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Author Topic: Of the infinite properties of transducers and other physical phenomena  (Read 6682 times)

Nika Aldrich

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Zoesch,

Two questions really quickly:

1.  Put an impulse into a physical space like a room and let the reverberant field decay.  Would you agree that the sound never completely decays and that the resulting sound has an effect on the air pressure behavior in the room ad infinitum?

2.  Take a speaker that you believe has a finite impulse response.  Put an impulse into it.  What would potentially be the amplitude of the last peak excursion before the speaker reaches a 100% rested state at equilibrium.  What would be the potential amplitude of, say, the last peak before that one?  Maybe .00000038M? and .00000076M?

Nika.  

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Daniel_Dettwiler

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practice vs theorie.

iir systems (infinite impulse response) works, because in practise they don't resonate for ever. The easiest digital lowpass filer is a  iir filter (I don't recall the formula, I am sure nika or someone can bring it...). Theoreticly if you give an impulse in this filter it would sound (resonate) for ever. Practically after a very very short time, the sound is gone into the last bit. So while the sound does not anymore exist in practise, in theorie this filter would sound for ever. Thats why the filter is an IIR Filter. It does not matter if in practise the sound goes a way, by any sort of limitations fo the system.

Most analog filters (if not all) are IIR (if im right), but same here, the signal is very fast down to the noise floor. But theoretically it would resonate for ever, thats why it is called IIR .

Divide 100 by two as many times as you want, it will never be zero. It will always be half as little as the number before.

A piano string (or any string for that reason) is an IIR System as well. After you hit the string, it would sound for ever. It does not matter if in practis at some point you think that the string does not anymore resonate because of some limitations of the system. In theorie a string would resonate for ever, and that is what matters.

So I think Loudspeaker are IIR Systems.

Daniel
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archtop

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Hi Smile

You know I been tryin' to follow along ( I have no idea why)

Physics in my tiny high school involved dodgeball and running

Nika, you  are sayin' the cymbal never stops,

at the molecular level maybe, but I don't hear that.

so for me, it does stop, the piano string too, thats why we hit 'em again.



is my zipper open, I feel funny, why am I reminded of the old saying
"Better to remain silent, and thought a fool than to open your mouth and remove all doubt"


alright, I'll get back outta the way now

Richard Williams




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steve parker

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" Equilibrium is the original state before exitation, you are getting complete equilibrium (Which you can only achieve at absolute zero) with thermal equilibrium. Thermal equilibrium will eventually happen as there's no more energy to dissipate."

if this were true would it not cut out the possibility of any IIR in the real world?

is this not just a case of modelling an "ideal" in which (as with most modelling) real-world things like friction are ignored?

sorry to quote myself (bad form and all that!)
thanks for your reply stefan but...are my statements above where your disagreements with nika are or am i missing the point somewhere?

where i'm struggling is that the real world always includes factors that negate infinities in mathematical models of anything. that doesn't stop the models being good ones and i can't think of any examples where the application is considered qualitatively different from the model, just because the application doesn't perform to the mathematical ideal.
or...do you disagree that even models of speakers and strings etc are IIRs?

all the best!

steve parker.
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Nika Aldrich

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fuze wrote on Fri, 18 June 2004 18:09

where i'm struggling is that the real world always includes factors that negate infinities in mathematical models of anything.


Mike,

No.  See Paul Frindle's post on the other thread.  The real world does not have factors that negate infinities.  It just adds more complex forces that make the equations more complex, but forces are always constant and thus infinity is still in play.  The real world also adds noise, but the addition of noise does not mean that the behavior doesn't still exist, at an amplitude that is lower than that of the noise.

Indeed IIR filters are NOT just an ideal model of the real world.  Transducers in the real world really ARE IIR filters.  Our models of them are often simplified and don't really fully demonstrate their movement.  We often simplify and only show one force acting.  But even if we show ALL of the forces acting, the transducer doesn't actually ever stop.  It just decreases its movement in amplitude much faster than the model shows.

Make sense?

Nika.
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Zoesch

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Nika, are you implying that the phenomena continues at a subatomic level?

