ARTA

Hi Ivo,

Now, few words about minimum phase concepts. Here I can’t agree with you, as every system that has more than one path in energy flow is non-minimum phase, no matter how that sideband energy flow is low.
I'm still not sure about this. More than one path makes non-minimum phase possible but it is not the only requirement. Please have a look at the following article to see if you agree with the conclusions or can find fault with it:

Digital Filters, Filter Inversion, Minimum Phase and All That (Part II )

In particular:

Things That Are Minimum Phase and Things That Are Not

For a filter to be non minimum phase, it has in effect to make some later parts of its impulse response very important and/or unpredictable compared to its initial output from an impulse. This is somewhat unusual behavior for a physical device. And most "analog" filters, filters that are in fact physical devices, are also minimum phase. Amplifiers, for instance, are minimum phase. So are speaker drivers, in enclosures or not. And, as we have observed already, a speaker's direct sound plus reflection(s) is typically minimum phase provided the reflected sound is lower in level than the direct sound.
I would add to this that empirically a traditional cone or dome driver measures as minimum phase even up to very high frequencies where the cone is multiple wavelengths in size and is experiencing cone breakup. I have not measured a traditional driver yet that was not exactly minimum phase at high frequencies no matter how bad it's cone breakup is.

However something like a dual cone (whizzer cone) full range driver is not minimum phase - because it is effectively a two way speaker with two displaced cones and a mechanical crossover instead of electrical, so naturally they develop excess phase.

I have many of these drivers and you can even work out what the mechanical crossover frequency and slope is based on the excess group delay hump which is easily measurable with ARTA. (About 6Khz and roughly 2nd order on the ones I have)

On the other hand a traditional cone driver shows a flat excess group delay response on ARTA except for some gradual curvature at low frequencies caused by measurement errors introduced by a finite measurement gate time. But at high frequencies there is none.

then all systems with wave manifestations (reflections and diffraction) - they have significant deviation from minimum phase when characteristic radiating dimensions are larger than 1/12- 1/6 of wave length.
Do you have any measurements of drivers on baffles that show this ?
Even the ¼ inch microphone can’t satisfy this requirement in whole audio band. All loudspeakers have minimum phase only in smaller part of its passband.
If reflections have to be greater in amplitude than the original signal at some frequency to become non-minimum phase then I doubt any reflections from the microphone boom and microphone itself would be strong enough. They would of course cause undesirable changes in frequency and phase response, but not make the response non-minimum phase.

Again, I've not detected any excess phase in measurements of minimum phase speakers by introducing deliberate reflection points near a measurement microphone, do you have any measurements showing this happening ?
Your reasoning is good if we look at practical side of design – a small phase error in crossover region will introduce small acceptable error.
But, everybody must decide which error level is acceptable as there is no theory for augment that decision.
From what I can see, when reflections are involved there is not a gradual increase in excess phase as reflection strength increases, but a threshold effect. If reflections are all lower in amplitude than the original signal at all frequencies, the response is of course modified by the reflections (amplitude and phase changes) but remains exactly minimum phase.

As soon as a reflection becomes greater in amplitude than the original at some frequency, there is a sudden change from minimum phase to non-minimum phase.

This is especially apparent when measuring room bass response where it can be exactly minimum phase over a wide range of frequencies then you will see a sudden "glitch" in the phase response across the boundary of a response null as the phase jumps suddenly on either side. If you add an additional bass driver to the room in another location that is not subject to the null condition to fill in the hole, the response "snaps" back to being exactly minimum phase through this frequency region.

Sorry if I seem to be labouring a point but I think the conditions under which drivers/microphones and speaker systems are minimum phase or not is quite important and useful to know and I am trying to get it 100% straight in my mind as there does seem to be significant disagreement between different sources.
 
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On the other hand a traditional cone driver shows a flat excess group delay response on ARTA except for some gradual curvature at low frequencies caused by measurement errors introduced by a finite measurement gate time.

Major challenge to investigate possible deviations from minimum-phase is composing the reference i.e. minimum phase response itself. Paradox is that both measured magnitude and measured phase are quite mandatory information to create minimum phase response which would be reliable enough as a reference.

