recording have ambient signatures which would be masked if you imposed a "big room sound" at the time of playback. The decay time in the listening room need to be short enough not to mask the signature of the recorded room or the artifically added room in the recording.
Well that's how I see it anyway!
/Peter
So the number of modes would be 35 x 35 x 35? Or did you just do 2-D? 35 x 35.
At any rate, I think that you and I agree that the direct field does not influence the results and that getting a spatially smooth response allows for global EQ correction, if EQ is used at all. This, to me, is the crux of the situation and I think that we are in complete agreement. Correct? How one achieves this may be different and I am sure that there are a myriad different algorithms, etc. that one can use, but in the end the goal is the same.
To me, personally, once the bass response is smooth, you are 90% of the way there. This spatial bass stuff may well be valid, I think that the jury is still out, but one has to have a smooth bass response first and formost before anything further can be considered.
At any rate, I think that you and I agree that the direct field does not influence the results and that getting a spatially smooth response allows for global EQ correction, if EQ is used at all. This, to me, is the crux of the situation and I think that we are in complete agreement. Correct? How one achieves this may be different and I am sure that there are a myriad different algorithms, etc. that one can use, but in the end the goal is the same.
To me, personally, once the bass response is smooth, you are 90% of the way there. This spatial bass stuff may well be valid, I think that the jury is still out, but one has to have a smooth bass response first and formost before anything further can be considered.
Todd,
My code does not have the direct source term. However, I believe the result I showed without the low frequency modes was fortuitous. It is a correct result to the equations solved for the position of the source and listener, but changing the position of the source or listener greatly effects the low frequency level. I'm not clear on why that is happening. I always recover the direct response at low frequency but at reduced level. I need to look into this further. I still think adding the direct term is a fudge, and I still think Walker added it for the reasons I said earlier, the modal expansion of the Green's function is not valid in heavily damped rooms. Obviously, in an anechoic chamber where all modes are damped to close to 100% the modal expansion would yield no SPL at all, clearly incorrect.
Earl,
Yes, agreed. The solution to to the wave equation in a reverberant, rectangular room is posed as two problems using superposition.
G(r|ro) = g(r|ro) + x(r)
where g(r|ro) is the free space Green's function ans x(r) is the solution to the to the homogeneous wave equation with appropriate boundary conditions. I have no argument there. But the way I interpreted Todd's remark was that he was expecting to see the free field SPL reappear is low frequency modes were eliminated, as would be the case in an anechoic chamber.
So certainly you can subtract off the contribution form the singularity, g(r|ro), and what remains is the contribution from X(r) which is the reverberant part of the solution. Likewise, once x(r) is found by that subtraction it could be subtracted leaving the free space result, i.e. the direct sound.
I also agree with Pan that as far as big room bass goes, the big room effect is captured on the recording. I believe this is very different than needing reverberation in a listening room above the Schroeder frequency to provide an illusion of "space".
Now, back to multiple subs. Are we placing them to smooth the response or at locations where modal contributions either cancel or are null? You claim your is the former. Todd's 4 woofer array with 1/4 L positioning seems to be the latter. If X and Z represent the plane of the floor, then such placement cancels odd order axial modes in the X and Z directions and the positions are nulls for 2nd , 6th 10th 14th... order even axis modes, and a bunch of tangential and oblique modes get eliminated as well. But what ever the approach, the modal behavior at the listening position have the final word as to which otherwise excited modes affect the SPL at that point.
My code does not have the direct source term. However, I believe the result I showed without the low frequency modes was fortuitous. It is a correct result to the equations solved for the position of the source and listener, but changing the position of the source or listener greatly effects the low frequency level. I'm not clear on why that is happening. I always recover the direct response at low frequency but at reduced level. I need to look into this further. I still think adding the direct term is a fudge, and I still think Walker added it for the reasons I said earlier, the modal expansion of the Green's function is not valid in heavily damped rooms. Obviously, in an anechoic chamber where all modes are damped to close to 100% the modal expansion would yield no SPL at all, clearly incorrect.
Earl,
Yes, agreed. The solution to to the wave equation in a reverberant, rectangular room is posed as two problems using superposition.
G(r|ro) = g(r|ro) + x(r)
where g(r|ro) is the free space Green's function ans x(r) is the solution to the to the homogeneous wave equation with appropriate boundary conditions. I have no argument there. But the way I interpreted Todd's remark was that he was expecting to see the free field SPL reappear is low frequency modes were eliminated, as would be the case in an anechoic chamber.
So certainly you can subtract off the contribution form the singularity, g(r|ro), and what remains is the contribution from X(r) which is the reverberant part of the solution. Likewise, once x(r) is found by that subtraction it could be subtracted leaving the free space result, i.e. the direct sound.
I also agree with Pan that as far as big room bass goes, the big room effect is captured on the recording. I believe this is very different than needing reverberation in a listening room above the Schroeder frequency to provide an illusion of "space".
