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Author Topic: Minimum phase and acoustics  (Read 14014 times)

AndreasN

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Minimum phase and acoustics
« on: September 25, 2010, 08:50:36 am »

Hello!

Have a question regarding minimum phase in acoustics. It's a common claim from the EQ camp that any phenomena that is indicated by a measurement system to be minimum phase is minimum phase.

Disregarding measurement systems for a while - is there a physical rationale behind such an assumption?

If a current in a voice coil makes a magnet move, that's a direct cause and consequence. That's minimum phase. So far, so good. If the membrane attached to the magnet starts flapping, it's not a direct cause->consequence, it's an indirect consequence. Ditto with edge diffraction and... Anything involving interactions between direct sound and reflections from a room! As in acoustics in general.

So how come some claim certain acoustical phenomena are minimum phase and hence can be corrected by EQ? I can't wrap my mind around this.. It seems to me that it's an outlandish claim. But I'm apt at jumping at too quick conclusion.

Thoughts?


Regards,

Andreas Nordenstam
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bruno putzeys

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Re: Minimum phase and acoustics
« Reply #1 on: September 25, 2010, 11:17:07 am »

AndreasN wrote on Sat, 25 September 2010 14:50

It's a common claim from the EQ camp that any phenomena that is indicated by a measurement system to be minimum phase is minimum phase.

There's no "EQ camp" claiming this. There is no such thing as a "minimum phase phenomenon". What exists is a minimum phase transfer function (=magnitude & phase response rolled into one). When, in acoustics, someone says that a measured transfer function is minimum phase they most certainly mean it's a combination of a minimum phase transfer function PLUS a pure delay (which is NOT minimum phase).

You can get an idea of whether a measured impulse response is that of a minimum phase transfer by looking at how it decays. If you see no echos or ringing bigger than the initial spike you can be reasonably sure that it's MP.

There's something pretty crucial about this. The response of a driver mounted in a cabinet, measured more or less on axis in a more or less reflection-free environment, is usually minimum phase (+delay). Turn the cabinet around and it's no longer the case. The first thing to hit the mic is the diffraction (a weak spike) followed by the first reflection which is much louder.

That's why you can't say some physical process is minimum phase. The response from the same speaker, as measured in different environments or from a different angle may or may not be minimum phase.

Minimum phase has several implications:
1) phase response can be derived directly from magnitude response and vice versa.
2) The phase responses of two MP transfer functions that have mirror-image magnitude responses (in dB), are mirror images as well.

Analogue EQ's normally have MP. If you use one to correct the magnitude response of another MP transfer function, the phase response is corrected as well. By necessity this means that the impulse response is also corrected. For instance, when designing a loudspeaker you're best off first correcting each drive unit separately, precisely because of this. A single wideband loudspeaker unit with an EQ in front of it can have a spectacularly tight impulse response, even if the same unit without EQ does not.

Non-minimum phase transfer functions can be corrected as well, to an arbitrary degree of precision but never exactly, and always at the expense of added delay. The complement of a non-minimum phase filter is a non-causal filter (one that has "pre-decay"), which can be approximated using an FIR filter provided you add as much delay as the amount of "pre-decay" you actually want to realise.
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Thomas Jouanjean

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Re: Minimum phase and acoustics
« Reply #2 on: September 26, 2010, 03:28:06 pm »

bruno putzeys wrote on Sat, 25 September 2010 10:17

When, in acoustics, someone says that a measured transfer function is minimum phase they most certainly mean it's a combination of a minimum phase transfer function PLUS a pure delay (which is NOT minimum phase).



Smile

And a pure delay in acoustics is very hard to achieve in a studio situation, for example because of the material's density vs behaviour with regards to different frequencies.
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Thomas Jouanjean
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AndreasN

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Re: Minimum phase and acoustics
« Reply #3 on: September 27, 2010, 07:35:06 am »

bruno putzeys wrote on Sat, 25 September 2010 17:17


There's no "EQ camp" claiming this. There is no such thing as a "minimum phase phenomenon". What exists is a minimum phase transfer function (=magnitude & phase response rolled into one). When, in acoustics, someone says that a measured transfer function is minimum phase they most certainly mean it's a combination of a minimum phase transfer function PLUS a pure delay (which is NOT minimum phase).


Thanks for the clarifications!