For example errors due to time windowing are more common in magnitude response than phase response. So it would be better to generate magnitude by phase and not how it's usually done. If we generate for example phase by magnitude, a human should make several subjective choices and guesses to crop and extend frequency range outside known and reliably measured range in order to create good basement for minimum-phase calculation. This is one reason why minimum phase extraction might be worth to skip while speaker design process.

I have done some research about possible non-minimum phase features of drivers (while trying to create tolerable automation for tail correction and minimum phase extraction to VCAD). Some deviations exist but usually they are not wide and high. Things get much uglier at cone breakup. Horns would be interesting measure again. Earlier studies were not reliable due to bad reference (minimum) phase.

Anyway, whole point is that "bad/unreliable minimum phase extraction is much worse than no minimum phase extraction".
 
I am making some simulation directly in ARTA code and tomorrow I will present results of influence of reflections on quality of minimum phase estimation.

Ivo
Will be interesting to see.

I was experimenting last night with some measurements taken at 1 metre in my living room looking at excess group delay.

Gate time long enough to include baffle diffraction but short enough to exclude floor/wall etc reflections - no deviation from minimum phase.

Gate time increased to include the first reflection, (floor bounce) clearly seen in the impulse window - still no deviation from minimum phase. Excess group delay tracks the previous measurement exactly. (Had to turn off overlay trace to be sure the new measurement was really there as it was exactly overlaid!)

Increasing gate time further to include sidewall reflections - starting to see some abrupt deviations from minimum phase but only at a few specific spot frequencies, elsewhere it still tracks exactly with previous measurements.

Full FFT with no window set - lots of deviations from minimum phase across most of the spectrum.

So clearly once the gate time is long enough to include most room reflections the sum of all reflections included in the measurement window becomes strong enough to produce a non-minimum phase result.

I also clearly observed the threshold effect I talked about earlier - as gate time was progressively increased to include more and more delayed reflections there was no deviation in excess group delay until suddenly there were large spikes at specific frequencies. There was not a gradual progressive increase in phase deviation from minimum phase.
 
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^Excess phase would be more revealing than excess group delay which is kinda divided by frequency.

These are measured responses divided by minimum phase response i.e. excess phase in gray:

Tweeter of 15" PA coax
An externally hosted image should be here but it was not working when we last tested it.


Woofer of 15" PA coax
An externally hosted image should be here but it was not working when we last tested it.


Producing of minimum phase response which is valid enough for comparison is quite slow and subjective work.
 
^Excess phase would be more revealing than excess group delay which is kinda divided by frequency.

These are measured responses divided by minimum phase response i.e. excess phase in gray:

Tweeter of 15" PA coax
An externally hosted image should be here but it was not working when we last tested it.
If excess phase is the grey line what is the blue line ?
 
Think you have interesting MP discussions going on here : ) especially because into own diy amateur invetigations so far can conclude the subjective outcome about musical resolution/3D/rhythm gets real better analog sounding (real world) the closer to a real standing MP doamin we arrive at.

Is there possibility improve measurement method by let it in bagground filter measured IR divided up in more than say +20 bands so as to when compared to a textbook domain at same samplerate it can better filter out what is possible reflection and what is real direct sound, hope not it sounds too stupid but a feeling is that if we look at below filtered graphs into REW of same measured IR that there is some pattern going on. Below live system is acoustic 2-way XOed at 180Hz with LP filter and system target domain is MP BW1 at 100Hz to BW2 at 20kHz inside a 96kHz measurement chain where excess input chain is corrected for in DSP with temporary inverse settings, and for info that target is later dialed into another house curve with a global EQ that suits and also extracts the particular room. Upper graphs is measured acoustic where left show raw non smoothed 500mS window and upper right is 1/6 FDW, lower left is the raw non smoothed textbook target for upper left and lower right is 1/6 FDW textbook target for upper right, and vertical Y axis is covering 150dB in steps of 10dB.
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More on minimum phase

In a linear system theory, the minimum phase property is defined as property that system transfer function H(s) can be invertible, which means that function 1/H(s) is finite (it also means that response has no zeros in right plane of complex frequency variable s). Practically, this also means that minimum phase system can be equalized.

