Beyond the Ariel

The engineer picks the log sweep, measures the loudspeaker and knocks off for the day, and everyone lives happily ever after.
Quite so. There is one gotcha which sometimes can fool you, like tweeter tests with higher power levels involved. There I find power compression visibly influence FR's obtained from logsweep+convolution, depending on the sweep direction. One might precondition the driver to factor out power compression.

- Klaus
 
Never heard of them.

Interesting stuff never is read in books first.
LOL


There simple aren't seveal steady states if the system is LTI. There is only one. Only nonlinear systems can have multiple steady states and that is because with a nonlinear system the steady state can depend on how it started.

Well *I* do not know if CMP is to be considered a LTI system - I proposed different points of view and you didn't tell us clearly (besides telling I'm wrong).
For me its not *that much important* as it would not change my core perspective on the subject anyway - though I'd like to know.


So - actually I'm interested how you would define steady state other than that there is no change in SPL (for given frequencies) over some delta time ?

As we saw in measurements and simus and by my example of CMP with a loooong delay time of a full day :
there actually *is* steady state for that first day and another steady state for the day after .



Michael
 
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Quite so. There is one gotcha which sometimes can fool you, like tweeter tests with higher power levels involved. There I find power compression visibly influence FR's obtained from logsweep+convolution, depending on the sweep direction. One might precondition the driver to factor out power compression.

- Klaus

As it just fits so well what I have lots of fun to read at the moment :

consider that preconditioning would need to determine the main thermal behaiour of the speaker at first - as there is no other way to precisely hit thermal steady state (equilibrium) during measurement otherwise.

This is of course of a nitpicking point of view - from a more practical point of view - as you most possibly meant it - quite *any* pre-heating in the same order as the measurement signal will improve the situation.

Michael
 
Hi,

Yes the classical LTI theory says there can be only one steady state, and it seems to be a reserved term, maybe the "steady state" in a CMP should be called something else like Pausa which would give a clue of it's true nature. CMP "steady state" is more like an intermediate state between two or more transient states.

However some interesting things can happen. It's time to review the definition of the "steady state" :D
In the boarder sense it can be said a system enters a steady state after the transient state has been passed.
How do we know when this happens? In steady state the system is constant so all the partial time derivatives of any properties of the system are zero.
How long we should wait for that to happen? Let's input a constant sinusoidal signal to the system and observe the output. The partial time derivative should be zero... Maybe better look at the waveform. System is at the steady state when the output waveform of the sinusoid does not deviate from the ideal with mathematical infinite precision. Then how long we should observe the waveform.. 1 sample point, 2 sample points, .. 1 period ? Clearly 1 point is not enough because derivative is not defined in a singlarity. 2 points define a straight line not a sinusoid so not enough.
Actually this is more of an sampling theorem problem: With infinity high sampling frequency we can immediately see in infinitesimal short time if the output signal is a sinusoidal signal (with infinite precision). However, with less than infinite sampling frequency we must observe until infinity until we can say that the output is a sinusoidal function with zero error.

But then we can only know when the system is at steady state if we know the impulse response beforehand. Sure, output can look like a steady state, but who knows, maybe soon it will burst an another transient and steady state will be ruined! In a more strict sense, a system enters the steady state after all the transients have passed.

There seems to be no way out from the restriction having to wait until infinity when dealing with the systems of unknown kind.


However, this Pausa, or intermediate state in a CMP is still having interesting observed consequences into the measured responses :D


- Elias


... there are *several steady states* in a CMP system - and given, we define "steady state" as having no SPL change over some delta time.


There simple aren't seveal steady states if the system is LTI. There is only one.
 
There seems to be no way out from the restriction having to wait until infinity when dealing with the systems of unknown kind.

Awaiting eternity with CMP isnt enough ;) - simply - if you shut down signal (at "precisely eternity" LOL) the "CMP tail" comes after - which is again a steady state (at least by my definition of no SPL change during some delta time)

So - we could state (a little bit pronounced possibly):
With CMP systems we simply wouldn't get FR's determined this side of eternity *by measurement*.
:D

Or - on the other hand - if we follow my proposal to look at steady states reached *immediately* (though consecutively) we just have to wait for delay time plus a little bit.

Again - all that "steady state" stuff does not "fit that well" for CMP systems.

Michael
 
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Hi,


However some interesting things can happen. It's time to review the definition of the "steady state" :D
In the boarder sense it can be said a system enters a steady state after the transient state has been passed.
How do we know when this happens? In steady state the system is constant so all the partial time derivatives of any properties of the system are zero.


- Elias

I guess you need to define "properties".
 
What an extraordinary amount of nonsense. Any LTI system is by definition always in steady state, it is time invariant :rolleyes: don't confuse the system with the output. If the input is periodic the output becomes periodic or zero after at most the duration of the impulse response. If the input is not periodic the output ceases after the input ceases plus the duration of the impulse response.
 