Sorry for the poor phrasing in the original post. What I was trying to address is the link between observation system and reality. Don't want to mention names here. There are however, in the room EQ industry, a typical assumption that parts of a room response is close enough to "being" minimum phase. Close enough that the resulting observed aberrations in frequency response can be corrected by minimum phase IIR filters where the poles and zeroes are set by virtue of the seemingly "minimum phase" behaviour in parts of the observed response. Typically done by finding areas where the excess phase calculation is flat. In other words, looking for "a pure delay + minimum phase" response in the room and then disregard the "pure delay" part.

It doesn't seem to me that it's a procedure that have any physical basis. How is a delay+minimum phase response supposed to be corrected by a pure minimum phase response?


(didn't intend to mention names, but here's an example to make it clearer)
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bruno putzeys

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Re: Minimum phase and acoustics
« Reply #4 on: September 27, 2010, 09:50:48 am »

Oh well I think the opinion held "here" with regards to room EQ in general is sufficiently known Wink

As your link shows, people run a lot of numbers on these problems whilst utterly failing to grasp the fundamental issues. Running through the text (approx. 20 seconds) I think their understanding of minimum phase etc is good enough, but the link between "minimum phase regions" and sensibility of room EQ is assumed, not demonstrated.
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AndreasN

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Re: Minimum phase and acoustics
« Reply #5 on: September 27, 2010, 10:31:26 am »

Thanks again! Glad you could help me with a reality check. Was starting to wonder if I was missing out on something fundamental.

bruno putzeys wrote on Mon, 27 September 2010 15:50

I think their understanding of minimum phase etc is good enough, but the link between "minimum phase regions" and sensibility of room EQ is assumed, not demonstrated.


This touches one of the most interesting aspects of room EQ'ing/DSP. There is actually a continual stream of practical tests that "proves" that the applied EQ/DSP treatment works as intended. It's a circular argument; using the same contrived observational setup to evaluate the problem, the treatment and the effect of the treatment.

A typical "proof of virtue" is to show that standing waves are hitting the noise floor at some earlier time than previously measured. Exactly what one expects when putting less energy into the system at the resonant frequency!

As frequency response is commonly evaluated using relatively long windows, the same circular argument is oftentimes found in that area.

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Ethan Winer

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Re: Minimum phase and acoustics
« Reply #6 on: September 27, 2010, 02:33:42 pm »

AndreasN wrote on Mon, 27 September 2010 10:31

There is actually a continual stream of practical tests that "proves" that the applied EQ/DSP treatment works as intended.


Andreas, I know you're aware of my position on this. I'm not a math guy like you and Bruno and others, so all I can do is actually test the claims. When I did that (LINK) the claims were proven false. It might be possible to tweak DSP to reduce ringing at the microphone position, though I was never able to confirm that either. Regardless, when you move the microphone even one inch all the ringing comes back. So what's the point?

--Ethan

bruno putzeys

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Re: Minimum phase and acoustics
« Reply #7 on: September 27, 2010, 04:26:37 pm »

Ethan Winer wrote on Mon, 27 September 2010 20:33

So what's the point?

The quotes, I think.
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Geoff Emerick de Fake

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Re: Minimum phase and acoustics
« Reply #8 on: September 28, 2010, 08:32:47 am »

AndreasN wrote on Mon, 27 September 2010 06:35

bruno putzeys wrote on Sat, 25 September 2010 17:17


There's no "EQ camp" claiming this. There is no such thing as a "minimum phase phenomenon". What exists is a minimum phase transfer function (=magnitude & phase response rolled into one). When, in acoustics, someone says that a measured transfer function is minimum phase they most certainly mean it's a combination of a minimum phase transfer function PLUS a pure delay (which is NOT minimum phase).


Thanks for the clarifications!

Sorry for the poor phrasing in the original post. What I was trying to address is the link between observation system and reality. Don't want to mention names here. There are however, in the room EQ industry, a typical assumption that parts of a room response is close enough to "being" minimum phase. Close enough that the resulting observed aberrations in frequency response can be corrected by minimum phase IIR filters where the poles and zeroes are set by virtue of the seemingly "minimum phase" behaviour in parts of the observed response. Typically done by finding areas where the excess phase calculation is flat. In other words, looking for "a pure delay + minimum phase" response in the room and then disregard the "pure delay" part.

It doesn't seem to me that it's a procedure that have any physical basis. How is a delay+minimum phase response supposed to be corrected by a pure minimum phase response?