In my paper "Loudspeaker Minimum Phase Estimation" that has been added to Artalabs support page, I have shown that there are significant errors with all known methods for calculation of minimum phase at higher frequencies. That errors can even be larger than errors introduced by slight non-minimum phase behaviour of loudspeaker systems.

ARTA uses DFT method which wrap phase due to DFT property that it treats spectrum as periodic with period equal to sampling frequency. The error also depends on antialiasing filter phase property if we measure in single channel mode, so errors can be specific to used soundcard if we measure in single channel mode.
The error is smaller if we measure in dual channel mode, but still some error exists as noise above antialiasing cut-off also affects magnitude/phase estimation.

In acoustical measurements we deal with response that contains discrete sum of direct wave and reflections. We can hardly say that it is a linear system. In my last post I promised that I will give some measurement results on systems with reflections, but here I will present an analytical analysis that will more clearly shows some fact about influence of reflections.

In further discussion I will take that system response is composed of direct wave and one reflection that has r-times lower amplitude than direct wave.
Assuming that system has direct wave frequency response H(jw) then total response can be expressed as

G(jw) = H(jw) * (1 + r * exp(-jwT))

T is reflection delay time, r is ratio of reflection and direct wave amplitude, and w is circular frequency.
By further calculation we get magnitude and phase of total response:

Magn(G(w)) = Magn(H(w)) * sqrt(1+ r^2 + 2*r*cos(wT))
Phase(G(w)) = Phase(H(w)) + arctg((r*sin(wT)/(1+ r*cos(wT)))

What is important to note is that reflection shows up as ripple of period 1/T both in magnitude and phase response.
Amplitude of ripples does not depend on delay just on level of reflections. For example, if reflection level is -20dB the ripple in magnitude is plus/minus 0.85dB, and ripple in phase is plus/minus 5 degrees.

Minimum phase calculation uses this “stationary” frequency response, so it does not differentiate whether ripple is caused by linear system behaviour without delay or with system with delay.

Our hearing system (on the contrary) differentiate responses with small and larger reflection delays. Delays smaller than 10ms degrade sound reproduction, while larger one can even enhance loudness. So, it is not good idea to change ripples that are results of reflections with large delays.
The problem arises if we want to radically equalize response with analog or digital filters, to get smoother response or better crossover adjustment. Almost all CAD systems uses filter design that is based on linear system theory (systems without discrete delayed reflections). They equalize peaks in frequency responses by treating them as system resonance, which they are not. Calculation of minimum phase also treats ripples as linear system behavior, therefore using minimum phase estimation for equalization of acoustical system is not the way to go. We have to apply additional techniques, like gating and smoothing, to get more useful results.

Ivo
 
In limp, is it possible to implemend a quick sweep test function too? I find the stepped sine test so slow and the mls test so inaccurate, i therefor think a quick sweep might be work best

This is most wanted feature in LIMP, but I have to disappoint you. The swept sine is worst type of excitation for impedance measurement.
As you know, during the measurements loudspeaker also acts as microphone and introduce environmental noise in measurement.
Swept sine processing is very sensitive to impulsive type of noise, and they usually manifest as false resonances, and on some frequencies errors can be very high.


Best,
Ivo
 
Ok, i knew it was something bad to it, but many thanks for your reply!

If you measure with multiple swept sines and do averaging, is it still worse then mls?

When i do sine impedance measurements my computer gives me error messages and the measurement freezes, if there was a splice function i could work around it by measuring small parts at a time. only mls works without any problem. However, i have noticed that on some drivers the difference in response curves are huge depending on stimuli and on some drivers there are hardly no differencies at all.
 
Hi,
I do not recommend averaging with swept sine.
MLS or random noise systems do distribute errors (noise) over all frequency, we call it a phase randomization property in correlation analysis. Averaging further reduce noise.
In swept sine analysis we do not have signal with such randomization property, so error from impulsive noise is concentrated on sweep frequency that has been captured in time when impulsive noise occured. That is why averaging has lower influence on S/N.
Otherwise, when there is no impulsive noise, swept sine gives better S/N than MLS.