Seems like lots of people interested in academic discussion.:D May I stick in a reminder that all these computational methods are developed to assist in reasonably predicting the design performance through application of theory to analysis and measurement.:cool: There is no really accurate model to the point that error is zero. Theoretically, steady state is reached at infinit time, in reality you can never get steady state due to noise. So it boils down to within what tolerance is acceptable for design work?:)
 
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So reading back through a few of these posts, let me see if I have understood correctly, what with it being so complex. The inhabitants of planet Michael Elias are so ignorant as to the physical nature of the systems they are observing they have no idea of whether their impulse response durations might be measured in seconds, hours or days. Being also blissfully unaware of even the basics of System Identification and not possessing the common sense required to agree on the period of continuously zero output after a transient input that would indicate they had indeed seen the end of the systems's impulse response, they instead indulged in wild speculation about whether an entirely new branch of system theory might be needed to describe these mysterious "systems whose impulse response duration we don't know yet".

Earth calling plant Michael Elias. Your atmosphere is dangerously low in oxygen. You have begun babbling incoherently. Suggest you come back down to earth immediately. Over. :)
 
John - we don't always agree, but here we are pretty much on the same page. I have been wondering this same thing myself, but, alas, Michael and I have long history and I didn't seem the point of "beating a dead horse". But it is good to see that others realize the situation, as I shudder to think what would become of DIY should people really buy into all this misinformation.
 
What an extraordinary amount of nonsense.
So reading back through a few of these posts, let me see if I have understood correctly, what with it being so complex.
….
The inhabitants of planet Michael Elias are so ignorant as to the physical nature of the systems they are observing …...
…. they instead indulged in wild speculation about whether an entirely new branch of system theory might be needed to describe these mysterious "systems whose impulse response duration we don't know yet".

Earth calling plant Michael Elias. Your atmosphere is dangerously low in oxygen. You have begun babbling incoherently. Suggest you come back down to earth immediately. Over. :)
...
I shudder to think what would become of DIY should people really buy into all this misinformation.


You are welcome to give any better explanations than „CMP“ behaviour or „frequency response changing with time we look at“ to the plots below (mind you - we could do the exact same discussion with an OB dipole):

FR_TDlessdamping_5ms-gating.png

http://www.diyaudio.com/forums/multi-way/100392-beyond-ariel-141.html#post2264530


182222d1280578890t-beyond-ariel-10-10k_2nd-try.png

http://www.diyaudio.com/forums/multi-way/100392-beyond-ariel-139.html#post2259010


and you are also welcome to *PROVE* that what I summarised about CMP behaviour at :

http://www.diyaudio.com/forums/multi-way/100392-beyond-ariel-136.html#post2249887
http://www.diyaudio.com/forums/multi-way/100392-beyond-ariel-136.html#post2250216

is flawed.
John K wasn't able so far - so it might be *your* chance
:)


Michael
 
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Michael !

Would't it be a good idéa to make a document (which you seem to like to do) with your CMP theories and put that at your place "Audio and Loudspeaker Design Guidelines". Make a link to it like you already do, and then end the CMP-discussion on this forum?

Yes, you see something than you want the rest of the world to see too, but please drop that prestigious side of yours and realize when to end a discussion.

Personally, I sometimes have a hard time following what you are writing. In this document that I propose, make it a challange and try be as clear as John K (to me he's a reference in clarity). This might give you new CMP-supporters. (Start a new thread on the subject)

You give a lot of energy to this forum, so keep up the good work !

No hard feelings...

Per
 
Michael !

Would't it be a good idéa to make a document (which you seem to like to do) with your CMP theories ...and then end the CMP-discussion on this forum?

No hard feelings...

Per

Excellent idea ! - where did I have my thoughts ?
;)

Possibly at the question : "LTI or not LTI, thats the question" (with respect to CMP behaviour) - though - thats actually not my problem...
:D

Michael
 
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You are welcome to give any better explanations than „CMP“ behaviour or „frequency response changing with time we look at“ to the plots below (mind you - we could do the exact same discussion with an OB dipole):
I'll just deal with your fundamental misunderstanding if that's OK, since all the rest seems to flow from that.

The Frequency Response aka Transfer Function of a system is the FT of the entire impulse response. Whilst it may be useful, instructive or simply amusing to look at the spectrum of windowed portions of the impulse response, the fact that the spectrum of those various windowed portions varies falls into the category of scientific knowledge we generally refer to as "blindingly obvious" and has no bearing on the LTI nature of the system whose impulse response is being examined. The impulse response and corresponding transfer function do not change regardless of how often or minutely you choose to observe little slices of it.

I hope that helps you get on with your life and find some constructive endeavours on which to devote your admirable enthusiasm.