Beyond the Ariel

[JohnPM]

Originally Posted by mige0

you didn't drop a single word about CMP systems for now.

Never heard of them.

[KSTR]

Originally Posted by JohnPM

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

[mige0]

Originally Posted by JohnPM

Never heard of them.

Interesting stuff never is read in books first.
LOL

Originally Posted by john k...

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

[JohnPM]

Originally Posted by mige0

Impulse response IMO is not compromised - but FR actually is - which shades some light on the swiss knife tool of FT and its usability and limitations in audio.

Hmmm. Have you heard the phrase "bad workmen blame their tools"?

[mige0]

Originally Posted by KSTR

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

[Elias]

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"
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


- Elias

Originally Posted by mige0

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

Originally Posted by john k...

There simple aren't seveal steady states if the system is LTI. There is only one.

[mige0]

Originally Posted by Elias

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*.


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

[john k...]

Originally Posted by Elias

Hi,


However some interesting things can happen. It's time to review the definition of the "steady state"
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".

[JohnPM]

What an extraordinary amount of nonsense. Any LTI system is by definition always in steady state, it is time invariant 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.

[soongsc]

Seems like lots of people interested in academic discussion. 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. 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?