It is quite normal that there is a shift of resonance frequency when measuring with stepped sine and with pink noise. The reason is larger excitation amplitude of stepped sine that changes effective driver compliance. Both measurements are useful as they represent small signal and large signal driver behavior.

Best,
Ivo
 
When i do sine impedance measurements my computer gives me error messages and the measurement freezes, if there was a splice function i could work around it by measuring small parts at a time.
What sound card do you use and do you use ASIO driver mode ?

If so, what sampling frequency, bitdepth etc do you use, and does your sound card provide any control panel that lets you customise properties such as buffer size ?

You might have the same issue I reported in post #619:

https://www.diyaudio.com/forums/multi-way/76977-arta-13.html#post5542995

I resolved it by changing the ASIO driver settings for my sound card.

However, i have noticed that on some drivers the difference in response curves are huge depending on stimuli and on some drivers there are hardly no differencies at all.

Hi,
It is quite normal that there is a shift of resonance frequency when measuring with stepped sine and with pink noise. The reason is larger excitation amplitude of stepped sine that changes effective driver compliance. Both measurements are useful as they represent small signal and large signal driver behavior.
To expand on this a little, (because I find it an interesting topic that is under appreciated when measuring thiele/small parameters) the shift in driver fundamental resonance with the amplitude of the excitation signal is a result of a non-linear compliance - in other words non-linearity in the suspension and/or surround of the driver.

If the suspension was perfectly linear there would be only one resonant frequency regardless of amplitude so a driver whose resonance hardly changes between small signal and large signal testing has a very linear suspension. A driver whose resonance frequency shifts a lot with amplitude has a much more non-linear suspension. Most drivers will show some shift in resonance with amplitude.

Whether this matters depends on the application of the driver. For example if you take a woofer with a somewhat non-linear suspension whose Fs shifts significantly with test level when freely suspended (no box) and place it in a small closed box, the compliance of the air in the box will dominate, and air is a much more linear spring than a typical spider/surround.

The result is that the combined compliance of suspension and air in the box will be very linear and the change in Fs (now at a much higher frequency) with level will no longer happen.

So it's more of a problem in bass alignments where the box is large compared to the drivers compliance, or in bass reflex designs above box tuning. (Near box tuning it doesn't matter because the driver is heavily loaded and linearised by the helmholtz resonance, but at the peak excursion area above the box resonance it does matter)

In the case of a midrange driver non-linearity of the suspension and shifting Fs may not even matter as long as the response of the driver is high pass filtered above the mechanical resonance in the enclosure because the driver is only operating in the mass controlled region, and even if you go into the compliance controlled region it will probably be dominated by the air in a small closed box. So seldom important for a midrange driver.

I agree that both small signal and large signal measurements are useful for a woofer - as you can simulate the bass response in the desired enclosure with both small signal and large signal T/S parameters and observe the difference in response to ensure that both are acceptable, which is what I do.

However if I had to choose only one measurement for a woofer/mid I would choose the large signal measurement - taken at about 1/4 to 1/2 of Xmax as being the more useful figure than a very low level measurement where the cone is not even visibly moving as there can be strange suspension non-linearities at very low drive levels due to material properties which will never be audible, especially with non-homogeneous materials like doped fabric surrounds often found in midrange or fullrange drivers.

Another point I'd make is that you often see people reporting quite large inconsistencies in measured Thiele/Small parameters between manufacturers figures and their own, or between their own and other 3rd party measurements.

While measurement error is certainly possible, as are driver variations, in most cases I think this can be explained by taking the measurements at different drive levels and/or using different stimulus (noise vs stepped sine vs swept sine etc) and not appreciating the fact that effective Cms (compliance) (and therefore all parameters that depend on Cms, such as Vas) is not a single figure but depends on amplitude and test signal type.

Of the different test signal types stepped sine is definitely the best and most consistent measurement method in respect to suspension non-linearity even though it does take a bit longer, and it's important to be consistent with your signal levels when testing to get consistent results. Pick a test amplitude relative to the driver's Xmax and stick with it.
 
