soongsc said:
Why? And why is the limit exactly at one wavelength? A similar question goes to john k.: Why is the transfer function subwoofer -> listener minimum-phase if the sub is not too far away? Does the transfer function become gradually non-MP or abruptly as the distance increases?
Furthermore, a room of say 4x5x2.5m (typical german living room) would be miminum-phase below 68Hz then, correct?
I really wish people would somehow try to prove their statements. Unfortunately (for me ...) those how say "rooms are minimum-phase at LF" (this statement is not uncommon) prove - nothing.
I think a very simple way is to first determine at what frequency you can consider the measured room setup minimum phase, send a simple sine wave in, and see what you get at the mic over a period of time. For a system to be considered minimum phase, the measured output should not vary much with time. Let's see someone do that with a room with multiple subs. I think you will find that only when room dimensions get close to half wave length of interest will you be able to see this characteristic. In most cases, you probably won't be able to see a decent sine wave at the output (listening position) with multiple subs.mat02ah said:
Why? And why is the limit exactly at one wavelength? A similar question goes to john k.: Why is the transfer function subwoofer -> listener minimum-phase if the sub is not too far away? Does the transfer function become gradually non-MP or abruptly as the distance increases?
Furthermore, a room of say 4x5x2.5m (typical german living room) would be miminum-phase below 68Hz then, correct?
I really wish people would somehow try to prove their statements. Unfortunately (for me ...) those how say "rooms are minimum-phase at LF" (this statement is not uncommon) prove - nothing.
mat02ah said:
I'm not going into a discussion about the software. It is certainly more linear than the real world. And with multiple woofers is does just fine.
Supperposition applies, not because the modal transfer functions are linear (in fact, they are not) but because the system from which they originate is linear. It is the linearity of the system which allows us to apply supperposition. (Note: in the real world the room itself, as a system, may not be a linear system.) This means that at any frequency the output is the sum of the output from all modes at that frequency. But the response is not the result at one frequency. It is the response as a (nonlinear) function of frequency. Remember it is a system that is stable and causal that is MP. That does not mean the system function is linear in either amplityde or phase. If fact the only MP system that is linear in amplitude ans phase is a flat MP response.
I'm not saying phase and transients don't matter. I am saying you can not correct phase using MP eq applied to the source unless the response at the measurement point is MP to start with. Earl's approach can only optimize amplitude response, not phase and transients.
I disagree with Earl and any research that say decay rate doesn't matter. After all, if we start with the same amplitude signal and in one case it decays by 60dB is 1 sec and in another case it decays in 10 seconds we just going to hear the 2nd case 10 time longer. Now Earl said that research indicates we aren't sensitive to decay rate. So I guess what is missing is what exactly is meant by sensitive?
Let me see if I can give you a simple example of how the output of two simple linear, MP systems sum to a non-MP result. Consider a a system composed of LR4 HP and LP electrical filters. Both the HP and LP filters hav eMP outputs derived from linear systems. When their output is summed the response is perfectly flat. A perfect flat MP response has zero phase shift. But the summed LR4 HP and LP response introduce a 360 degree phase shift. The sum is not MP.
mat02ah said:
I really wish people would somehow try to prove their statements. Unfortunately (for me ...) those how say "rooms are minimum-phase at LF" (this statement is not uncommon) prove - nothing.
It is not a matter of proof. If you have read my comment thoroughly you would have read that if you are close enough to the source then the response can be MP, if the source is MP. When and if the transition to non-M occurs, as I have said repeatedly, is a matter of the relative strengths and delays of the reflected sound compared to the direct sound.
Now it you want someone to demonstrate that the sum of the direct sound plus some number of delayed reflections of varying magnitude can be non-MP then I would suggest that you look at Kates' 1977 AES article on loudspeaker cabinet reflection effects. He considers a minimum phase source and points of reflections giving rise to primary and secondary reflections. He then goes on to show the limitation on the amplitude of the reflections which would render the sum of the direct and reflected sound MP.
Now consider staring in an anechoic chamber. Provided the sound radiated from the in the direction towards some measurement point was MP, then the sound at the measurement point will also be MP. As the absorption of the walls in the chamber is reduced we introduce reflections and at some point the amplitude of the reflections will be sufficient to render the response at the measurement point non-MP. So it is not a matter of proving this one way or the other. The in room response can be both MP and non-MP depending upon where in the room the measurement is taken and the relative strength of the direct and reflected sound at that point.
At least we seem to be getting somewhere ...
