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Author Topic: Of the infinite properties of transducers and other physical phenomena  (Read 6683 times)

Nika Aldrich

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Zoesch wrote on Sat, 19 June 2004 18:27

I told you before that the answer to both is no, they are not... \


Then WHY IN THE WORLD ARE YOU PICKING THIS BLOODY FIGHT??

If you want to rename IIR filters to recognize that at the subatomic level there is still some mystery then that is a completely separate discussion.  But by the definitions in use for IIR filters both transducers and electrical feedback systems are IIR filters, granted that at some nanoscopic level both fade into question.  Either transducers and feedback systems are both FIR filters or they are both IIR filters, but they are the same, and you are intentionally obscuring that fact because you realize you made a mistake several pages ago and now you're just being stubborn for the sake of procrastinating an acknowledgement that you were out of line.  You've now had both myself and Paul tell you that yet you persist with the same "when they reach equilibrium" now, wasting my time for pages.  Of course if they "reach" equilibrium at a steady state then they are the same.   They will never reach equilibrium, per the fact that forces are constants.

Can you just apologize for the error and let us drop this ridiculous thread before it gets even more embarassing?  

Transducers, as with ANY natural resonating object, are IIR filters.  FIR filters, per Paul's statement that you said you agree with, are only figments of mathematical limitations that do not accurately model anything in the natural world.  You said you agree with Paul, so great, we'll put that to rest.  Transducers are NOT FIR filters.

Great.

I'm done.

Nika.
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ajmogis

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Yes Zoesch.  Nika's right.  Your hang-up with this seems to be the word "infinite."  While the dynamic range of math is definitely infinite, the dynamic range of the real world seems to be...fuzzy (from a quantum mehcanical perspective).  This is where the confusion lies.  

Think about a digital IIR filter.  At some point it will stop resonating and all you're left with is digital zero and the dither bubbling away.  It might in some way still be mathematically resonating to infinity (and minus infinity for that matter!), but that's neither terrribly useful or important.  There's still a point at which there's no more signal.  You run out of bits.

In the "real" world it is the same.  At some point the cymbal stops resonating and you're left with the thermal vibrations of the molecules.  Infinity is still there, it's just not important.  The definition of something having an IIR or an FIR has more to do with the other characteristics of how they work and how they're constructed, not whether or not they REALLY go on forever.  It's just an easy way to name the two varieties so you can talk about them.

As far as I know FIRs exist only in the digital world.

-AJ
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Johnny B

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Here's my dumb question:

If I bang the hell out of a guitar that's
plugged into a Marshall half stack and get
screaming feedback with it, but then turn
the amp off, unplug it from the wall, and
come back 3 months later, are any of the
Greenback speakers still vibrating?

My guess would be, "No."
But I could be wrong, I often am.  
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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
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---Albert Einstein---

I'm also uncertain about everything.

steve parker

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" If I bang the hell out of a guitar that's
plugged into a Marshall half stack and get
screaming feedback with it, but then turn
the amp off, unplug it from the wall, and
come back 3 months later, are any of the
Greenback speakers still vibrating?"

stefan would say no....
nika might say yes.........(actually i doubt it)..

the only answer i'm happy with is "no - but due only to outside influences - friction etc."

steve parker

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Zoesch

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Nika Aldrich wrote on Sun, 20 June 2004 04:11

Then WHY IN THE WORLD ARE YOU PICKING THIS BLOODY FIGHT??


Sorry, I didn't get the memo that this was a fight... I intend to keep my composture, I'd suggest you do the same.

Quote:

If you want to rename IIR filters to recognize that at the subatomic level there is still some mystery then that is a completely separate discussion.


That's not the issue, you said on the other thread "Oh, BTW, transducers are IIR systems" and I said no... if you had said "Oh, BTW, transducer mathematical models exhibit an infinite impulse response, in real life they will return to the initial pre-impulse state due to the rejection properties of materials" and this thread wouldn't exit.

