With regards to a room I would say it depends on how you define "system". Referring back to my equation for the SPL at a point in a room, there are an infinite number of system functions for the 3-D space. However, once the source and listening positions are defined we can consider the source-listener transfer function for SPL to be the system function for that "system". It will or will not be minimum phase. Now when I say MP let me expand. Any system function can always be decomposed into MP and an all pass components. We can therefore always define the inverses system function of the MP component. The problem then lies with the all pass component. The all pass component will contain all the phase deviation form MP. If this is the result of a simple delay then it is of no consequence since it would only mean that what we would hear is a MP response as but later time. In this case we can consider the system function reducible to a MP response and correctable by MP eq. However, if the all pass is not linear phase it is not a simple delay, and since by definition it is not MP, then a stable, casual inverse does not exist and the arbitrary phase distortion it represents can not be corrected, at least not in real time.
But even if the in room system function between source and listener is reducible to MP, we still have the problem that the system function is different for every change in listener or source position. So the best we could hope for is to find a single listening where the response is reducible to MP and eq for that position. That may be fine for a single listener but does little for a broad seating arrangement.
So we might ask when is the source-listener system function reducible to MP? The first requirement is that the source must be MP. From there is becomes rather complex and a general statement can not be made. It would be, in theory, necessary to examine the system function for each specific source/listener position. However, there do seem to be a few exceptions. The first is when the listener is very close to the source. The second, and I say this with caution since I haven't fully investigated it, is when only those modes in a given direction contribute to the system function. Such a situation might exist, for example, if the listening environment were a quais-anechoic chamber where only the forn and back walls were reflective. That is, only axial modes in the front to back directions would contribute to the system function. The picture below shows a simulation of such a case.
Here the green trace is the response of a MP system with 20 Hz, Q=0.5 HP and 120 Hz B4 LP response. The blue line is the response at the listening position when the system function is eq'ed to the same response. In this case the response is very similar to that of the MP system, only delayed.
But even if the in room system function between source and listener is reducible to MP, we still have the problem that the system function is different for every change in listener or source position. So the best we could hope for is to find a single listening where the response is reducible to MP and eq for that position. That may be fine for a single listener but does little for a broad seating arrangement.
So we might ask when is the source-listener system function reducible to MP? The first requirement is that the source must be MP. From there is becomes rather complex and a general statement can not be made. It would be, in theory, necessary to examine the system function for each specific source/listener position. However, there do seem to be a few exceptions. The first is when the listener is very close to the source. The second, and I say this with caution since I haven't fully investigated it, is when only those modes in a given direction contribute to the system function. Such a situation might exist, for example, if the listening environment were a quais-anechoic chamber where only the forn and back walls were reflective. That is, only axial modes in the front to back directions would contribute to the system function. The picture below shows a simulation of such a case.
An externally hosted image should be here but it was not working when we last tested it.
Here the green trace is the response of a MP system with 20 Hz, Q=0.5 HP and 120 Hz B4 LP response. The blue line is the response at the listening position when the system function is eq'ed to the same response. In this case the response is very similar to that of the MP system, only delayed.
John
Agreed - I had the same idea about axial modes only.
I have never seen a proof that an arbitray point in a real room would be minimum phase or not. It seems unlikely to me since the requiremenets for MP are reasonably restrictive - in a sense.
It seems (guessing here) that any system with pure delays - no matter how many - would still be MP. But as soon as there is any frequency dependence of any of those delays then the resulting system could no longer be MP. Since all acoustic sources have angle dependent FRs any reflections would have to create Non-MP responses.
It might then be possible to get a near MP response at LFs, but clearly this is not possible at HFs.
Agreed - I had the same idea about axial modes only.
I have never seen a proof that an arbitray point in a real room would be minimum phase or not. It seems unlikely to me since the requiremenets for MP are reasonably restrictive - in a sense.
It seems (guessing here) that any system with pure delays - no matter how many - would still be MP. But as soon as there is any frequency dependence of any of those delays then the resulting system could no longer be MP. Since all acoustic sources have angle dependent FRs any reflections would have to create Non-MP responses.
It might then be possible to get a near MP response at LFs, but clearly this is not possible at HFs.
gedlee said:
Earl,
You recommend to have as much damping as possible in the lower frequency domain. The idea behind is that it will provide a smoother low frequency field, meaning that the tops and the valleys coming from the room modes will be respectively less high and less deep.
My readings about acoustics told me that the higher the damping, the lower the decay rate.
So, somehow, you are looking for quite fast decay rate at low frequency even if your primary goal is the high damping, isn't it?
I'm confused...
Regards,
Etienne
Etienne
That high damping reults in high decay is obvious, but its actually the modal interaction that results form the broader modes that I am interested in. I mean really, its all good - lower peaks, shorter decay, broader modes, beter coupling. Which is the "most important" is kind of moot. I dod not see the interest in whether or not EQ changes the decay rate - I just don't see the importance.