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However if I had to choose only one measurement for a woofer/mid I would choose the large signal measurement - taken at about 1/4 to 1/2 of Xmax as being the more useful figure than a very low level measurement where the cone is not even visibly moving as there can be strange suspension non-linearities at very low drive levels due to material properties which will never be audible, especially with non-homogeneous materials like doped fabric surrounds often found in midrange or fullrange drivers.


Just, following your discussion, I want point to AES2-2012 standard that recommends sine amplitude of 0,1 Vrms for TSP measurements.


And, ...
I want to all of you happy New Year.

Ivo
 
In my paper "Loudspeaker Minimum Phase Estimation" that has been added to Artalabs support page, I have shown that there are significant errors with all known methods for calculation of minimum phase at higher frequencies. That errors can even be larger than errors introduced by slight non-minimum phase behaviour of loudspeaker systems.

ARTA uses DFT method which wrap phase due to DFT property that it treats spectrum as periodic with period equal to sampling frequency. The error also depends on antialiasing filter phase property if we measure in single channel mode, so errors can be specific to used soundcard if we measure in single channel mode.
The error is smaller if we measure in dual channel mode, but still some error exists as noise above antialiasing cut-off also affects magnitude/phase estimation.
So what you are saying is minimum phase estimation can be unreliable near the upper frequency limits imposed by the sample rate ?

Perhaps this explains why I get (seemingly) very good results with minimum phase estimation, excess phase, and excess group delay with ARTA, as I always use a 192Khz sample rate on a sound card that truly supports this sample rate. (Not fake or resampled)

So at frequencies of interest up to a maximum of 20-30Khz I would not see errors in phase estimation due to this being a long way from the upper bandwidth limit imposed by the sampling rate. I also always use full dual channel mode.

I can certainly see that if I used a sample rate of say 48Khz that phase data at 20Khz would be questionable, but not with a 192Khz sample rate and dual channel mode.

I think your algorithms to derive minimum phase, excess phase and excess group delay are much better than you give them credit for. I have certainly been impressed by how cleanly ARTA can extract an accurate, smooth excess group delay curve (for example of a multiway speaker) when the group delay itself can be extremely lumpy (due to poor amplitude response of the speaker) with variations of an order of magnitude or more greater than the excess group delay. Yet none of those group delay variations bleed into the excess group delay. This suggests a very high accuracy of minimum phase and therefore excess phase estimation.
 
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Ivo, you too.
0.1 volt is the terminal voltage or voltage after connecting the speaker?

Standard ase02-2012 gives guidelines:
"Suspend the driver in free air and supply a variable-frequency sinusoidal signal at a low level (typically 0,1 V)."

There is no strict requirement, but if you want be close to this value on speaker terminals use in LIMP measurements lower value reference resistor.

Ivo
 
So what you are saying is minimum phase estimation can be unreliable near the upper frequency limits imposed by the sample rate ?

Perhaps this explains why I get (seemingly) very good results with minimum phase estimation, excess phase, and excess group delay with ARTA, as I always use a 192Khz sample rate on a sound card that truly supports this sample rate.

As a audio engineer I am very happy when I have measured response uncertainty lower than 1dB in level and 5 degree in phase.
But as a designer of measurement device I must unveil what are limitations of some method.

Using higher sample rate (x4) gives much better min.phase estimation.
It is a consequence of simple fact: In computer based measurement we deal with discrete image of analog system. Discretization of signals makes their spectrum periodic with period equal to sampling frequency. If we measure driver which response is significantly reduced below fs/2 we get high quality estimation of analog system response.

Ivo
 
ARTA Issues

Can anyone help me with the following issue I'm having with ARTA:

I'm trying to take gated measurements of a Woofer. I performed 4 measurements with the mic on axis with the woofer.

For all 4 measurements, no settings were changed: The mic location was kept the same, the speaker location was kept the same, same gating, same software settings....same everything.

However, my low-frequency response changes with every measurement. Anyone know why this would be the case?
 

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