Call me anal retentive, but last thing that I want is people to believe that their speakers and microphone capsules are still vibrating after they have been left alone.

Quote:

 But by the definitions in use for IIR filters both transducers and electrical feedback systems are IIR filters, granted that at some nanoscopic level both fade into question.


Micro and macroscopic, again, take a speaker cone, you have a free field magnetic coil that pushes an elastic cone, this elastic cone exhibits inertia and you need a tensor for it to move, any force below this tensor value will not make the speaker cone move, comprende? The coil might be oscillating ad infinitum (It won't) but those oscillatons won't affect the speaker cone at the macro and microscopic levels.

The transducer is a system to convert electrical energy into mechanical energy and has to be treated as such... if you want to use a simplified model, be my guest, make sure you label it as such.

That's like taking the small signal transistor model of one resistor and one current source to be the exact behavior of the transistor for all inputs.

Quote:


Either transducers and feedback systems are both FIR filters or they are both IIR filters, but they are the same, and you are intentionally obscuring that fact because you realize you made a mistake several pages ago and now you're just being stubborn for the sake of procrastinating an acknowledgement that you were out of line.


Excuse me, but I'm not intentionally or stubbornly obscuring anything... I'm being crystal clear with you... does the model exhibit an infinite impulse response? Yes, does the physical system exhibit that behavior? No.

Quote:

You've now had both myself and Paul tell you that yet you persist with the same "when they reach equilibrium" now, wasting my time for pages.


And mine as well...

Quote:

Of course if they "reach" equilibrium at a steady state then they are the same.


Thank you, that would've saved you pages of debate... but moving on...

Quote:

They will never reach equilibrium, per the fact that forces are constants.


Oh, but they are not, if you blast air into a room expect a change in room pressure for a while, if your sound wave hits a wall expect a reflection... hardly constant right?

If you take a simple second order low pass filter and measure its output with no input you get a measurement right? That's your equilibrium, and that's not zero, so any exponential decay function will converge to it.

You are stubbornly going on about equilibrium being "zero" and I'm stubbornly going on about equilibrium being that initial measurement.

Quote:

Can you just apologize for the error and let us drop this ridiculous thread before it gets even more embarassing?


Didn't know I owed you an apology or anything.  

Quote:

Transducers, as with ANY natural resonating object, are IIR filters.  FIR filters, per Paul's statement that you said you agree with, are only figments of mathematical limitations that do not accurately model anything in the natural world.


FIR filters are not implementable in the analog domain... big difference between that an your statement.

Quote:

You said you agree with Paul, so great, we'll put that to rest.  Transducers are NOT FIR filters.


What Paul and I are agreeing with is not what you and I are disagreeing with, you are standing on a mathematical premise that has no resemblance to physical behavior, but so be it.

Quote:


Great.

I'm done.

Nika.


Great, so am I... George can decide whether to leave this thread up or delete it as he sees fit.
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PP

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Gentlemen!

There is an extremely useful lesson to be learnt here.

This thread eloquently demonstrates the advantages of allowing people to be able to post their views whilst others (with a differing view) can post theirs separately, giving their views and opinions.

This allows those interested enough in this forum to read it allowing them the respect of being able to utilise their own brains, experience and personal judgement in order to decide the relative merits between the respective views.

We have an excellent moderator, highly acclaimed throughout the entire world for his far reaching contributions to the professional recording industry that does intervene very decisively, when he feels it is necessary and properly merited.

None of us should presume ourselves worthy to usurp the moderator’s role and overstep our authority in this forum by doing so ourselves.

Enduing upon ourselves an authority we do not in fact possess, and then using it to effectively censure others whose views differ from our own.

This is of concern to me, as several internationally regarded engineers have commented that they would indeed have liked to participate in this forum at times.

But do not wish to have their views pulled apart piece meal by others with a lot more time to spare, that are far less experienced, and a whole way further down the food chain to boot!

They want to be able to express their opinions without the NECESSITY of engaging in a time consuming argument involving complex matters where semantics alone can give a completely false representation of their views.

