That's consistent with my measurements of excess phase - as I mentioned at the end of my previous post I've never been able to measure any excess phase resulting from baffle diffraction even when the window time is long enough to include the impulses resulting from the diffraction, hence questioning whether diffraction was indeed non minimum phase or not.
So you're saying that because a drivers direct wave + diffraction signature is still minimum phase, a minimum phase EQ/crossover that corrects the frequency response and phase can somehow eliminate the delayed impulses in the impulse response ? I don't see how.
If it's not eliminating the delayed impulse but merely correcting the frequency/phase response (as integrated over a long enough time window to include both direct and delayed impulses) then that contradicts speaker dave's assertion that a given frequency/phase response will map back to a unique impulse response.
Still confused. I suspect that the key is the definition of the window time over which the FFT is performed, and that some of our reasoning is making assumptions about this which may not hold when energy is spread out over such a large time period, as it is with delayed reflections.
It still doesn't seem to me that summed frequency and phase response alone are enough to fully describe a situation where significantly delayed reflections are present.
But is it correcting just the frequency/phase response, or is it also resulting in the exact same impulse response (at one location in space) that you would get without diffraction ? Eg a single impulse rather than two or more impulses. I'm not convinced that this has been proven.
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See, this is where I have a problem. Because if the system is MP then it is exactly correctable with a MP filter. But diffraction is not correctable with any filter! Yes, it is correctable at a point, but then at any other point it is made worse. So it has not been globally corrected only at a point. So if what you say is true (and I have not seen the math so I can't say either way) then MP as a concept is not applicable in three dimensional space because its concepts don't hold spacially.
And IF the signal level (or the diffraction level) changing can change the system from MP to non-MP then the system is nonlinear and MP nor the entire Fourier transform concepts even apply.
So something is inconsistant in what you are saying.
I don't think anyone in the discussion is suggesting that diffraction can be fixed in 3 dimensional space with any type of filter - clearly it can't, anything you do to fix one direction makes another direction worse.
However there does seem to be some disagreement over whether a minimum phase filter can actually "fix" diffraction at a single point in space.
Fix how ? Frequency and phase response ? Impulse response ? Frequency and phase response, sure. But how can you fix an impulse response that includes a delayed reflection using only a minimum phase filter ?
If the total spectral energy balance is the same (same frequency response and phase averaged over time) but the distribution of energy in time is different, is it really the same, and will it sound the same ?
That worries me too. I think I've seen something similar to this when taking in-room bass measurements at a distance - much of the bass region will measure as minmum phase but certain types of notches in the bass response due to boundary cancellations will cause sudden "jumps" in the phase response that will cause some parts of the bass region to be non-minimum phase at the listening position.
I think this is happening when the direct wave is being self cancelled by a boundary reflection but a reflection at a different angle is still arriving at the listening position, time delayed compared to what the direct wave would have been had it not been cancelling itself.
So in this instance we have a time delayed reflection that is stronger than the missing or subdued direct wave.
I remember reading a thread discussing whether bass response in rooms was minimum phase or not, and I'm not sure that any agreement was reached in that thread either
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No, you can't correct the frequency/phase response without eliminating the delayed impulse. If you fix one you will fix both. If your corrected frequency response doesn't eliminate the delayed impulse then by extension the phase must still be off.
You really need to accept as an article of faith (if not of full understanding) that there is a 1 to 1 correspondence between time and amplitude/phase. The transform/inverse transform process can be repeated ad nauseum and will always return to the same previous impulse response and the same magnitude/phase (or real/imaginary): 1 to 1 correspondence.
The only question is whether diffraction is a minimum phase event. My general understanding is that most systems with parallel paths and delay on one or the other of the paths are typically non-MP (picking my words carefully here). I don't know that that is universally true. I do remember a Bell Labs paper where they wanted to correct speaker phone response (in a live room) and found that it could be MP under some conditions.
This isn't really the issue here. Lets assume that we are only considering a case where the total response falls within the measuring window. The discussion is about sytems with edge reflections and we will measure them correctly with respect to the length of their impulse response.
Don Keele and I had a similar debate to this about delayed resonances. "What if the resonance was well down in level and didn't show up in the frequency response. Two systems would have the same frequency response but a different impulse response." The answer is that a delayed resonance that is visible in the impulse always creates a visible perturbation of frequency response. (It must, this once again protects the 1 to 1 correspondence requirement.)
Is it minimum phase to start with? Then yes.
If not? Then no.
Yes, that is the crux of the situation. Diffraction results in a delayed impulse which when summed to the initial impulse seems to me has to be non-minimum phase. A MP filter can correct the frequency response of that result at any point in space by adding in a "counter response" to the initial impulse response. This result would then not be MP, but will have a corrected amplitude response.
So the response is "fixed" if you are considering only the magnitude response, but it is not fixed in time nor in space.