Ideally, in my mind, I would heavily damp the LFs in a small room, but then add back LF reverberation - i.e increase the decay rate. However, please note here that this added reverb is broadband NOT modal - big difference.
That high damping reults in high decay is obvious, but its actually the modal interaction that results form the broader modes that I am interested in. I mean really, its all good - lower peaks, shorter decay, broader modes, beter coupling. Which is the "most important" is kind of moot. I dod not see the interest in whether or not EQ changes the decay rate - I just don't see the importance.
Ideally, in my mind, I would heavily damp the LFs in a small room, but then add back LF reverberation - i.e increase the decay rate. However, please note here that this added reverb is broadband NOT modal - big difference.
gedlee said:
This exactly is why I (and others ...) thought (and still think) that the speaker-room system can considered to be MP at LFs. And (that's where the discussion started over there at the forum where Markus took my images from): One consequence of a MP system is that constant amplitude response inevitably means that phase response is also constant.
Returning to the Geddes approach to multiple sub placement, this means that by optimizing the amplitude response at LFs (it's the only frequency range where the MP approach is valid!) you're optimizing phase response (this includes settling and ringing) as well.
Agreed
But then a decay rate change - or not - is kind of unimportant because if you get the amplitude right then everything is right. But I'd also say that the system being MP - or not - is not that important either. Phase and decay rate just don't seem that important to me at LFs when compared to the vastly larger problem of creating even a reasonably smooth response in space and frequency.
Its a little like worring about the color of your lipstick when you go out but forgot to put your clothes on. No one is going to notice.
But then a decay rate change - or not - is kind of unimportant because if you get the amplitude right then everything is right. But I'd also say that the system being MP - or not - is not that important either. Phase and decay rate just don't seem that important to me at LFs when compared to the vastly larger problem of creating even a reasonably smooth response in space and frequency.
Its a little like worring about the color of your lipstick when you go out but forgot to put your clothes on. No one is going to notice.
Fine.gedlee said:
gedlee said:
Since you are not listening to steady state sine waves, a constant amplitude response alone wouldn't help much. That's exactly the point: "If you get the amplitude right then everything is right" is only valid for MP systems. I am pretty sure (at least I hope so) that you wouldn't state this for the frequency range > 500Hz.
Of course not. We are only talking about modal dependent issues here, this is about multiple subs. Once one is above the modal region everything changes. The audibility of group delay and non-MP aberations - which can have flat amplitude response - is a very real concern.
I'm not sure that I understand the statement:
"Since you are not listening to steady state sine waves, a constant amplitude response alone wouldn't help much. "
I don't see the connection between the two things.
I'm not sure that I understand the statement:
"Since you are not listening to steady state sine waves, a constant amplitude response alone wouldn't help much. "
I don't see the connection between the two things.
gedlee said:
Constant amplitude response and absence of settling and ringing (of resonances) is only guaranteed in MP systems. In non-MP systems you can have ringing without affecting the amplitude response - simply by adding a (strongly) frequency dependent all-pass/delay. But in this case you won't see settling and ringing in steady state.
As an example: Ringing of a square wave at constant amplitude response but non-constant group delay (all-pass with high Q factor): Group delay and transient response. Quote: "If the allpass Q0 is significantly higher, like Q0 = 2.5, then the phase distortion does become audible. In the case of the 100 Hz square-wave a high pitched sound is added. The frequency response, though, is completely flat."
But I thought that we had decided that the LF modes were at least "nearly" MP. In which case what you describe wouldn't apply.
All that you say is well know but I'm still not sure that I follow the connection to the discussion at hand. Decay rate only has a meaning for non-steady state signals.
All that you say is well know but I'm still not sure that I follow the connection to the discussion at hand. Decay rate only has a meaning for non-steady state signals.
Multi subs + dipole mains
Sorry to interrupt the MP debate. Perhaps a new, but plenty on-topic thought for discussion will be welcome:
I will be sampling the Geddes multi-sub approach soon (when my new nicely-damped listening cave is complete), but initially using dipole mains, rather than monopole mains as assumed in the discussion-to-date. Sub 2 will be a modest IB located above wall midpoint, Subs 1 and 3 boxed. Dipole mains strong down to ~50 Hz, so they are certainly IN da mix.
As I grasp the concept, my application of the method should be unchanged, regardless of the radiating pattern of the numerous sources, Correct? --place mains where they "work" best, then Methodically optimize/dial-in the subs in succession -- the METHOD accounts for whatever actual phase and modal excitation issues occur with any given setup in the room, so source radiation pattern (below Schroeder freq) is MOOT.
Comments? Detractors be gentle - I'm recovering from hernia surgery this week . . .
--TubaMark
Sorry to interrupt the MP debate. Perhaps a new, but plenty on-topic thought for discussion will be welcome:
I will be sampling the Geddes multi-sub approach soon (when my new nicely-damped listening cave is complete), but initially using dipole mains, rather than monopole mains as assumed in the discussion-to-date. Sub 2 will be a modest IB located above wall midpoint, Subs 1 and 3 boxed. Dipole mains strong down to ~50 Hz, so they are certainly IN da mix.