Now, back to multiple subs. Are we placing them to smooth the response or at locations where modal contributions either cancel or are null? You claim your is the former. Todd's 4 woofer array with 1/4 L positioning seems to be the latter. If X and Z represent the plane of the floor, then such placement cancels odd order axial modes in the X and Z directions and the positions are nulls for 2nd , 6th 10th 14th... order even axis modes, and a bunch of tangential and oblique modes get eliminated as well. But what ever the approach, the modal behavior at the listening position have the final word as to which otherwise excited modes affect the SPL at that point.
john k... said:
John we've had this agrument before and I still don't agree. Yes you can seperate off the singularity part, which ends up being the free space Green's function, but what is left, the x(r) is not the same modal solution as the homogeneous solution to the wave equation. It will meet the boundary conditions, however it has a different set of coefficients in the series. I directed you to Morse the last time that you said this. I guess you didn't read it.
gedlee said:
This is semantics Earl. I never said anything about the form of X(r). But it's a smiple matter that if A = B + C and B is the direct sound from a point source and A is the total response including the reverberation, then subtracting of the direct field can only leave that fraction of the solution which represented the boundary conditions which give rise to the reflections. That is also right out of Morse, (in my own words).
gedlee said:
No there is not a problem. I've verified my code against FEM where possible. As you said in an earlier post, to paraphrase, the higher order modes don't contribute much to the low frequency response therefore only a few modes need be considered for low frequency. I find that to be true. If I run the modal index form 0 to 5 I see very little difference below 100 Hz compared to running the indexes for 0 to 10. So it seems quite reasonable that if I run the indexes from 5 to 10 the low frequency should drop off in general.
john k... said:
If you switch the source and the receiver the response has to remain the same. I thought you said it changed (which is wrong), but I think I misinterpreted your statement. Do you mean moving the source OR moving the receiver changes the LF level? (Now that I reread it I can see that's what you meant). In a normal room of course this would happen. Or do you mean even when there are no modes? In that case it does seem odd.
I'm still at a loss to understand what you are getting at.
Todd and I have studied this problem as much, if not more, than anyone else on the planet. We see things exactly the same. But you seem to disagree and I'm having trouble understanding why.
john k... said:
You did say that it was a solution to the homogeneous wave equation in a rectangular room. That's not correct. The solution of the homogeneous wave equation is an infinite set, of eigenfrequencies and eigenmodes, it IS NOT a series with set coefficients. The series only comes about when there is a source - the inhomogeneous solution. The set of coefficients for this series is well known, you show it yourself. When the free space Greens function singularity is subtracted off, a new series remains, but with a different set of coefficients. However, this new series IS NOT a solution of the homogeneous wave equation - its a series, not a set - and so it cannot be X(r) as you have defined it.
Maybe it is semantics, but then why not just say it correctly.
gedlee said:
From Morse
An externally hosted image should be here but it was not working when we last tested it.
Quicky derivation of the wave equation for sinusoidal pressure.
An externally hosted image should be here but it was not working when we last tested it.
Sure looks like the eqaution for X(r) to me. I'll stick by what I said, X(r) is a solution to the homogeneous wave equation with approppriate boundary conditions. Do I need to add the subsctipt, omega, to X(r)? Do I need to say a eignvalue problem requires an eigensolution? Are youy really telling me that since I know gw(r|ro) and I have a modal expansion for Gw(R|ro) I can't directly compute Xw(r) by subtraction for what ever frequency I desire? Do I need to write it down and post a picture?
gedlee said:
I think we all have the same goal, smooth bass response. But I don't think you and Todd are on the same page as to how to achieve it. It is clear from Todd's paper that his 4 woofer array is positioning to remove low frequency modal effects from the response.
This is in the plane of the floor. In reality a lot more modes are canceled, for example even order axial modes of order 6, 10, 14.... since these axial modes have nulls at the same location as the 2nd order axial mode. And there are a number of tangential and oblique modes that drop out as well. So I see Todd as looking to limit modal influence where as your approach is ad hoc push the woofers around to yield the smoothest response. You have said a number of time that elimination of modal contributions will not result in good sounding bass. That you want "big room bass". I don't see that as the same. If it is, Todd please correct me. If I look at it differently it is because I have no bias or preconceived notions. I'll look at the physics and come to my own conclusions.
john k... said:
I'll let you guys argue the maths, I probably am leaning more towards an engineering approach to things. I'm defining a goal (consistent bass response in the seats) and looking for the best solution.
The first paper (placement only) I would say that it does reduce modal excitation, however in SFM it makes more sense to say that the optimization simply tweaks the modal excitation to optimize the result at a few particular locations. I have found that the low frequency response in a room is much more complicated than one might think from the simple mode diagrams on a napkin that we all know and love (for their simplicity). For example, I have observed that the largest cancellations in the frequency response often occur between eigenfrequencies. Also the dips in the spatial response in the room exist and move around not just at the eigenfrequencies, but at frequencies near them. So, in general the response is more complicated than many realize. That's why I say that at least for SFM, saying it just reduces modal excitation might be an oversimplification.