I would have said nearly the same: If the speaker-room system is not MP at LFs, Earl's approach can only optimize amplitude response, not phase and transients.
It was (and - sorry - somehow still is) my opinion that the usefulness of Earl's approach is based (among others like averaging over multiple, pseudo-random listener positions) on minimum-phase properties of the speaker-room system at LFs which allows you use only the amplitude response as the parameter to be optimized.
Obviously, Earl disagrees on this point as well, right?
Ah, finally ... point taken. But it's an example where the two transfer functions cancel each other out in the amplitude response. Which makes me think the following:
Could it be that the idea of a MP LF response of the speaker-room system requires modes/resonances that do not (within reason ...) overlap in the amplitude response or that you can see clearly ringing in a waterfall diagram? At least for these modes/resonances I would still expect the total response to be (nearly) MP. That's probably where the "minimum-phase at LF" idea started: At LFs (where the mode density is low) modes can show up as discrete peaks in the amplitude response and can be treated independently. If the single modes are MP then the LF range can be approximated as MP. Sounds reasonable to me ...
Which leads me to the "proof" thing: I haven't read much more than blanket statements like "rooms are MP at LF". I'd like to read something where somebody explains why. There has to be a reason for this assumption.
john k... said:
I would have said nearly the same: If the speaker-room system is not MP at LFs, Earl's approach can only optimize amplitude response, not phase and transients.
It was (and - sorry - somehow still is) my opinion that the usefulness of Earl's approach is based (among others like averaging over multiple, pseudo-random listener positions) on minimum-phase properties of the speaker-room system at LFs which allows you use only the amplitude response as the parameter to be optimized.
Obviously, Earl disagrees on this point as well, right?
john k... said:
Ah, finally ... point taken. But it's an example where the two transfer functions cancel each other out in the amplitude response. Which makes me think the following:
Could it be that the idea of a MP LF response of the speaker-room system requires modes/resonances that do not (within reason ...) overlap in the amplitude response or that you can see clearly ringing in a waterfall diagram? At least for these modes/resonances I would still expect the total response to be (nearly) MP. That's probably where the "minimum-phase at LF" idea started: At LFs (where the mode density is low) modes can show up as discrete peaks in the amplitude response and can be treated independently. If the single modes are MP then the LF range can be approximated as MP. Sounds reasonable to me ...
Which leads me to the "proof" thing: I haven't read much more than blanket statements like "rooms are MP at LF". I'd like to read something where somebody explains why. There has to be a reason for this assumption.
mat02ah said:
There are so many misleading points in the discussion that its hard to follow. John uses the term "linear" in a manner not consistant with "linear systems theory" and this gets confusing. He seems to mean "flat" or "straight" when he says "linear", but I guess I don't know what he means when he says that the modes are not "linear". The wave equation IS linear and anything derived from it is linear.
And I agree that if the system is not MP then my technique will not "prefectly" correct the magnitude and phase or transients at LFs, to which I say, "So what?". John uses an extreme example of 1 second versus 10 seconds and yes in this case the longer time decay will be more audible. But in reality we are talking about differences of milliseconds and these differences would not be audible. At LFs its the amplitude response that dominates the problem, MP or not MP, and correcting the amplitude response will be a vast improvement in the perceived quality regardless of any effect on the phase (whcih is completely irrelavent) or the decay (which is insignificant within the values found in a real room.)
As to the "a room is MP" or not question. We must always assume non-MP as this does not require any assumptions. One must then prove that the room is MP and I have not seen this, nor do I see any reason why it should be. Clearly, the conditions for MP are more likely to be obtainable at LFs than HFs. So I would agree that its "likely" that the room response is "nearly" MP at LFs and as such correcting the magnitude also goes a long way towards correcting the decay and phase. But even if it doesn't, correcting the magnitude is still the right thing to do.
But one thing that has not been shown is why it is assumed that because a room does not meet the conditions for MP that it should have the same characteristics as an electronic circuit that is not MP. I do not see how one can make this assumption. In other words, since a real room has a multitude of transfer functions can one assume that minimizing the "mean magnitude response" of these functions does not minimize their "mean decay" just because one or more of those transfer functions is not MP, or even if all of them are not MP. I just don't see how this leap can be made. Its certainly not been shown.
This thread and other reading convinced me to start playing with sub placement and measurements, which has further convinced me to add additional subs. Right now, my "subs" are incorporated into the mains. These subs are crossed over to the mid bass at 80 Hz using a transient perfect filter, calculated with John's program. My plan is to leave those as is, and add additional subs to smooth out the overall room response.
