Multiple Small Subs - Geddes Approach

[gedlee]

Originally posted by mat02ah


The point was Earl's statement "No electronic system can do this". And he said this in order to "prove" that my experiment (whose results were presented incomplete here at diyaudio.com and without asking me) and the results are wrong.

Frankly, his statement shows lack of very basic knowledge and is a bit surprising considering Earl's profile as all knowing acoustics guru.

You misunderstood my point. My point was that the room response was NOT minimum phase, which John agrees with. I was not trying to prove your experiments right or wrong, just pointing out that in theory the decay is independent of the level and can't be argued from a minimum phase standpoint. If your experiments disagree with this then they are in question.

And you didn't just quote "No electronic system can do this", which I agree is not completely true since it is possible to do a non-minimum phase electronic system, but you quoted the whole statement about the acoustic example, implying that it was wrong, and its not. If you think that the room acoustic example is wrong then you need to read Morse like I suggested.

But at any rate John and I agree on this point and maybe its you who doesn't understand it.

[gedlee]

Originally posted by markus76


Aki Mäkivirta et al from Genelec show increased decay rates after EQing in this paper:
http://www.genelec-ht.com/documents/...aes111th_2.pdf

If you consider the example that I gave then it could be possible for either an increase or a decrease to happen depending upon the rates of two different systems and which one prevails in energy at the onset. So I guess that it would be possible for the apparant rate to change depending on how the intial conditions were set up in two different scenarios. But the actual system rates are not changing only the combinations of two - or more I suppose - different rates.

[mat02ah]

Originally posted by gedlee
My point was that the room response was NOT minimum phase, which John agrees with. I was not trying to prove your experiments right or wrong, just pointing out that in theory the decay is independent of the level and can't be argued from a minimum phase standpoint. If your experiments disagree with this then they are in question.

You wrote "The EQ does nothing more than reduce the energy injected, it can't change the energy lost". This completely ingnores the settling and the decay of the PEQ filtering.

Of course the decay rate of the mode does not depend on the level if things are linear. But the minimum-phase PEQ does more than a constant reduction of level - it settles and decays as well. And if you can fully compensate (frequency AND time or phase) a phenomenon with a minimum-phase PEQ I think it's save to assume that the phenomenon itself is minimum-phase as well.

So, if things are linear, why are 10 or 20 modes not minimum-phase, if one mode is?

I've repeated the experiment with a lower Q so that it's within the parameter range of the PEQ in Audacity. Results are shown here.

[john k...]

Originally posted by mat02ah




So, if things are linear, why are 10 or 20 modes not minimum-phase, if one mode is?

Linear has nothing to do with it. Why the sum of 10 or 20 modes is of is or is not minimum phase is a complex mathematical problem. It depends on how the modes sum, relative amplitudes and delays..... It is an easy task, however, to take a measurment (at a point) and determine if it has minimum phase characteristics which can then be corrected in amplitude and time using minimum phase eq. What is required is that the measured response be reducable to a minimum phase response plus a constant (or zero) time delay. You will find that, unless you are sufficiently close to the sound source, this will not be the case for an in room response.

[mat02ah]

Originally posted by john k...

Linear has nothing to do with it. Why the sum of 10 or 20 modes is of is or is not minimum phase is a complex mathematical problem. It depends on how the modes sum, relative amplitudes and delays.....

Linear of course has to do with it. If you have n modes and you can prove that you can compensate each single mode with a PEQ, than all n modes together can be compensated with n PEQs. If this does not hold true, the system is not linear. The prerequisites for being "linear" in the mathematical sense are:

1.) a*f(x)=f(a*x)

and

2.) f(x)+f(y)=f(x+y)

So: Why are modes (in the low frequency regime of a room) not linearly independent? Why is the addition of sound waves not linear (at typical listening levels)? Please note that I'm not saying it's not (too) complicated.

The only problem obvious to me is that you can't compensate a zero in the magnitude of the transfer function.