They don’t want line by line dissections of their postings reposted and twisted against other unrelated comments they have made, that give a wholly unrepresentative view of their opinion.

This is not unreasonable.

They just want a chance to have their say without a wrangle. This drives contributors away from the forum as regards to being willing to post here themselves.

Surely,

This is DEMOCRACY!




This particular threads debate reminds me of a conversation I had with someone a while ago regarding aerodynamics.

Basically the young man (thankfully working now for Mercedes Benz) was seeking to explain to me that if a 747 flew through the sky creating spiralling patterns of air from its wing edges, those spiralling patterns would continue in infinity right round the earth’s atmosphere and go on ad infinitum.

Theoretically, this may be so,

Real life is not theoretical though is it?

Other air currents will eventually dominate and control the flow of air and at times that air might even be completely still.

But let’s not linger in the doldrums.

Perhaps this will help.

http://www.whale.to/m/cathie.html

Let’s lighten up a little and allow others to have their view expressed.

The world will NOT spontaneously combust if we do.

Best Wishes to all

Peter


Peter Poyser
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Paul Frindle

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ajmogis wrote on Sat, 19 June 2004 19:46


Think about a digital IIR filter.  At some point it will stop resonating and all you're left with is digital zero and the dither bubbling away.  It might in some way still be mathematically resonating to infinity (and minus infinity for that matter!), but that's neither terrribly useful or important.  There's still a point at which there's no more signal.  You run out of bits.

In the "real" world it is the same.  At some point the cymbal stops resonating and you're left with the thermal vibrations of the molecules.  Infinity is still there, it's just not important.  The definition of something having an IIR or an FIR has more to do with the other characteristics of how they work and how they're constructed, not whether or not they REALLY go on forever.  It's just an easy way to name the two varieties so you can talk about them.

As far as I know FIRs exist only in the digital world.

-AJ


Yes this illustrates a good point. The digital filter IIR model you quote is actualy NOT an accurate IIR in a natural sense because you have allowed it to 'run out of bits' - it has therefore been allowed to stop - i.e. it's no longer infinite.

And this is the hub of the misunderstanding.

In reality what SHOULD happen with a digital IIR (and in fact we always ensure it does) is that the dither (very very importantly) will prevent the filter from stopping and therefore the transfer charateristic of the IIR remains in permanence - like natural physical systems in the real world. What this means is the the freq response that the filter applies to the noise - or dither - or ANY possible stimulus however small, will remain true to the IIR implementation. I.e. it does not need an external stimulus to 'become' a filter and it never stops being one Smile

As would be the case with say a cymbal - i.e. its transfer characteristic is essentially constant (leaving out the possibility of material being modified by the force of a loud smash) whether responding to a smash, resonating with external ambient sound in the environment, or just being moved by the noise of the Brownian motion of air molecules due to temperature. I.e. it does not stop having resonance or the ability to modify signal at ANY time.
However long you left it in the quiet you would theoretically be able to extract it's resonances and freq responses - provided you could do a long enough FFT analysis - it's just that it would appear to tend towards becoming constant energy (noise filtered by the cymbals response) in the end cos the noise would eventually overwhelm the exponential decay of the original stimulus.
Even if the cymbal were placed in a complete vaccuum without any losses (and no external stimuli by definition) it would still produce it's charateristic response due to molecular movement because it was not completely cold - it would just be somewhat quieter (i.e. the molecular noise would have the response of the cymbal imposed on it). The only time it would ever come to a complete (absolute) rest and cease being a filter of some kind (or in fact even a cymbal at all) would be at absolute zero temperature - i.e. infinitely cold, i.e. electrons at rest with no atomic movement - no longer matter as we know it - and impossible by definition to achieve fully.

