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Author Topic: Of the infinite properties of transducers and other physical phenomena  (Read 6684 times)

Zoesch

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Alright... not to cloud the other thread...

Nika Aldrich wrote on Thu, 17 June 2004 03:25

Transducers are indeed infinite impulse response filters in that the impulse response of them has infinite characteristics, and when convolved with a stimulus the response does ring infinitely.  Indeed the devices listed all have infinite impulse responses and they all are convolved with stimuli.  



To which I say, no they are not... infinite impulse response means that the response to an impulse exhibits infinite oscillations, this is what you would expect from a full-feedback system with no damping.

A transducer won't exhibit that behaviour, if excited with an impulse it will show a finite number of oscillations until it reaches equilibrium (Goes back to zero). If excited with a step function it will experience a finite number of oscillations until it reaches equilibrium.

This is consistent with control theory, if electromechanical transducers had infinite impulse responses simple things like a gearbox wouldn't work Very Happy

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Since this seems wholy unrelated to Chuck's issue, perhaps this part of the discussion should be taken offline?  I'd rather keep the topic focussed and helpful.



It is related, IIR's weren't chosen on the reconstruction filter because of their impulse response characteristics, they were chosen because they are computationally efficient and easy to implement in a low power low cost device.
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Nika Aldrich

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Zoesch wrote on Thu, 17 June 2004 00:36

A transducer won't exhibit that behaviour, if excited with an impulse it will show a finite number of oscillations until it reaches equilibrium (Goes back to zero).


It never reaches equilibrium at a quantum level.  It may APPEAR to reach equilibrium, but transducers do indeed have infinite impulse responses.  Think of the forces at work against the transducer, like friction.  Friction is a constant, so if you calculate the rate of decreasing displacement of a transducer it will continue to get smaller in perpetuitum but never actually reach the asymptote of equilibrium.  That's not complex math.   Transducers most definitely have infinite impulse responses.  

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If excited with a step function it will experience a finite number of oscillations until it reaches equilibrium.


How do you propose to calculate the exact number of oscillations?  And what happens at the last oscillation - does it just SNAP into equilibrium?

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It is related, IIR's weren't chosen on the reconstruction filter because of their impulse response characteristics, they were chosen because they are computationally efficient and easy to implement in a low power low cost device.



If you don't have an IIR filter then your waveform will never conform to Nyquist.  If the waveform is time-limited it inherently has infinite bandwidth.  Since infinite bandwidth is illegal we have to have a time-unlimited waveform - ergo it must be an IIR.  

It has nothing to do with "computations."   The IIR filter as after the conversion occurs - in the analog world.  

Nika.
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Zoesch

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Nika Aldrich wrote on Thu, 17 June 2004 10:02

It never reaches equilibrium at a quantum level.


Nothing is at equilibrium at quantum level, but that's not what we're discussing here.

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It may APPEAR to reach equilibrium, but transducers do indeed have infinite impulse responses.


I can prove to you that no, that's never the case, a system will reach equilibrium once the energy contributions prior and after the impulse, over time, are equal.

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Think of the forces at work against the transducer, like friction.  Friction is a constant, so if you calculate the rate of decreasing displacement of a transducer it will continue to get smaller in perpetuitum but never actually reach the asymptote of equilibrium.


It will once it reaches thermal equilibrium, WTF are you onto here? At one point in time the oscilation amplitude will be equal than the amplitude of the thermal movements of the material's molecules, how fast does that happen depends on the material, the temperature, the amplitude of the impulse and so on, but it WILL reach equilibrium, there's no running from the Laws of Thermodynamics.

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That's not complex math.   Transducers most definitely have infinite impulse responses.  



This is basic physics, math can substantiate anything, even erroneous assumptions.

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How do you propose to calculate the exact number of oscillations?  And what happens at the last oscillation - does it just SNAP into equilibrium?


I don't propose, that's why control theory and impulse response characterization were invented/discovered.