Hi Todd,
I would call it arguing. It' just healthy discussion. From my seat it all very clear. If G is the green's function for the in room response, which includes all the boundary effects, and g is the free space (or unbounded) Green's function, and X the correction to the free space Green's function which brings in the boundary conditions then once I have an expression for G, and knowing g, I don't have to solve the wave equation to find out what X is. It's a simple matter of subtraction. It's like if I know between you and I we have $10 and I know I have $4 I don't need to ask you how much you have. Obviously some mathematician went through the trouble solving the wave equation for X in the process of coming up with the modal expansion for G. I don't see the need to repeat it. But I do know that as a result, X = G - g allows be to find the value of X(r) for andyvalue of r in the bounded region.
Also, remember that g is a smooth exponential
g = 1/(4 Pi R) exp(ikR)
So all those modes in the summation form of G ultimately arise from X. And there in lies another observation. Note that my quote from Morse says that if there are no boundaries X = 0. That is we have G = g = free space response = spatially smooth bass with only level dependent on listening distance. So in my mind the objective should be how to we make the room look like X = 0, at least from the point of low frequency reproduction. If that produces bass that is subjectively unsatisfactory, well that is a separate issue. But if you approach the problem form the other direction while you might get acceptable smooth low frequency amplitude response the time response will still be a mess. I've shown that by looking at the amplitude response at a given point in a room, equalizing to to match some woofer target response, then computing the impulse response and comparing it to the impulse of the target. The result is that even though the amplitude is good, the impulse is highly distorted, and generally rings well past the decay time for the target. Here is a sample result. The woofer is equalized to a 20 Hz Q= 0.5 HP and 120 Hz B4 LP. Green is what the impulse of such a response would look like in free space. Blue, in a room. I guess I just don't believe that booOOooooooom is going to sound better than Boom.
I would call it arguing. It' just healthy discussion. From my seat it all very clear. If G is the green's function for the in room response, which includes all the boundary effects, and g is the free space (or unbounded) Green's function, and X the correction to the free space Green's function which brings in the boundary conditions then once I have an expression for G, and knowing g, I don't have to solve the wave equation to find out what X is. It's a simple matter of subtraction. It's like if I know between you and I we have $10 and I know I have $4 I don't need to ask you how much you have. Obviously some mathematician went through the trouble solving the wave equation for X in the process of coming up with the modal expansion for G. I don't see the need to repeat it. But I do know that as a result, X = G - g allows be to find the value of X(r) for andyvalue of r in the bounded region.
Also, remember that g is a smooth exponential
g = 1/(4 Pi R) exp(ikR)
So all those modes in the summation form of G ultimately arise from X. And there in lies another observation. Note that my quote from Morse says that if there are no boundaries X = 0. That is we have G = g = free space response = spatially smooth bass with only level dependent on listening distance. So in my mind the objective should be how to we make the room look like X = 0, at least from the point of low frequency reproduction. If that produces bass that is subjectively unsatisfactory, well that is a separate issue. But if you approach the problem form the other direction while you might get acceptable smooth low frequency amplitude response the time response will still be a mess. I've shown that by looking at the amplitude response at a given point in a room, equalizing to to match some woofer target response, then computing the impulse response and comparing it to the impulse of the target. The result is that even though the amplitude is good, the impulse is highly distorted, and generally rings well past the decay time for the target. Here is a sample result. The woofer is equalized to a 20 Hz Q= 0.5 HP and 120 Hz B4 LP. Green is what the impulse of such a response would look like in free space. Blue, in a room. I guess I just don't believe that booOOooooooom is going to sound better than Boom.
An externally hosted image should be here but it was not working when we last tested it.
booOOooooooom is going to give an impresson of more boom than Boom. Some people think it's better. It creates a more sensational experience even though it may not be real. Additionally, when at frequencies below the room modes, it becomes difficult to get the Boom effect so there needs to be a way of creating it.
Hi George,
My response would be that once you achieve Boom you can manipulate it to boOOooom or what ever you like (BOooOOooom) fairly easily. But going the other way is very difficult. That, I believe, is exactly why we see these different attempts at low frequency response in small rooms with different people claiming theirs is the best approach. Even the approach I have recently experimented with, while moving is the direction I think is correct, has significant limitations and flaws. The only approach I have seen that moves unilaterally in the correct direction (IMO, according to my simulations) in terms of both amplitude and time response is the DBA. The argument that it is impractical, or inefficient are implementation issues and not something that concerns me. I can tell you right now that I will at some point set up a DBA 4x4 system and listen to it before I pass any judgment on it.
My response would be that once you achieve Boom you can manipulate it to boOOooom or what ever you like (BOooOOooom) fairly easily. But going the other way is very difficult. That, I believe, is exactly why we see these different attempts at low frequency response in small rooms with different people claiming theirs is the best approach. Even the approach I have recently experimented with, while moving is the direction I think is correct, has significant limitations and flaws. The only approach I have seen that moves unilaterally in the correct direction (IMO, according to my simulations) in terms of both amplitude and time response is the DBA. The argument that it is impractical, or inefficient are implementation issues and not something that concerns me. I can tell you right now that I will at some point set up a DBA 4x4 system and listen to it before I pass any judgment on it.