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Multi-Way Conventional loudspeakers with crossovers

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Old 22nd November 2018, 10:19 AM   #661
DBMandrake is offline DBMandrake  Scotland
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Hi Ivo,

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Originally Posted by iMat View Post
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:

Quote:
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.

Quote:
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 ?
Quote:
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 ?
Quote:
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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Last edited by DBMandrake; 22nd November 2018 at 10:23 AM.
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Old 23rd November 2018, 01:19 PM   #662
kimmosto is offline kimmosto  Finland
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Quote:
Originally Posted by DBMandrake View Post
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".
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Old 23rd November 2018, 11:13 PM   #663
iMat is offline iMat  Croatia
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Default on minimum phase

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
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Old 24th November 2018, 08:22 AM   #664
DBMandrake is offline DBMandrake  Scotland
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Quote:
Originally Posted by iMat View Post
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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Last edited by DBMandrake; 24th November 2018 at 08:28 AM.
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Old 24th November 2018, 09:32 AM   #665
kimmosto is offline kimmosto  Finland
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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
Click the image to open in full size.

Woofer of 15" PA coax
Click the image to open in full size.

Producing of minimum phase response which is valid enough for comparison is quite slow and subjective work.
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Old 24th November 2018, 10:25 AM   #666
DBMandrake is offline DBMandrake  Scotland
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Quote:
Originally Posted by kimmosto View Post
^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
Click the image to open in full size.
If excess phase is the grey line what is the blue line ?
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Old 24th November 2018, 12:00 PM   #667
kimmosto is offline kimmosto  Finland
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^Measured magnitude divided by magnitude of minimum phase response = 1.000 between cropped and manually extended tails of m.p. response.
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Old 24th November 2018, 03:08 PM   #668
BYRTT is offline BYRTT  Denmark
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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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Old 24th November 2018, 05:36 PM   #669
iMat is offline iMat  Croatia
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Default 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
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