(didn't intend to mention names, but here's an example to make it clearer)
I'll try to shed a different light on this.
Note: I assume here for simplification that direct signal is time-normalised at the listening position, hence qualified of "undelayed".
Many people think that since many acoustic problems are caused by delays and combination of non-delayed and several differently delayed signals, the cure can only be using time-delay techniques to fix them.
Although this may be philosophically true if one wants to address the whole frequency spectrum, it turns out that, at lower frequencies, the effect of combining these signals is merely a modification of the frequency (and phase) response that can generally be addressed by rather conventional EQ techniques. It is clear that, if we consider the simplest comb-filtering effect, which shows complete phase-cancellation when two signals of equal amplitude are delayed by a half-wave, there is no way an EQ would fix this (the least difficult aspect being capable of producing infinite boost).
But in fact, it has largely been demonstrated that up to half the cancellation frequency, standard EQ can be applied, that will correct both amplitude and phase response.
In a real-world situation, there are an infinite number of reflections, but generally, there's not one of sufficient amplitude to introduce complete phase-cancellation, but rather a series of smaller reflections of more or less spread delay, which a good acoustic designer will "tame" in order to make them closer to minimum-phase behaviour, and as a consequence, more EQ-friendly.
Indeed, it is not possible to solve delay-related problems with EQ at MF and HF, but neither is it actually practically doable with delay techniques.
Most of the "reverse impulse response techniques" end up doing just about the same as their purely EQ counterparts. Those techniques that are supposed to work at MF are plagued with a too-narrow sweet spot.
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JohnM

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Re: Minimum phase and acoustics
« Reply #9 on: October 02, 2010, 06:15:28 pm »

AndreasN wrote on Mon, 27 September 2010 12:35

Sorry for the poor phrasing in the original post. What I was trying to address is the link between observation system and reality. Don't want to mention names here. There are however, in the room EQ industry, a typical assumption that parts of a room response is close enough to "being" minimum phase. Close enough that the resulting observed aberrations in frequency response can be corrected by minimum phase IIR filters where the poles and zeroes are set by virtue of the seemingly "minimum phase" behaviour in parts of the observed response. Typically done by finding areas where the excess phase calculation is flat. In other words, looking for "a pure delay + minimum phase" response in the room and then disregard the "pure delay" part.

It doesn't seem to me that it's a procedure that have any physical basis. How is a delay+minimum phase response supposed to be corrected by a pure minimum phase response?

(didn't intend to mention names, but here's an example to make it clearer)
Hello Andreas,

Since I'm the author of your example text, I thought I should respond. That text was written to help non-technical users gain a basic understanding of what minimum phase means. I would not consider myself to be "in the room EQ industry", not least because I make my living in an unrelated industry and provide the REW software without charge. The "Room EQ Wizard" name dates back to the origins of the code about 8 years ago, when it was aimed at helping users of parametric EQ visualise the effect their settings would have on a response. It has since developed into an acoustic measurement package, but still offers tools to examine the effects of and configure equalisers. My position on the merits of EQ should be fairly clear from this article, which is also part of the help text you linked to: Why can't I fix all my acoustic problems with EQ?. The reason for largely disregarding delay in the minimum phase article is that the bulk of the delay is typically a time of flight issue in the measurement setup rather than inherent in the system being measured, and is not something that would be "seen" by an equaliser in series with the original system, particularly when looking at the subwoofer range where EQ can provide useful benefit. The delay also has no effect on the locations of the poles of the transfer function, which is where EQ should be targeted.

Best regards,

John
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JohnM

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Re: Minimum phase and acoustics
« Reply #10 on: October 02, 2010, 06:33:27 pm »

AndreasN wrote on Mon, 27 September 2010 15:31

A typical "proof of virtue" is to show that standing waves are hitting the noise floor at some earlier time than previously measured. Exactly what one expects when putting less energy into the system at the resonant frequency!
If an EQ filter has been adjusted to accurately target the poles of a transfer function resonance, the zeroes of the EQ filter lie on the poles of the resonance, cancelling it. The filter itself has poles, which (for a filter which cuts the response, as one would use to address a resonant peak) have faster decay than the resonance the filter targets. The poles of the resonance have in effect been replaced by those of the filter. The greater the cut, the greater the difference between the decay rates of the original resonance and the filter aimed at it. It is the greater rate of decay at the resonant frequency that indicates whether or not the filter has achieved its goal, i.e. the slope of the decay plot, how fast the response is dropping in any given time interval, not whether it reaches some fixed threshold at a given time.
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Thomas Jouanjean

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Re: Minimum phase and acoustics
« Reply #11 on: October 04, 2010, 05:58:15 pm »

Thanks for your participation John. Minimum phase is not an easy thing to explain, but it is an important subject.