And yes you are right in saying that an Finite IR filter (with an impulse response that ends after the calculation has finished) is an oddity that can only exist within a mathematical environment and has no parallel in the physical world AFAIK - because nature does not 'calculate' within the human paradigm of a 'finite math precision' representation. It is only humans that evaluate by 'counting' and give up looking when things get beyond our reasonable perceptions and therefore seek to percieve reality as 'numerically quantised'.
Nature has no need to. And in fact neither do we ultimately Smile
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Paul Frindle

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Peter  Oxford wrote on Sun, 20 June 2004 13:31

Gentlemen!

<snip)

Let’s lighten up a little and allow others to have their view expressed.

The world will NOT spontaneously combust if we do.

Best Wishes to all

Peter


Peter Poyser



Here here Smile In fact this argument is a philosophical one - but none the less it is becoming one of great importance IMO, since it is exposing the thinking concepts and perceptual mutual exclusions that underpin much of the popular unease with digital processing.
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Nika Aldrich

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Thank you, Paul.  Great post.  I think that sums that up fairly well.  FIR systems can only occur in the mathematical realm and cannot occur in the natural realm.  All devices that resonate in the natural world are filters of an IIR variety, including, therefore, transducers.

Nika.
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Zoesch

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Nika Aldrich wrote on Tue, 22 June 2004 00:43

Thank you, Paul.  Great post.  I think that sums that up fairly well.  FIR systems can only occur in the mathematical realm and cannot occur in the natural realm.  All devices that resonate in the natural world are filters of an IIR variety, including, therefore, transducers.

Nika.


I hope you have the presence of mind to realize that what Paul is saying and what you are saying aren't the same. Paul is talking about the cymbal's transfer function, being infinite (Which it is, as it exists for all points in time), that its properties being continuous (Which they  are, as they are continuous for all points in time) and that if it is a filter, it never stops being one (Which it won't, of course). He is not saying that the phenomena will continue below the noise floor, again, unless you have measured it you are only inferring that it happens.

This is a hell of a lot different than saying All transducers (Including those on free field configurations?) are IIR Filters.

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Eliott James

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Nika Aldrich wrote on Mon, 21 June 2004 10:43

Thank you, Paul.  Great post.  I think that sums that up fairly well.  FIR systems can only occur in the mathematical realm and cannot occur in the natural realm.  All devices that resonate in the natural world are filters of an IIR variety, including, therefore, transducers.

Nika.



Do you realize that all we have in reality IS the natural realm? All your mind can conceive of math and any other thing is part of the natural realm.
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Nika Aldrich

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Zoesch wrote on Mon, 21 June 2004 20:19



I hope you have the presence of mind to realize that what Paul is saying and what you are saying aren't the same. Paul is talking about the cymbal's transfer function, being infinite, that its properties being continuous and that if it is a filter, it never stops being one . He is not saying that the phenomena will continue below the noise floor, again, unless you have measured it you are only inferring that it happens.

This is a hell of a lot different than saying All transducers (Including those on free field configurations?) are IIR Filters.




Well let's see.  The following are quotes from Paul's messages on this board (both under this thread and the tremolo thread.

After excitation, the decay of all these systems is exponential meaning they never actually reach zero action. The rate at which this exponential decay happens is determined by the loss - but it's still exponential - so still never 'gets there' theoretically. We give up and say it stopped when we can no longer percieve it - for electical signal this 'might' be when the action drops below noise due to temperature.

This means that after an impulse is put into the device the device never reaches equilibrium.

What is a pendulum, what is a tuning fork, what is a piano string, what is a simple L/C network, what is a glass tumbler etc etc I.e. anything with resonance?
All are systems with mechanical, acoustic or electrical feedback - with a gain of something less then unity - which prevents them being oscillators


This means that all resonant devices have feedback loops, like IIR filters.

The fact the we CAN model them with IIR representations (analogue or digtial) does not mean they are NOT IIR systems fundamentally. It's just that some exist in domains other than electricity or signal processing

He is saying that IIR filters in the electrical world are simulating IIR transfer functions in the natural world.