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If you don't have an IIR filter then your waveform will never conform to Nyquist.  If the waveform is time-limited it inherently has infinite bandwidth.  Since infinite bandwidth is illegal we have to have a time-unlimited waveform - ergo it must be an IIR


Nope, you can have a FIR filter for reconstruction, look up Quadrature Modulation Filters and see for yourself.

Again, it's all about efficiency... computational efficiency.

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It has nothing to do with "computations."   The IIR filter as after the conversion occurs - in the analog world.  



Can you show me how you implement such a large summing network in analog? DAC's have a digital brickwall filter (IIR) that is followed by an analog LPF, so the IIR filter is in the boundary between digital and analog signals.
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Nika Aldrich

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Zoesch wrote on Thu, 17 June 2004 04:59


I can prove to you that no, that's never the case, a system will reach equilibrium once the energy contributions prior and after the impulse, over time, are equal.


If they continue to dissipate at a fixed rate then how do they ever reach equilibrium?  Equilibrium is the asymptote.

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Nika:  
It has nothing to do with "computations."   The IIR filter as after the conversion occurs - in the analog world.  



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Zoesch:  Can you show me how you implement such a large summing network in analog? DAC's have a digital brickwall filter (IIR) that is followed by an analog LPF, so the IIR filter is in the boundary between digital and analog signals.



The analog LPF is an IIR filter.  A simple feedback loop is an IIR filter - a filter with an infinite impulse response.

Also, typically the digital LPF is a linear phase FIR, but that's beside the point.  

Nika.
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Erik

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Zoesch wrote on Wed, 16 June 2004 23:59

DAC's have a digital brickwall filter (IIR) that is followed by an analog LPF, so the IIR filter is in the boundary between digital and analog signals.


1) DACs commonly use an FIR
2) An IIR can be represented as two FIRs

So really, what's the point of this thread other than to confuse newbies and make George nauseated by the drivel?

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Zoesch

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Erik wrote on Thu, 17 June 2004 14:27

So really, what's the point of this thread other than to confuse newbies and make George nauseated by the drivel?



To make you come in and add to the drivel of course...
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Zoesch

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Nika Aldrich wrote on Thu, 17 June 2004 14:11

If they continue to dissipate at a fixed rate then how do they ever reach equilibrium?  Equilibrium is the asymptote.



No, 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.

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The analog LPF is an IIR filter.  A simple feedback loop is an IIR filter - a filter with an infinite impulse response.


A simple negative feedback loop on an ideal opamp that has zero losses is an IIR system (it's a buffer)... however, show me a perfect substractive device with no losses?

And again, this is not a transducer, there's no negative feedback on a speaker cone, there is lossy negative feedback on a speaker cabinet.
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steve parker

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apologies for butting in to the thread - i'm swimming a bit and trying to learn....

" 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?

steve parker.

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Zoesch

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Not really... Oscillators are real world IIR systems, the catch being, Vo will be always less than the voltage that feeds the circuit (Vcc-Vee).

But negative feedback systems ARE NOT IIR systems, which is what's being tossed around as being the case  Smile
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Nika Aldrich

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Stefan,

Sorry, we are not in agreement on this, the other thread.   Can you just give me a formula that models the behavior of a transducer and the forces that act on it?  Make it as simple as you'd like.  I'd like to run the model and figure out when the result really becomes "0."

Nika.
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Nika Aldrich

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FWIW, I just got this email from Paul Frindle.  I asked him to come on and give a more comprehensive explanation of his perspective.  He's a busy man - I'm not sure he'll have the time.

>I would say that all natural resonant system are IIR in nature
>up to the point where the oscillations become unmeasurable due
>to noise over time. Also resonant systems
>in the natural world DO have feedback - always. I.e, a guitar
>string or a pipe in an organ has mechanical and acoustic
>feedback. There is no such thing in the natural
>world as resonance without feedback of some kind. The FIR is an
>unnatural filter in the real world that can only exist within
>the bounds of math and signal processing.