Are you implying that no system returns to its original state?

You were asking me about what amplitude will the ripple have before it gets cancelled, which is easy, again, just calculate where the speaker motion is equal to the atmospheric pressure, your transducer can't go any lower than that.

Atomic resonance has nothing to do with mechanical feedback... just like potential wells have nothing to do with friction. Every atomic structure will resonate at a specific frequency that is given by its structural composition and energy levels, and this is the energy level in which energy transfer is maximized.

Atoms are oscillators in perpetual motion, but they also lose energy over time, shed electrons, become ionized and so on.

Once the impulse response amplitude is down at the original motion of the material the impulse response becomes finite, again, you can't generate energy out of nowhere, unless you are implying that every real world exitation results in atomic fission.

Is the measured time for the system to reach equilibrium inconmensurably large? Yes, well, not really but let's assume so.

Is it infinite? No.
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Nika Aldrich

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Zoesch wrote on Fri, 18 June 2004 22:02

Nika, are you implying that the phenomena continues at a subatomic level?


Yes.  Just like a single bit can represent infinite dynamic range, though much of it is well below the noise floor.  

Quote:

Are you implying that no system returns to its original state?


Yes.  

Quote:

You were asking me about what amplitude will the ripple have before it gets cancelled, which is easy, again, just calculate where the speaker motion is equal to the atmospheric pressure, your transducer can't go any lower than that.


If the forces on it are a constant it will never equal the atmospheric pressure of its environment.


Did you read Paul's post last night on the tremolo thread?  He seems to ardently disagree with you.

Nika.
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Zoesch

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I think that unless you found the Unifying theory and the source for infinite energy, your phenomena stops at the electron motility levels.

Take potential wells/barriers, in a Josephson junction for example (Which has a boundary condition that violently disagrees with most of the basic principles of system equilibrium) there's a measurable current output as temperature lowers even when there's no potential difference across the electrodes, but it's because both superconductors having different ranges need to maintain phase coherency at the barrier.

In semiconductive materials the electrons need to have enough energy to traverse the potential barrier, so yes, once your energy is below that barrier you are done,a dn if you lower the temperature the material becomes less conductive.

In non-conductive material the potential barrier is much higher, your electrons must have a very high enery level to traverse the barrier or be exited with a tremendous amount of energy.

All materials have potential wells and barriers, some are lower than others.

Now in your impulse response dilemma, the energy of the impulse will eventually fall below the potential barrier of the material, the result? No more contributions to the material's movement and the response.

On resonances... all atoms resonate, not all molecules resonate (And some who resonate change states after resonation), why do you think that is happening?

I read Paul's posts, I don't see the ardent part... he's arguing this:

We have experimentally concluded that within observable intervals the energy decreases exponentially, ergo the energy in the system decreases exponentially and thus never approaches equilibrium.

That's the conclusion out of observable phenomena, what happens where we can't measure we can only infer with a mathematical model.

Again, what we know of the system is that it approaches a state where the phenomena is unobservable and it resembles the original state.

I'm not saying that the model is wrong, it's a model, but the model doesn't return to equilibrium, and that's a modellic assumption.

Say you want to make the model more complex, add all the forces, mechanical and electric, that affect your system, add losses, add leakage, add feedback and add random variations on those forces, does it mean that the observation of exponential loss is valid? Only on those intervals where it is observable and quantifiable... where you can't measure you can only infer.
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Nika Aldrich

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Zoesch,

And explain to me how this differs from an IIR filter in the electrical world?  Is an electrical IIR filter a "true" IIR filter based on your understanding of the atomic level physics involved, any more so than a transducer is?

Nika.
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Erik

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This reminds me of the debate where Zoesch tried to claim that using convolution would generate better, more accurate results for non-LTI systems than using a model.

After giving up on the basic math proof, I argued everything from meteorology to the fact that black people don't rely on samplers to put the pump in the thump for bass lines -- they use synths.

He responded with more of the high school debate club antics you're seeing here.  You can keep pointing out the obvious until you're blue in the face -- but he'll squirm and suddenly start talking about how lift isn't bernoulli, it's newton.