Most designers know indeed how to "tame" all these problems, but let's be honest here, there are no miracles. Just educated compromises.

When I think about subjects like minimum phase which are being discussed a lot on some forums (it is THE buzz word lately it seems!) I cannot help but (still) be surprised that in the light of these discussions some of the wild numbers claimed every now and then when it comes to room responses are not questioned. Who can seriously claim responses within 3dB and be taken seriously? Basic floor, console surface and other random reflections will impose variations of anywhere between +/- 3 and 6dB at best.

If you're reaching a stable response within the 10/12dB benchmark in a control room, it is quite an achievement. I've noticed that all rooms that exceed these numbers (which is expensive) are getting dull and lifeless pretty fast, which isn't a good thing.

In short, I'm happy subjects like non-minimum phase are brought to the table because it allows a reality check - which is more and more needed in this field.

Another important subject that is never discussed is re emission (stress energy release via a given material) and damping to manage it.

'nyway, thanks all Smile
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Thomas Jouanjean
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bruno putzeys

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Re: Minimum phase and acoustics
« Reply #12 on: October 05, 2010, 02:45:26 am »

JohnM wrote on Sun, 03 October 2010 00:15

My position on the merits of EQ should be fairly clear from this article, which is also part of the help text you linked to: Why can't I fix all my acoustic problems with EQ?.


Indeed, you do mention the fatal flaw in room EQ in the linked text. But to me that's precisely what it is: fatal Smile

JohnM wrote on Sun, 03 October 2010 00:33

The greater the cut, the greater the difference between the decay rates of the original resonance and the filter aimed at it.


That one bears emphasizing because both in loudspeaker EQ and in control theory I find intuition often gives out.
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Geoff Emerick de Fake

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Re: Minimum phase and acoustics
« Reply #13 on: October 08, 2010, 10:01:14 am »

JohnM wrote on Sat, 02 October 2010 17:33

AndreasN wrote on Mon, 27 September 2010 15:31

A typical "proof of virtue" is to show that standing waves are hitting the noise floor at some earlier time than previously measured. Exactly what one expects when putting less energy into the system at the resonant frequency!
If an EQ filter has been adjusted to accurately target the poles of a transfer function resonance, the zeroes of the EQ filter lie on the poles of the resonance, cancelling it. The filter itself has poles, which (for a filter which cuts the response, as one would use to address a resonant peak) have faster decay than the resonance the filter targets.
I don't get it... Sad If the room response is approximated by a biquad, the transfer function is 1 + (ks/as
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JohnM

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Re: Minimum phase and acoustics
« Reply #14 on: October 08, 2010, 01:06:04 pm »

Geoff Emerick de Fake wrote on Fri, 08 October 2010 15:01

I don't get it...
I'm not too clear from your post what you don't get exactly, but I'll expand on my comments, which may help either make clear what I'm saying or provide some specifics for objection.

I suspect you may be considering this in terms of providing a perfect inverse for a room's transfer function by means of suitably chosen biquads. Whilst the TF of a room response from a specific source position to a specific receiver position can be broken down into its constituent poles and zeroes, which can then be grouped as biquads, that of course does not make it invertible - there are non-minimum phase zeroes in most such responses, even at very low frequencies, hence stable inverses do not exist whether constructed from biquads or anything else.

My post was about EQ filters however, not biquads in general. EQ filters have constraints on their biquad coefficients to allow them to function as intended, they do not allow independent placement of the filter poles and zeroes. I'll illustrate this with some Z-plane plots (I operate in a sampled data world Smile) and since the poles and zeroes come in conjugate pairs I'll only show the upper half plane - in fact, I've produced the plots to span a frequency range of 210Hz and will look at a 50Hz filter, so the area of interest is in the upper right quadrant. The first plot shows the pole and zero locations for a 50Hz EQ filter with a Q of 10 (using the RBJ definition of Q from filter bandwidth at half gain) and with gain of zero. The pole and zero are at the same location. The T60 annotation (433ms) expresses the radius at which the pole and zero are located in terms of the time the pole resonance would take to decay by 60dB, as a convenience for use when examining decays of acoustic resonances.
index.php/fa/15563/0/

As it seems I can only upload 1 file per post, I'll continue this in another couple of posts below.
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