In reality what SHOULD happen with a digital IIR (and in fact we always ensure it does) is that the dither (very very importantly) will prevent the filter from stopping

and then

As would be the case with say a cymbal - i.e. its transfer characteristic is essentially constant (leaving out the possibility of material being modified by the force of a loud smash) whether responding to a smash, resonating with external ambient sound in the environment, or just being moved by the noise of the Brownian motion of air molecules due to temperature. I.e. it does not stop having resonance or the ability to modify signal at ANY time.

This means that a cymbal continues to resonate even when its motion wrt to the initial impulse is lower than the noisefloor of the environment it is in.

The only time it would ever come to a complete (absolute) rest and cease being a filter of some kind (or in fact even a cymbal at all) would be at absolute zero temperature

He says that the cymbal is a filter, and that it continues to filter any transient played into it until it is at a state of rest, and the state of rest only happens at 0degrees Kelvin.

And yes you are right in saying that an Finite IR filter (with an impulse response that ends after the calculation has finished) is an oddity that can only exist within a mathematical environment and has no parallel in the physical world AFAIK

I thought this was pretty black and white but you seem to have a hard time with this one.  This means that a cymbal, being a filter, is not an FIR filter.  Ergo, if it is not a FINITE impulse response filter it is inherently an INfinite impulse response filter.  I think Paul and I are basically saying the same thing, there.  But just to make sure that Paul really meant what he said, let's go here, from page 1 of this thread:

The FIR is an unnatural filter in the real world that can only exist within the bounds of math and signal processing.

Also, from the same post, regarding feedback again,

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 naturalworld as resonance without feedback of some kind.

And finally, with respect to the essential question, Paul writes:

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.

Again, you wrote:

Quote:

This is a hell of a lot different than saying All transducers are IIR Filters.


Hmmm.  I'm led to think that there is NOT a hell of a lot of difference between what Paul is saying and what I'm saying.  

Nobody necessarily said Paul possessed absolute truth on all of this, and you can certainly disagree with him, but as I see it now, Paul is pretty clear that any transducer (ANY resonant device, for that matter) is, as a filter, an IIR filter.

Nika.








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Zoesch

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I'm going to hold any long response until you understand the basics of equilibrium... the SUM of all forces on the system is zero, not the forces, the sum of all the forces acting on the system.

Once you get this we can continue talking about the subject, but if you keep insisting that equilibrium means that the forces are zero we won't get anywhere.
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Paul Frindle

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[quote title=Nika Aldrich wrote on Mon, 21 June 2004 21:20]
Zoesch wrote on Mon, 21 June 2004 20:19



I hope you have the presence of mind to realize that what Paul is saying and what you are saying aren't the same. Paul is talking about the cymbal's transfer function, being infinite, that its properties being continuous and that if it is a filter, it never stops being one . He is not saying that the phenomena will continue below the noise floor, again, unless you have measured it you are only inferring that it happens.

This is a hell of a lot different than saying All transducers (Including those on free field configurations?) are IIR Filters.  

Nobody necessarily said Paul possessed absolute truth on all of this, and you can certainly disagree with him, but as I see it now, Paul is pretty clear that any transducer (ANY resonant device, for that matter) is, as a filter, an IIR filter.

Nika.





Oh guy's this is surely getting silly. I am nothing more than a guy who works with this stuff and thinks about it all the time - that's all. But to take this one step further:

The theoretical timing window for a filter is not defined by us deciding ourselves 'it's done sounding' Sad The fact that you stop playing and/or unplug an instrument and walk away at the moment YOU decide it's gone completely quiet, does not make it an FIR system. We cannot impose the condition of everything n the natural world being 'practically finite' cos we have given up looking and so decide - as this cannot wash - because there are other factors that give the game away.

A fundamental difference between an IIR filter and an FIR is that the FIR only computes it's response over a limited range of time (its time window). Therefore the only reason the impulse response is 'finite' is that once the impulse has been calculated for all the terms contained in the FIR filter - no more calculation is done and no more output results. Can anyone think of any natural system where there is resonance and filtering where this is true - surely not?