In these types of discussions (and especially that 'tremolo' thread), it's always fun to take some things people are saying when they obviously don't understand what they mean, put them between quote marks, and then paste it into Google.  

Turns the sites they're plagiarizing right up.  (Works great on the DUC, too.)

--Erik
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Zoesch

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Ah, Erik, the endless baiting of the disgruntled Nerd... don't you have a cracked plugin auction to shut down or another Mellotron to buy so you can take your picture next to it in a Hawaiian shirt?

BTW Erik, before you enter a debate make sure you at least understand what an inductor is... since your models are so exact that not even convolution can touch them I assume that you understand impedance and inductance.

Ta!
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Nika Aldrich

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Zoesch,

Still waiting on an answer to the question...

Zoesch wrote on Sat, 19 June 2004 07:15

BTW Erik, before you enter a debate make sure you at least understand what an inductor is... since your models are so exact that not even convolution can touch them I assume that you understand impedance and inductance.


Hmm.  Seems totally unrelated to me.  I fail to see how choosing the appropriate mathematical modelling to simulate a non-linear process requires an understanding of inductors.   Frankly, I don't understand inductance at all, but I know where convolution is appropriate and where it is not.  I also don't know the proper methods for making an electro-optical circuit, but I know how to count in two's complement.  So?  

I also fail to see how any of this is related to the slowly-ending mystery of whether or not transducers are IIR filters.  

Nika.
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Zoesch

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Nika Aldrich wrote on Sat, 19 June 2004 16:34

Zoesch,

Still waiting on an answer to the question...


So am I, I asked you ages ago to prove that the system after a period of time isn't at the same state as the system before the exitation... so far, I'm still waiting. I also asked you where's the feedback loop on a speaker cone or a microphone capsule, still no answer on that one either.

Quote:

Hmm.  Seems totally unrelated to me.  I fail to see how choosing the appropriate mathematical modelling to simulate a non-linear process requires an understanding of inductors.   Frankly, I don't understand inductance at all, but I know where convolution is appropriate and where it is not.  I also don't know the proper methods for making an electro-optical circuit, but I know how to count in two's complement.  So?


So? I know both, I ... and one thing that you don't know is the context in which that conversation happened and of this remark, which as far as I can see wasn't directed to you.

And again, put emphasis on the word appropriate... is the model appropriate because it is 100% correct or because it is 100% solvable (And those two might be mutually exclusive)... nevermind, I think this is heading down the path of arguing that Carbon, Graphite and Diamonds are exactly the same.

BTW so it seems that the new trend is to only understand what you do, grab a mathematical model of an inductor and assume is correct without understanding how one in real life work. Choose your poison.

Quote:


I also fail to see how any of this is related to the slowly-ending mystery of whether or not transducers are IIR filters.  

Nika.



Don't know, you tell me...
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Nika Aldrich

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Zoesch wrote on Sat, 19 June 2004 09:20

Nika Aldrich wrote on Sat, 19 June 2004 16:34

Zoesch,

Still waiting on an answer to the question...


So am I, I asked you ages ago to prove that the system after a period of time isn't at the same state as the system before the exitation... so far, I'm still waiting.


I have tried to prove it to you in any way I know how to no avail.

Quote:

I also asked you where's the feedback loop on a speaker cone or a microphone capsule, still no answer on that one either.


And I told you that Paul Frindle would be able to answer that better than I.  I simply don't see the significance of the presence of feedback on an IIR filter like Paul does.  If the impulse response of a device is infinite it is an IIR filter - regardless of what causes it to be that way.  Feedback loops are how we mimic that behavior in the electrical world.

But again, if you argue that a speaker is not a true IIR filter because the physics breaks down at some sub-atomic level, then I ask how that is different from an electrical IIR filter?  Are either of them "true" IIR filters?   It appears to me that you are avoiding this question.

Nika.
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Zoesch

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I told you before that the answer to both is no, they are not... BTW your explanations about how the system never reaches equilibrium fell short of being completely wrong, the counter argument if easy, if the measurements at t-1, t+m, t+m+1 are the same is the system at equilibrium or not?
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