[john k...]

linearity isn't the issue. The issue is whether or not the resulting sumation is minimum phase or not. This is a separate issue which has noting to do with linearity. For example, sum the output of an LR4 HP and LP section. You get flat amplitude response but it is not minimum phase even though the HP and LP sectiuons are minimum phase.

[gedlee]

It seems to me that we are all talking in semantics and may all agree on the same mathematical details. I will first say this - minimum phase (MP) is not a concept used in acoustics, its not in a single text on the subject that I know of. Its also never used in physics and hence, as a physicist, I was never taught the concept so my understanding is not world class. It's an electrical engineers concept and its application to acoustics is weak at best.

The general ARMA transfer function is NOT MP, that is for sure. Only in certain situation is this function MP and as it turns out the circumstances for passive electronics are such that the functions that are created will always be MP. This is a real benefit to circuit analysis. But in problem that can have multiple paths where the signals are simply delayed by the path and not by the dealy inherent to some electrical component like an inductor or capacitor then the conditions for a guaranteed MP transfer function no longer exist. All room acoustics problems are multi-path, because the sound wave can take many paths in the room, so in general one must assume that the ARMA filters that are created by the room modes are not MP. Unless someone can prove otherwise, I have to assume this to be true. I have never seen a proof that says that the room response will be MP and if one exists then I'd love to see it. It is well know that the room response is not invertable and I believe that this alone implies that it is non-MP. But as I said, MP is not a concept that you will find in acoustics.

So back to the problem, while it may be interesting to argue these points, I just don't see the point. I don't think that there is a strong reason to care what the decay of a room mode is. It is not IMO what we hear or care about at LFs.

It appears from all thats been said here that we all agree that a smooth LF response via multiple subs is the solution. What difference does it make if a PEQ reduces the "decay rate" or not. If the response is spacially and spectrally smooth then this is what we are after. If there is still a strong peak left after we set up our subs, then a PEQ can be used to reduce this peak. The decay time, or any changes thereof, are academic.

If however it is being claimed that EQ can correct the LF modal problem then this is clearly false and easily shown, because the room averaged response will not be improved by such a technique only a single point can be. But the decay rate is still academic.

Its clear to me know that a general system composed of multiple subsystems can have multiple decay rates and that these decay rates are seen in the resulting system response differently depending of the systems initial conditions. So yes, in a test which varies these initial conditions one may well see different decay rates taking precidence over others. There won't be any fixed answer, it will all depend on the experiment. And is all quite academic.

[john k...]

Form the purely academic point of view I would say the concept of minimum phase (MP) is not solely electrical engineering term, though frequently used in that field. The definition I have seen comes out of the mathematics of basic systems engineering; A system with system function (transfer function) which is stable and causal and has a stable and causal inverse is referred to as a minimum phase system.

I think we see the term used most frequently in EE because in signal processing we are very often concerned with pre and post processing. For example, RIAA equalization must be minimum phase otherwise the inverse equalization found in phono preamps would not be stable and causal. When the system function is MP it allows us to undo what we have done.

[gedlee]

The "causal inverse" would be a typical problem in acoustics. We know that the room impulse response is not invertable so any room impulse response would not be MP. So by that logic no portion of the rooms trsnefer function would be MP and hence we certainly cannot assume that any mode would thus be MP.

I've always had trouble with the MP concept for a three dimensional system since is that system not MP if at ANY point it is not MP? How does one define MP in a multidimensional sense? How does one "invert" a polar response? We can invert any given point, but each point is different and some may not be MP even if others are. Quite honestly the whole concept seems lacking for acoustical problems IMO.

As I said, we never studied the concept in school. I learned it from some EE texts. The most general definition that I have heard is that there cannot be any zeros in the right half plane of the transfer function. These of course become poles when inverted and poles in the RHP are unstable. But how this is manifested in the system is not clear. I was under the assumption that zeros in the right half pane meant that there was "excess" delay, which comes from a mutipath situation. Three dimensional acoustics problems are almost always multipath.

[soongsc]

If a PHD thesis results from all this. I would be interested in what is written in it.