I would just add that resonant systems don't cease their impulse responses just because they become unmeasurablely low amongst the noise.  The behavior exists whether we have the tools to measure it or not.

Nika.
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Zoesch

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And that is correct, however, a speaker cone has no feedback in itself, it's a pistonic device, a speaker system could have feedback depending on the design.

And that's where the all transducers are IIR system assumption is wrong.

Want to model it for yourself?

Model the speaker excursion, find the point where it becomes zero... that would be the point where all forces are at equilibrium (That's Newton, not me)... find the value of the tensor, input it back into the formula for V to SPL and find the voltage that matches that tensor.

There's your system at equilibrium

Not when the response becomes zero.

I can have a system whose electrical impulse response is infinite yet its mechanical response is finite, not asymptotically approaching zero.

And this is the danger of math without physics.
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Nika Aldrich

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Zoesch wrote on Thu, 17 June 2004 20:45

And that is correct,


then:

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I can have a system whose electrical impulse response is infinite yet its mechanical response is finite


How can Paul's quote be correct - that any resonant device in nature has an infinite impulse response and that a finite impulse response is a creation of mathematics that can't happen in the natural world...

... yet you have a device with a finite impulse response when stimulated?  

A cymbal - finite or infinite impulse response?  According to you it has a finite impulse response.  According to Paul it can't.  How can you both be correct?  And how can you be correct that Paul is correct when he disagrees with what you say?

Nika.
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Zoesch

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Are Paul and I disagreeing?

Not really.

Again, let's go back to the basics of a cymbal...

It gets struck by a stick (It's impulse response) and it vibrates in response to that impulse... it's surface will exhibit modes as the vibrations travel the surface of the cymbal and yet the cymbal itself will move in an elliptic fashion following the force and direction of the impact.

So far so good right?

The cymbal has to displace air in order for it to be heard, air which has a weight, air which due to its properties will do its damn best to go back and fill the space that was left void.

Air who also acts as a dampener, because it has friction, because work has to be done for the cymbal to displace that air, work which dissipates as heat, heat which is not infinite because neither is the work nor the initial force.

So as you dissipate heat, you have less energy to work, and after each oscillation you'll have less and less energy, until you reach thermal equilibrium... you have no more energy to dissipate, your initial hit, which exerted a work potential on your system has dissipated.

And so far you are in agreement with Thermodynamics.

Your cymbal will return to its original state before the impulse, it might be a long time, it might be a short time, it all depends on the efficiency of heat transfer and the work efficiency.

So far you are in agreement with basic Newtonian physics.

There's no feedback on the system.

But what if you were actually playing against a wall? Wouldn't reflections act as feedback? No, simply because their force contribution would be significantly less than those of the system and they will also diminish with time.

If a butterfly batters its wings in china, do I feel it on my cymbals? Sure, does it change the state of the system? No...

Likewise with a speaker cone, a microphone diaphragm, and even a tuned pipe on an acoustic organ.

And here's where people get their cables crossed.

If I model a speaker, I can simply model its frequency response as the product of two bandpass filters (One high, the tweeter and one low, the woofer), if I take that model and look at its impulse response it will have an infinite impulse response... sure, and that's not contradictory, it's a model.

But if you want a real world extension of your model you need to add losses, non-linear behaviour of the speaker cones, breakup modes on the cone and so on...

It's no longer the product of two band pass filters. It becomes a complex differential non-linear system, whose impulse response is not infinite.

So Paul is right, and I am right, and so far neither of us are contradicting each other.

To the experiment yourself, grab a speaker cone, wire it to a toggle switch and press it, recording the output with a measurement microphone, leave it a long time...

You won't be able to measure below the noise floor of the microphone however, but if you have a spectral interferometer and a couple of lasers handy it makes for a very fun experiment.
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Nika Aldrich

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Zoesch wrote on Thu, 17 June 2004 22:01

Are Paul and I disagreeing?