The other imnportant side effect of finite time filters is that because they work over a limited period of the passing signal, they produce an error function in the filtering characteristic. I.e. so even if the excitation signal were perfect, starting at - infinity and going on for + infinity, the FIR acting on it will exhibit transitional freq response distortions because IT looks at the signal only during the finite length of the filter calculation. We can obviously make this better by windowing the coefficients (i.e. smoothing the beginning and end at the boundaries of the filters time window so as to reduce the effects of the transistion), but unless the FIR has infinite length these artefacts will always exist to some degree or other. If it HAD infinite length of course, it would no longer be an FIR but an IIR because it would possess an infinite number of calculating terms.

Can anyone think of ANY natural system that is 'aware' of the number of total 'operations' it has made within a given period and decides to end when a certain fixed number have passed - surely not?

And can anyone think of a natural system that produces boundary disturbances in it's freq response because it 'looks' at the signal only over a limited, fixed and finite time window? I certainly can't think of any that would apply to musical instrument mechanisms.

If your guitar string were an FIR mechanism it would cease producing it's natural tone after a fixed length of time - however hard or soft you plucked it! Can anyone think of any instrument that exhibits this anomaly - surely not?

Honsetly guy's I can't understand what the argument is all about, why people are getting so het-up and why it continues Sad

Are you sure that its not simply that someone did a typo or got their FIRs and IIRs mixed up earlier in this thread?
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Paul Frindle

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Zoesch wrote on Tue, 22 June 2004 00:54

I'm going to hold any long response until you understand the basics of equilibrium... the SUM of all forces on the system is zero, not the forces, the sum of all the forces acting on the system.

Once you get this we can continue talking about the subject, but if you keep insisting that equilibrium means that the forces are zero we won't get anywhere.


No this cannot be, because you are not specifying the time period within which this summation is being conducted. Over an infinite period, any combination of forces could be said to have been in equilibrium during that period - provided that they consisted of an equal spread of integrally equivalent +ve and -ve events.

Actually this reminds me of a story from an analogue design I did around 20 years ago. I got a job as a design engineer for a high end console company trying to make a digitally controlled analogue assignable desk (SSL). One of the new components around at the time that looked promising was the MDAC - a kind of bipolar digital divider that allowed you to change the gain of an analogue signal with a digital code. Problem was that the damned thing clicked because at every change of its digital code it let out a very fast pulse (around 1 to 2uS long) of varying size and polarity depending on the code. This was optimistically termed as 'charge injection' in the data sheet. Since the pulse was essentially unipolar it could not be filtered out, since this only stretched the energy dissipation over a longer period - making it even more audible in some cases.
When I turned up various elaborate schemes had been hatched and tried to avoid this, including cross fade schemes bewteen 2 devices and 'silent period' generators that cut the signal during the changes etc etc - all of which were variously flawed and the project was stuck because of it. One very respected engineer from Danish Radio (I think) had reasonably stated at the time that "it would always be impossible to change the gain of the device whilst listening to it, for the simple reason that the energy of the transition could never be lost"!

My trick was realising (lateral thinking) that although the energy could indeed never be lost - it COULD be turned into something the integral of which over time would tend towards zero polarity - and therefore could be filtered out in the audio freq band by conventional means. So I got the darned pulse and subjected it to a resonant L/C network. The result then was that the energy pulse caused HF 'ringing' which produced a sine wave that dropped exponentially over time as the energy was dissipated. Point being, that because the ringing energy was bipolar going equally +ve and -ve, (and it was a high freq >100KHz) it could be filtered out of the audio band, simply because the average energy over time (its integral) tended towards zero polarity. The click duly disappeared below -80dB (despite dire predictions by people much brighter than myself) and it worked just fine after that Smile

The (on topic) moral of the (long) story is that the concept of 'equilibrium' is something that requires definition in the time domain - or misunderstanding can result and very important and useful things can get missed.

In this case, that the summation of forces over time apparently equaling zero is not a reliable indicator of 'nothing significant happening' Sad
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