I don't think I'm being inconsistent. As was pointed out, the correction isn't global (polar) and any correction to a flat response will not hold at other points in space. However, what I believe will hold is that if make a set of polar measurements and apply a filter, then the response at any of those polar points will be predictable, despite not being flat except at the specified design point. In that sense, diffraction is M-P in polar response. If by definition you require that correction applied to achieve flat response must do so on a polar basis, it fails, of course. But I think part of this is how one defines it. You wish to define it as correction on a polar basis. I would define it as the response of source/diffraction/filter at any selected point in space. On that basis, it's M-P at all points since we can predict the response at any point in space to measurements made at those points in space.
Some of this is, I think, semantics.
Dave
Yes, I agree, mostly semantics. MP is not defined spatially so I guess anyone can have any deffinition that they want. But its usefulness as a concept in acoustics, like it is in linear systems theory, becomes minimal when it cannot be applied spatially, i.e. correcting one spatial point corrects all spatial points. From my reading people seem to assume that the concept does apply spatially (Eqing one point "corrects the response") and I think that we are all agreeing that it does not. I suppose this is why acousticians never use the concept - it doesn't offer any insight, widening of understanding or simplifications to spatial problems.
But a system does not even have to be MP to be able to do that. All I need is the impulse response, which need not be minimum phase.
But a system does not even have to be MP to be able to do that. All I need is the impulse response, which need not be minimum phase.
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but how do we counter response it in every point in space professor ged?
can it be done electronically?
I'm not sure it can unless the signal is also considered in a fixed state. A non-MP resultant from two sources will have a start and end tail. These single-source contributions will have a fixed magnitude independent of phase. The relative contribution of the tails to the total is dependent on the length of the signal.
Thank you Simon, this is the missing piece to the lower midrange puzzle in my mind. My wife is very accepting but she'd rather I not use ceiling treatment so I can see I have little choice but to greatly restrict vertical directivity.
I've gone through the sub set up dozens of times, almost always 3 + mains. Every different option sounds a little different and sometimes greatly different. Always close to flat, confirmed spatially, and then EQed just a little as needed. It can range from phenomenal to average, and sometimes boomy and sometimes lacking. Sometimes I can even hear delays, sometimes hangover.I remember reading a thread discussing whether bass response in rooms was minimum phase or not, and I'm not sure that any agreement was reached in that thread either
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That worries me too. I think I've seen something similar to this when taking in-room bass measurements at a distance - much of the bass region will measure as minmum phase but certain types of notches in the bass response due to boundary cancellations will cause sudden "jumps" in the phase response that will cause some parts of the bass region to be non-minimum phase at the listening position.
I think this is happening when the direct wave is being self cancelled by a boundary reflection but a reflection at a different angle is still arriving at the listening position, time delayed compared to what the direct wave would have been had it not been cancelling itself.
So in this instance we have a time delayed reflection that is stronger than the missing or subdued direct wave.
I remember reading a thread discussing whether bass response in rooms was minimum phase or not, and I'm not sure that any agreement was reached in that thread either
John Mulcahy (REW author) provides a good discussion here: Minimum Phase
Ah, brilliant. Great article
It explains and clarifies some things I'd sort of noticed or figured out myself but didn't quite understand or fully put together.
Interesting that he identifies excess group delay as the right tool to look for non-minimum phase behaviour in room modes, it looks like it can be quite informative regarding the bass response behaviour of a room and help identify what things can and can't be corrected with EQ.
I've measured excess group delay in a number of contexts before including room bass measurements, and had noticed the spikes that occur at frequencies where cancellation is occurring and surmised that it had something to do with a phase reversal occurring when the two out of phase signals shifted balance from one to the other.
For example in my room at the listening position there is an 80ms spike in the excess group delay at around 83Hz, but its otherwise fairly low from 40-300Hz. That spike is right where the worst cancellation is in the bass.
In fact I'm wondering whether looking at the excess group delay of room bass measurements (at multiple locations) is an effective tool in establishing whether a multi-sub configuration is optimally set up ? In theory modal smoothing provided by a good multi-sub setup should prevent the deep cancellations and position/frequency dependent phase reversals that would cause large spikes in group delay, thus leading to a response that is a lot closer to minimum phase and thus more EQ'able.
Perhaps there is a discernible quality improvement with a bass response which has no large spikes in excess group delay ?
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Does the article posted by Markus provide any insight on either of your points ? Have you tried measuring excess group delay of the different configurations ? (I presume when you say you've set up the subs many times you mean you've tried different locations in the room etc ?)
I found the article generally good but a couple of things trouble me. If the three individual responses of the room are minimum phase, how can their addition be non-minimum phase?
I also worry that calculatons with deep nulls and phase reversals don't put error into the group delay. Since group delay is a differentiation it is prone to exageration of any errors in the associated phase curves.
David S.
I also worry that calculatons with deep nulls and phase reversals don't put error into the group delay. Since group delay is a differentiation it is prone to exageration of any errors in the associated phase curves.
David S.
In the same way that two minimum phase drivers crossed over with each other result in a non minimum phase result ?
In a crossover you have filters that are explicitly transitioning the response from one driver to another - at some frequencies one driver dominates, at other frequencies the other driver dominates.
