You're right, but this doesn't really have anything to do with my reply, which was specifically addressing the misconception that applying EQ to fix a resonance somehow could only address the amplitude response error and yet leave all the ringing in the time domain there. On the contrary fixing the amplitude and phase error with a notch also fixes the ringing in the time domain, and that was all I was talking about.
Non linear distortion is a separate matter, and it is true that at cone breakup resonances you normally see a significant increase in non linear distortion due to that being a point of maximum cone flexing, and the flexing of cone materials is not completely linear.
But the amount of distortion you get is going to be highly dependent on the materials the cone is made of as some will bend more linearly than others.
What would you rather have though - a driver that generates additional distortion at resonance and has a peak in the amplitude response and ringing in the time domain, or has the amplitude, phase and time domain responses fixed with EQ but still has a bump in distortion at that frequency that is no worse than before ?
In fact you're probably going to see a small reduction in distortion when correcting a resonance with EQ simply because you're not driving the driver as hard at its resonance.
If you have a 3dB peak at 2Khz and you apply a 3dB notch, for a given average program material the resonance is being excited by 3dB less, so that's still a net improvement in distortion generation by the bending modes of the driver.
It will still show up in a distortion sweep of course but if the increased distortion is still low it is probably inaudible.
It's better to solve as many resonances as possible mechanically with driver design and damping of course. The approach I take is to do as much as I can to the driver first to tackle any specific resonances, and then "mop up" the remaining more benign low Q resonances left over with EQ in the crossover.
I did exactly that on my current speakers which are a two way using a Coral Flat 8 II full range with an Aurum Cantus G2 ribbon tweeter.
The Coral's have had a carefully optimised pattern of foam strips added on the rear outer of the cone that dramatically smooth the response from 2-5Khz and tame what began realistically as un-EQ'able high Q resonances into two relatively benign discrete 1/4 octave resonances of around 2-3dB amplitude each at about 2Khz and 4Khz.
I then precisely correct these two resonances with notches in the crossover, which leave no trace of the original resonances in the amplitude/phase response and no ringing at those frequencies. Music that previously excited these resonances (even after the damping foam strips improved things) now show no audible colouration and I can't hear any traces of the former resonances.
I'm sure if I did a distortion sweep of the driver that there would still be bumps in the distortion products at those frequencies but they are probably below audible levels as the mechanical resonances are already low Q and fairly benign being a paper cone. We're not talking about a metal cone driver here with 12dB+ out of band resonances.
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It really depends on what measurement you base the FIR filter on and how you tune it. If your measurement contains room high levels of room reflection, enclosure diffraction, etc, then the problems you mention do appear.
In the above you are right of course.
I thought the discussion was about drivers or systems ringing out in time after the signal had stopped as measured with waterfall plots. This is neither linear or minimum phase and as such cannot be corrected with EQ.
I may have miss understood the conversation.
Barry.
No, but you've misunderstood how EQ works. Read my original post again as it already explains exactly how EQ can cancel the ringing of a mechanical resonance and thus clean up a waterfall plot as if the resonance had never existed in the first place.
Linear phase is nothing to do with anything. No mechanical resonance is linear phase. They are minimum phase though, and that includes all the typical cone breakup resonances that we might be trying to correct.
Don't believe me ? Pretty easy to prove. Take a measurement of the raw driver response of a driver with a resonance in a program that is capable of measuring true phase response as well as calculating excess phase and/or excess group delay.
Then either overlay the calculated minimum phase response (calculated from the amplitude response by the software) over the actual measured phase, and look for any deviation between the two, or look at the excess group delay - which in a minimum phase system will be a straight, level line.
If the resonance is not minimum phase you would see a kink in the excess group delay response, but because it is minimum phase it will be a dead straight line.
I've done enough of these kind of measurements to know that all normal driver resonances are minimum phase at a single point in space and are thus correctable with EQ.
So your assertion that they can't be corrected with EQ because they are not minimum phase is demonstrably false.
Whether it makes sense to correct a resonance with EQ depends on other factors - if the resonance isn't the same at different off axis angles it wouldn't necessarily be a good idea to try to correct it, also if the resonance Q is too high (more than about 5) the resonance becomes too narrow and potentially unstable with mechanical movement of the cone, also it means the notch filters become unreasonably critical to tune to match the resonance. I typically wouldn't try to notch a resonance that was any higher Q than 5 or greater than about 3dB.
So there are practical limits on how sharp or large a resonance you could correct are, but this is nothing to do with whether they are minimum phase.
One other point of possible confusion - when I talk about correcting a driver resonance with EQ, I am referring to EQ'ing only that driver. So if you have a multiway system it is not equivalent to apply EQ to the whole system.