However, the midbass unit has significant output below 80 Hz. Dr. Geddes recommends allowing the mains to run to their full extension and blend in the subs. The question is; should I treat the sub portion of my mains as just an extended main speaker and blend in the additional subs with the mains as they are now? Or, should I treat the mains subs, as I do the added subs and blend them as I would the added subs? I'm leaning toward the former, but eliminating the EQ that I have added to the lower couple of octaves.
Sheldon
However, the midbass unit has significant output below 80 Hz. Dr. Geddes recommends allowing the mains to run to their full extension and blend in the subs. The question is; should I treat the sub portion of my mains as just an extended main speaker and blend in the additional subs with the mains as they are now? Or, should I treat the mains subs, as I do the added subs and blend them as I would the added subs? I'm leaning toward the former, but eliminating the EQ that I have added to the lower couple of octaves.
Sheldon
gedlee said:
Earl,
I use the term linear in the only way it applies: A system is a linear system if the equation governing the behavior of the system is linear.
F = M x" + B x' + k x
is the equation for a linear spring, mass damper system.
F = M x" = B x' + k x^2
is a nonlinear system
However the transfer function (or system function) for the linear system need not be linear and in general is not.
For example, a 2nd order LP filter has
T(s) = 1/(1 +Qs + s^2)
This is not a linear function (of s).
But
O(s) = T(s) x I(s)
constitutes a linear relationship between input and output because T(s) is not a function of I(s). It is just a scale factor which is constant for any fixed value of s, but varies (nonlinearly) with s. That was the point I was trying to get across. I was trying to clarify the difference between a system being linear and whether or not the system's transfer function is linear or not. I guess I confused things instead of making the distinction clearer.
I would also agree that even if the room response is MP at some x,y,z point in the room, so what? In that case the response can be corrected in both time and amplitude, but what about the rest of the room? As you and I have both indicated the in room response is composed of an infinite number of transfer functions, even for fixed source location, one for ever x,y,z coordinate defining a point within the room boundaries.
For a given amplitude response there's only one way for a system to be MP but there are many ways (infinite?) to be non-MP. So, being "non-MP" doesn't make systems comparable.gedlee said:
gedlee said:
I was trying to make the leap in the other direction: If the transfer function(s) were MP, improving the flatness (I guess that's what you meant instead of 'minimizing') of the mean magnitude response of these functions will minimize decay.
In terms of logics: (flat AND minimum-phase) -> perfect transient.
The negation of this
NOT(flat AND minimum-phase) -> NOT (perfect transient)
is of course not necessarily true.
"Ex falso sequitur quodlibet " - From falsehood follows anything.
I still think that the (near) MP property of the speaker-room system at LFs is one of the reasons why your optimizing method works and is justified. I'm stubborn, I know ...
John
I still think that your use of the term "linear" in the context that you were using it was not consistant with "linear systems theory" where the filter is still linear even though the transfer function is not a linear function of omega. The assumption of superposition still holds and hence the transfer function is "linear" in the systems theory sense. Only confusion will result if you change this convention.
I still think that your use of the term "linear" in the context that you were using it was not consistant with "linear systems theory" where the filter is still linear even though the transfer function is not a linear function of omega. The assumption of superposition still holds and hence the transfer function is "linear" in the systems theory sense. Only confusion will result if you change this convention.
mat02ah said:
I don't know that this is true. I am not talking about a single transfer function, but an average of many. I don't think that it follows that minimizing the average magnitude deviation from the mean (to be more precise) will minimize the average decay, or any decay. You would need to prove this, not just state it. But don't bother, because its really academic. If it were important I might look at it myself, but I don't see it as important. What I want to do is minimize the average deviation from the mean and I really don't care what else this does. (Although I suspect that it does work as you suggest, I just don't see this as something that you can assume.)
I would be careful mixing the terms "system" and "transfer function" as they are not synonimous. A system, such as a room, can have many transfer functions, but is still only one system. You can talk about any one transfer function being MP, but I am not sure that the system can be so easily described if there are many transfer functions and not all of them need be MP. Any one of them might be, but the system would not then become MP for all the others.
""Ex falso sequitur quodlibet " - From falsehood follows anything."
Thats a great phrase. I'll remember it.