In a room you don't have an explicit crossover but you have a multi-path situation where there are a multitude of reflections with different total path lengths and varying amplitudes.
According to the article (and in agreement with my own measurements) if a time delayed reflection is greater in amplitude than the direct signal there will be a "glitch" in the excess group delay.
Imagine an example of a woofer in front of the front wall in the room - at the frequency where the woofer is 1/4 wavelength from the front wall (assuming the listener/woofer axis is at a normal to the wall) the reflected signal will be 1/2 wavelength out of phase with the direct signal leading to almost complete cancellation of the direct signal at that frequency.
Now imagine a reflection that travels from the woofer at 45 degrees and bounces off a side wall, perhaps the far side wall, to reach the listener this will be delayed considerably compared to the direct signal. If it arrives in phase with what the original would have been there will be a small increase in excess group delay equal to the extra path length, (the bump at 85Hz in the last graph in the article) but if it arrives at the listener out of phase with the (suppressed) original it will cause an abrupt phase transition on either side of the front wall notch resulting in a huge spike in excess group delay as seen at 110Hz.
So for excess group delay to appear in a room measurement due to reflections there has to be a minimum of the direct signal and two reflections. One or more reflections have to provide sufficient cancellation of the direct signal, and one or more other reflections provide a delayed alternative path of sufficient amplitude.
Effectively the notch of the direct signal is your "crossover" that is transitioning the dominant signal from the direct signal to one or more delayed reflections over a narrow range of frequencies...
If it'll put your mind at ease, I'll attach an actual measured excess group delay taken in my room
If you remember the reverse phase L-R noise measurements we made a while back in another thread, here is the frequency response and excess group delay of the left speaker as measured at the listening position at the opposite end of the room. Both measurements are from the same impulse, and both use the full available window period of about 2 seconds - essentially steady state measurements capturing all significant reflections.
If you remember the listening position is also fairly close to the "critical" distance, and I think this is where excess group delay really starts to show up, since the direct to reflected ratio is low and there is more chance for summed reflections to exceed the amplitude of the direct path, especially where the direct path is experiencing cancellation from for example a front wall reflection. (I know for example that if I move the microphone position half way up the room most of the excess group delay spikes in the midrange disappear due to a much greater direct to reflected ratio)
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Markus
Good paper, nothing revolutionary, but insightful. My take-away is just what I said before: in acoustics the MP concept really doesn't add much since, as he pointed out at any point or frequency range the response may or may not be MP. What he did not state explicitly is that these regions will be also be different at every point. SO basically there is not much that one can state categorically about MP in real rooms.
I do agree that when you sum two signals there is always the possibility that the result will be non-minimum phase. This is why I do not believe that diffraction can always be said to be minimum phase - it may be and maybe not. Not a very solid concept to work with IMO.
Now a direct field response from a loudspeaker that is psudo point source and has minimized diffraction and no near-field reflections will most likely be MP everywhere. But not if there are baffle diffractions, or nearby reflections etc. These will make the result non-MP at least somewhere and a little non-MP everywhere.
Good paper, nothing revolutionary, but insightful. My take-away is just what I said before: in acoustics the MP concept really doesn't add much since, as he pointed out at any point or frequency range the response may or may not be MP. What he did not state explicitly is that these regions will be also be different at every point. SO basically there is not much that one can state categorically about MP in real rooms.
I do agree that when you sum two signals there is always the possibility that the result will be non-minimum phase. This is why I do not believe that diffraction can always be said to be minimum phase - it may be and maybe not. Not a very solid concept to work with IMO.
Now a direct field response from a loudspeaker that is psudo point source and has minimized diffraction and no near-field reflections will most likely be MP everywhere. But not if there are baffle diffractions, or nearby reflections etc. These will make the result non-MP at least somewhere and a little non-MP everywhere.
That's only frequency response data, so we have no idea whats happening to the phase / excess group delay and whether the multi-sub result is closer to minimum phase or not.
Do you still have the original impulses that you could generate excess group delay responses from ?
The article was very informative. I haven't attached that much importance to excess group delay before, just as I have thought about the tale of two reflections but never seemed to attach enough importance to that in the past.
@ Earl, I can't tell from your comments whether what I suggested to you was useful. I'm not sure I'm capable of presenting things to your level of understanding, though on the other hand we seem to prefer different approaches to some of the same problems. Anyway the point is that I personally can't see reconciling two practical, time separated sources as being summable and I aim to reduce this as I can.
Simon, I've tried different locations and different cutoff frequencies. I try running each sub in its own best range (for its location). I've tried dealing with lower midrange reflections with them, at one stage used them as flanking woofers etc.
...and that is another benefit I gues I'll learn from this approach. Differentiating the success of driving a mode versus swamping a reflection cancellation. Even across the spectrum I can see I'll have clear data showing me what I may EQ, and what I must fix. Excellent.
I almost feel as if I could now set up subs using nothing but excess group delay. Well, off to try then.
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