For example imagine a 2 way system with a 3Khz crossover where the woofer has a resonance at 4Khz. If you try to notch that resonance by applying EQ to the system as a whole (before the crossover) you will not be successful because the speaker as a whole system is not minimum phase through the overlap region where both drivers are radiating. So you might flatten the frequency response but not the phase response, so the speaker as a whole will still ring to some degree at the resonance.
Also this will cause weird off axis effects because you would be trying to EQ a peak in the on axis response that may not exist off axis where the woofer has reduced output relative to the tweeter... not a good idea.
However if you EQ the resonance on the individual driver in its section of the crossover the resonance can be exactly corrected for phase and time response, and without introducing odd off axis response anomalies.
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This?
Are we talking about the disipation of stored energy in a transducer? Similarly to stored energy disipation in an acoustical space?
Thank you.
Barry.
I was referring to applying EQ to mechanical resonances in a driver, yes, which are minimum phase in all "conventional" single diaphragm cone and dome drivers.
The same can apply to bass room modes below the Schroeder frequency of the room though, although interestingly unlike a driver resonance, the bass response at a given point in the room can be either entirely minimum phase or non minimum phase over part of the range depending on how the different reflections and modes combine.
Any time the delayed reflections are greater in amplitude than the direct signal there is at least the possibility for the result to become non minimum phase.
Specifically, around the point of a deep notch due to room modes or boundary cancellation you can experience a sudden phase reversal on either side of the notch which causes the response to be non minimum phase due to the sudden phase discontinuity.
This doesn't sound good and can't be corrected with EQ, even at that single point in space, it can only be solved by moving either the listening position, the speakers, or adding additional displaced speakers. (Multi-sub approach)
However peaks in the bass response resulting from room effects will be minimum phase so can be corrected with minimum phase EQ, while simultaneously correcting the phase/transient response - at least at that one point in space.
This is why you can EQ bass peaks successfully (at least at one point in space) but not notches.
It's quite informative looking at the excess group delay of the bass response at the listening position - it should be a flat line representing minimum phase but any sudden large jumps/discontinuity in excess group delay show a point where phase reversal is occurring around a notch and needs to be addressed by moving speakers or listener before attempting to EQ.
The same can apply to bass room modes below the Schroeder frequency of the room though, although interestingly unlike a driver resonance, the bass response at a given point in the room can be either entirely minimum phase or non minimum phase over part of the range depending on how the different reflections and modes combine.
Any time the delayed reflections are greater in amplitude than the direct signal there is at least the possibility for the result to become non minimum phase.
Specifically, around the point of a deep notch due to room modes or boundary cancellation you can experience a sudden phase reversal on either side of the notch which causes the response to be non minimum phase due to the sudden phase discontinuity.
This doesn't sound good and can't be corrected with EQ, even at that single point in space, it can only be solved by moving either the listening position, the speakers, or adding additional displaced speakers. (Multi-sub approach)
However peaks in the bass response resulting from room effects will be minimum phase so can be corrected with minimum phase EQ, while simultaneously correcting the phase/transient response - at least at that one point in space.
This is why you can EQ bass peaks successfully (at least at one point in space) but not notches.
It's quite informative looking at the excess group delay of the bass response at the listening position - it should be a flat line representing minimum phase but any sudden large jumps/discontinuity in excess group delay show a point where phase reversal is occurring around a notch and needs to be addressed by moving speakers or listener before attempting to EQ.
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Thanks for this explanation, I had been trying to find out about that for a while now. There does seem to be some disagreement about the effects of equalization on resonances.
I'm not sure if a notch from a linear phase equalizer like equalizer APO (which I have been recommending to people for a while now) is "minimum phase" like you describe.
There is a long thread over at head fi on this and some actual measurements were taken that seem to support that equalizing a resonance certainly affects the time domain as well.
Headphone CSD waterfall plots | Page 48 | Head-Fi.org
Sometimes mechanically damping a driver can suck the life out of it (low qms), so I wouldn't say its always better to solve problems mechanically, but a lot of people are still suspicious of dsp or see it as a hack.
Linear phase equalization and dsp can cause ringing, but I will venture to suggest that this is a lot less noticeable than the issues of conventional crossovers.
Linear Phase EQ Explained - Crave DSP
Pre and Post Effin Ringing and **** like that | Super Best Audio Friends
Also the only way to a perfect sound bubble is a brick wall filter that prevents lobing and beaming, as discussed here. Note that this kind of filter can increase digital artifacts.
Equalizer APO, REW and Rephase WOW!
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I went to the dark side (dsp) once I realized that the room has such a strong effect on the sound that no "sane" amount of mechanical perfection can do what a PC and dsp can.
It's not, it's linear phase. Linear phase EQ is only useful (read: with no side effects) to correct linear phase problems, which we do not encounter in the real world. One of the few limited uses in audio is high pass filters (subsonic low cuts) because "they keep the bass tight" as no phase shift is introduced. But the cost is symmetrical ringing, a broadened impulse response which makes for strong artifacts with certain signals.