Not really.

Again, let's go back to the basics of a cymbal...

It gets struck by a stick (It's impulse response) and it vibrates in response to that impulse... it's surface will exhibit modes as the vibrations travel the surface of the cymbal and yet the cymbal itself will move in an elliptic fashion following the force and direction of the impact.

So far so good right?



Yes.  And just for the record, I really am genuinely interested in understanding your perspective on this.  I do believe that you are incorrect, but I am interested in seeing if our perspectives meet at a mutual understanding.  So yes, I'm following along, and we hit the cymbal with an impulse...

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The cymbal has to displace air in order for it to be heard, air which has a weight, air which due to its properties will do its damn best to go back and fill the space that was left void.

...

So as you dissipate heat, you have less energy to work, and after each oscillation you'll have less and less energy, until you reach thermal equilibrium... you have no more energy to dissipate, your initial hit, which exerted a work potential on your system has dissipated.

And so far you are in agreement with Thermodynamics.


Check.  We're on the same page so far.

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Your cymbal will return to its original state before the impulse, it might be a long time, it might be a short time, it all depends on the efficiency of heat transfer and the work efficiency.


This is where we disagree.  The rate in which the energy is converted from the cymbal's behavior into heat is a constant, and the resonation of the cymbal decreases in amplitude at a fixed percentage over like moments in time.  Kinetic friction is a constant force, and as a constant force it will decrease the movement of the cymbal a like percentage in like amounts of time.  As such it will never return to a fixed state but will rather always be in motion.  Start with an impulse of amplitude 1 and use any force constant to ascertain the point at which it's movement ceases and you will find that it never does.  

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There's no feedback on the system.


The feedback has to do with the mechanical structure of the device acting on itself, but I don't want to go down that path.  I'm not as comfortable thinking of it that way - I'll leave that to Paul.  It was his quote that all resonant devices have mechanical feedback in them.

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But what if you were actually playing against a wall? Wouldn't reflections act as feedback? No, simply because their force contribution would be significantly less than those of the system and they will also diminish with time.


Key word here is "diminish."  Yes, the movement of all mechanical devices will diminish over time, but it never completely stops.

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But if you want a real world extension of your model you need to add losses, non-linear behaviour of the speaker cones, breakup modes on the cone and so on...

It's no longer the product of two band pass filters. It becomes a complex differential non-linear system, whose impulse response is not infinite.


I agree that it becomes a complex, differential, non-linear system, but all forces acting on the speaker are still constant and thus the impulse response remains infinite.  Take all of the combined forces acting on the speaker in all directions and add them all together and then run the speaker.  It still has constant forces acting on it in the end.  And as long as forces are constant its movement will never cease.

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So Paul is right, and I am right, and so far neither of us are contradicting each other.


I'm not here to battle who is wrong and who is right, but you are insisting that a speaker has a finite impulse response and Paul and I are both saying that no such thing exists in the natural world, and that all mechanical devices - namely all devices with elasticity exhibit infinite behaviour as the response to an impulse.  I don't possibly see how we can all be right about this issue together.  

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To the experiment yourself, grab a speaker cone, wire it to a toggle switch and press it, recording the output with a measurement microphone, leave it a long time...

You won't be able to measure below the noise floor of the microphone...



Right!  But not being able to measure it does not mean that the behavior ceases to continue.  The original transient still has an effect on the cymbal even though the amplitude of the movement becomes less than the amplitude of the random movement of the measuring device, the air around it, etc.  The impulse's effect is still present if we could only measure it.  We humans, for example, can measure the amplitude of waveforms that are as small as 1/16 the amplitude of random noise that it exists within, as that is the limitation of our temporal masking.  More precise devices can measure the amplitude with filters far deeper into the noisefloor than that.  The behavior exists whether we can measure it or not.  It is still an infinite impulse response.

Nika.
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