As I grasp the concept, my application of the method should be unchanged, regardless of the radiating pattern of the numerous sources, Correct? --place mains where they "work" best, then Methodically optimize/dial-in the subs in succession -- the METHOD accounts for whatever actual phase and modal excitation issues occur with any given setup in the room, so source radiation pattern (below Schroeder freq) is MOOT.
Comments? Detractors be gentle - I'm recovering from hernia surgery this week . . .
--TubaMark
would be interesting to know what kind of music you listen to. Posting covers of CDs and LPs used for listenign tests is a given when they are serious. Most of the time when we see the cover, we know if we have it in our collections.
Normally hernia takes about a week to recover, so probably the hard stuff next week.
Normally hernia takes about a week to recover, so probably the hard stuff next week.
gedlee said:
Exactly. That's the point.
With your approach you are optimizing the amplitude response. Since the speaker-room system is MP at LFs, you are optimizing phase response and the transient response as well. That's why your approach is useful. If the system wasn't MP at LFs, your approach probably wouldn't be useful.
The only point we seem to disagree upon is the usefulness of the MP concept for the problem at hand.
soongsc said:
I don't think it's a valid way if the wavelenghts are not notably smaller than the dimensions of the room. The source image method works like ray optics. For ray optics the wavelenghts have to be significantly smaller than the dimensions of the objects involved (mirrors, apertures, slits, ...).
At LFs in small rooms (that's what we're talking about here, right?) the wavelengths are not significantly smaller than the dimensions of the room.
mat02ah said:
It doesn't hold. MP is not valid at low frequency. Here is a series of figures based on simulation where we can control which modes are included constructing the SPL response at a point in a room.
An externally hosted image should be here but it was not working when we last tested it.
The top three response plots are each for the case where only the DC mode and a the first axial mode in either the x, y or z direction are included in the response calculation. In all three cases the response is reducible to a MP response as is indicated by the thin blue line overlaying the thicker green line. The thicker green line is the computed phase of the response and the thin blue line is the MP corresponding to the amplitude.
Now look at the bottom three curves. In this case the response is composed of the DC mode, the first axial mode in each direction, the first three tangential modes and the first oblique mode. All these modes result from consideration of the DC mode and combination of the first axial mode in each direction. At the left we see the amplitude response in violet, the computed phase in green and the MP corresponding to the amplitude in green. The second curve shows the phase of the all pass component of the computed response curve, and the phase which would result if the all pass were a constant delay with the first wrap in phase occurring at the same frequency as the all pass phase. It should be apparent that the all pass phase is not a pure delay. The third figure on the bottom right is a plot of the reconstructed in room response found by multiplying the MP response times the all pass response. As you can see, it is identical to the green phase shown at the left.
What this shows is that even when only the very low frequency modes are considered the response is still not MP at low frequency. There is a highly nonlinear, non MP component to the phase. The only way for the in room response to be reducible to MP (that is, MP plus a pure time delay) is to have the listening position very close to the source. In such a case the direct sound dominated and if the direct sound is MP then the sound at the listening position can also be MP, though it won't necessarily have the same amplitude as the source. Think of it like this; very, very close to the source we would measure the radiation of the source (a near filed measurement). As we move the measurement point away the relative strength of the reflected sound increases. At first this only introduced ripples in the response which remain MP. However, as we move further away for the source the relative strength of the reflected sound may start to dominate the response and there is a departure form MP.
I started putting this together last night but didn't get to post it until this morning so I guess there are several posts in between.
Just another brief addition. You must also consider that the contributions from different modes can also be inverted in phase depening on the sign of the eigen function of that mode at both the source ans listener position. So the sumation over many modes means many in and out of phase contributions.
john k... said:
What simulation? How was it done? Your own software? What conditions were used, what assumptions were made? You certainly don't expect anyone to accept these barely readable screen shot cut-outs as proof of anything, do you?
How is this simulation going to look like, if you simulate multiple subs (either the randomly placed for best amplitude response or symmetrically)? Will your simulation show the same improvements the measurements show?
john k... said:
Where does this non-linearity come from? Why is the superposition principle not valid here? This is where you could convince me.
edit: Quote from your web site: "We must recall that the in room SPL can be considered as being built from sum of the responses of the excited modes."
So you're considering this to be a linear system.
How can the summation of modes that are MP be non-MP?
Or are some of the modes you included (tangential or oblique ones) non-MP by themselves?
If the speaker-room-system is not MP, then looking at a steady state amplitude response as Earl suggests shouldn't be enough to optimize LF performance. Are you saying that? Or are you saying that phase and transient response don't matter at LF?
As long as one dimension is longer than the wavelength of interest, then there is a mixture of non-minimum phase which makes the whole analysis and measurement non-minimum phase.mat02ah said:
If anyone can tell by what criteria room response can be considered minimum phase, then we can face the issue in a very clear technical approach.