A lin-phase notch is a bad as it gets in terms of ringing. All lin-phase filters/EQs have symmetrical pre- and post ringing (by definition).
As for damping, as long as it is linear it doesn't have much effect on sound quality. Especially you don't want any mechanical friction as this always leads to stick-slip action (very bad). Best way to do this is eddy current brake, hard to realise for the cone area of a driver, of course.
No it wouldn't be, as KSTR replied.
If you want to correct a cone resonance, which is minimum phase, using a notch filter you would use a conventional minimum phase parametric notch with adjustable centre frequency, gain/cut and Q/bandwidth. All three parameters have to be adjusted to match the resonance correctly.
In the digital domain I use the PEQ module of my DEQ2496. In the analogue domain in a passive crossover I just use a shunt LCR notch filter, assuming the network topology allows for a shunt notch, such as having a baffle step compensation resistor before the notch.
I find in a passive crossover shunt notches are easier to deal with and adjust independently without interaction if you need more than one notch, and don't increase the resistance in series with the driver so don't affect sensitivity or damping of the driver.
R adjusts the attenuation of the notch naturally, L and C tune the centre frequency and the L/C ratio adjusts the Q/bandwidth for a given R.
It definitely does. Frequency and time domain are just two sides of the same coin. If a PEQ corrects both the amplitude and phase response error caused by a resonance then the time domain response has no choice but to be corrected as well.
I agree that higher Qms drivers tend to sound better as the bulk of the damping then comes electrically from Qes and this tends to be more linear than damping provided by having low Qms by using stiff lossy surrounds.
However cone breakup resonances aren't related to the Qms of a driver - Qms only relates to the fundamental mechanical resonance formed by the mass of the entire cone/voicecoil etc and the compliance of the suspension.
When I talk about mechanical damping for cone breakup resonances (at high frequencies) I'm talking about things like adhesive foam strips stuck to the back of the cone which will absorb energy from bending waves - they don't affect the Qms of the driver except by slightly increasing it as a side effect of the weight they add to the cone. But that is only a side effect not the reason for adding them.
When I added foam strips to my Coral drivers the added weight reduced the overall driver sensitivity by almost 1dB and increased the Qms noticeably (and improved the bass response as a side effect) but it was worth it to deal with the resonances in the upper midrange.
"Suck the life out of it" is a bit of a vague description. If you over correct for a resonance by reducing it too much so that you now have a dip, and that dip is in the presence region it would subjectively "suck the life out of it" yes. The damping needs to be correct, not too little and not too much.
I think this is a little misleading. Yes if you add too much damping the results are bad but in a different way. If you cause a dip where there used to be a peak, that is equally wrong.
But by definition if you had a resonance peak to begin with and you precisely correct the amplitude and phase response, "onset transients" will also be optimal.
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thanks for the reply. It does seem like if driver makers were willing to give up some flatness of the frequency response at some points they could gain performance in other areas like dynamics. Frequency response is the most important measurement but as you confirm it is correctable.
Also I have a theory that for low volume listening a stiff cone, and high qms are best. Also raising the qes with impedance. Overall quick energy transfer is good. On the right track?
My current speakers use a cheap aurasound whisper as the tweeter. I chose it because it has a hard piston, low fs, and qts around .7 but with a decently powerful magnet. So it seemed like a good choice for low volume, but it does have energy storage issues. Also the accutons are a nice option as well, but even they have energy storage issues as certain points.
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You've essentially described Fostex.
e.g. this is ~5dB more sensitive than other wideband drivers of similar size. The down side is that is has about 1/10th the Xmax, and has bigger peaks in the frequency response.
Fostex FE126En 4" Full Range
I'm a little embarrassed to ask this question because it might just be daft, but I can't find the answer anywhere else, anyway here goes. As I understand it a drivers natural acoustic roll off includes a phase shift, do the peaks and dips in its frequency response have a corresponding phase response?
Yes, they do, and if they are minimum phase, as they almost always are, then the phase response is intimately tied to the frequency response, just like the temporal response is intimately tied to the frequency response. That is why I don't bother with waterfalls. They don't tell you much that isn't in the zero delay frequency response. Some things are easier to see in waterfalls, but nothing is there that isn't in an impulse response for example.
I have come to dislike the term "stored energy" as it has almost no meaning in the context that it is being used - usually wrong. Sure things "store energy" that's what oscillation is all about, energy sloshing back and forth between potential and kinetic, but again its not a new concept, it's just gotten to be used as a false concept that misleads so many.
I have come to dislike the term "stored energy" as it has almost no meaning in the context that it is being used - usually wrong. Sure things "store energy" that's what oscillation is all about, energy sloshing back and forth between potential and kinetic, but again its not a new concept, it's just gotten to be used as a false concept that misleads so many.