Sheldon said:
I would make the mains as smooth as possible for a free field situation, then leave them fixed and place them for best usage as stereo sources. Then add in the subs and manipulate only those. If there is room EQ used then this can be global in the sense that all LF sources are affected, but you can also do this only the subs only. Although there could be situations that may be more effective globally applied. In other words, the mains COULD excite a particular mode that the subs had a hard time correcting, in which case EQing only the subs would not be very effective. But this is completely situation specific.
It's true that I've been thinking about a single transfer function (fixed speakers, one listening position).gedlee said:
This of course depends on the definiton of the system. If you make the listener (and the speakers) part of the system, the system has one transfer function. If you have multiple listeners, it's certainly useful to split it up into one system (speakers + room) with multiple outputs (listeners). Point taken.gedlee said:
It's a basic principle of logics. From:gedlee said:
it rains -> the street is wet
does not necessarily follow (but may follow)
it does NOT rain -> the street is NOT wet
because someone might be hosing the street ...
To summarise: Methods for multiple sub placement strictly optimize for minimum variations of the amplitude response at multiple listening positions. Transients, decay are not taken into account. Welti and Devantier (2006) are very clear about this - they never mention it (they do however mention (non-)minimum phase transfer functions). Your statements here about this are also clear. And while the assumption of minimum-phase at LFs may sound reasonable and may explain, why optimising amplitude response using multiple subs can or could also improve transient response (decay), it's just that: An unproven assumption.
It's embarrassing: Earl, is there a paper of you describing your method? Up to now my informations are "second hand" ... I didn't find anything in the AES E-library and google wasn't helpful neither. If there is one, do you happen to have an electronic pre-print?
I am glad that we managed not to turn this into a flame war. Sorry if I was a bit direct (rude...) at times. A discussion like this would be so much easier sitting at a table and having paper and pencil at hand ...
Thomas
gedlee said:
I guess I have to disagree. Superposition holds only because because the the system equation (the PDE of the system) is linear. The transfer function is just a convenient means of expressing the the solution of the system equation to any input that can be expressed as exp(st) where s is s general complex number s = a + jb. Superposition allows us to say that the solution to and input of the form I(s) = exp(s1 x t) + exp(s2 x t) + ....+ exp(sn x t) is the sum of the solutions for each additive component the input.
But let's agree to drop it because it isn't going to help here.
mat02ah said:
Not to wax on endlessly on this but it's not something that can be subjected to proof. However, in any specific case, like your listening environment, it is a simple matter to set up a sub, or multiple subs, measure the response and decompose it into minimum phase and an all pass components and see if the allpass is a pure time delay.
Here is such a result for a single woofer.
An externally hosted image should be here but it was not working when we last tested it.
I have presented the data in two equivalent formats. The upper plot shows the the measured phase data in green and amplitude in fuchsia. The thin blue line overlaying the phase data is the MP computed from the measured amplitude data with the addition of a delay of about 14 msec. There is good agreement up to about 35 Hz but above that the deviation from MP plus delay indicated that the measurement is not just MP with a delay, but some non-MP response.
In the lower figure I removed a 14 msec delay from the measured data rather than add it to the MP result. The thin blue phase line is therefore just the MP computed from the measured amplitude. Again, there is agreement to only about 35 Hz. Here we see a phase wrap associated with the notch at 40 Hz where as the MP phase shows a wiggle. above 40 Hz it looks like the MP response follows the measured data for a while but remember to compare the data the 360 degree phase rap must be accounted for. This is a clear indication of non-MP response.
For what it's worth, here is a simulation of the response of the woofer system to a 1. msec pulse:
An externally hosted image should be here but it was not working when we last tested it.
Green is the pulse, brownish red the response when the woofer is MP and blue the response of the woofer based on the measured phase. No amplitude eq has been applied in either case.
And while I'm at my desk, here is a simulation of the impulse response when the amplitude is eq'ed to the smooth response shown in red in the upper plot of the figure below. The red impulse trace is what would happen is the woofer response was MP and the blue response is what happens when the actual woofer response is eq'ed to the smooth response. As can be seen, due to the non-MP nature of the real woofer response, when the amplitude is eq'ed there is still a lot of trailing "noise in the impulse.
An externally hosted image should be here but it was not working when we last tested it.
Nothin' say lovin' like something from the oven.
mat02ah said:
Thomas
No, I have never gotten arround to writting it up - thats embarassing! Life has been just too hectic for me the last few years. Markus wrote up the proceedure, but I have never published my results comparing my approach with Welti.
Discussions like this can often get out of hand and would be better in person, but alas thats not going to happen, so struggling with the difficulties of the format are what we have to learn to do.
John
Interesting results. What software do you use for the simulations?