Sure, a directional tweeter won't "illuminate" the edges, at least not at high frequencies. Except for the top 2 octaves, most tweeters have sufficient energy at 90 degrees to have noticeable diffraction/reflection issues.
DLR's curves show this pretty well.
David S.
Nice speaker. Any one here had a chance to listen to this speaker? Specs look great!
I think re-radiation best describes it, as it acts like a new source of sound radiating in all directions irrespective of the original source location.
Ah, now I see your reasoning for the use of the word reflection, based on a transmission line analogy. 🙂
What you say about transmission lines is true, the return wave caused due to an impedance mismatch is referred to as a reflection, but while there are many similarities between an acoustic wave propagating along a baffle surface and an electrical transmission line I think the analogy doesn't fully hold up because there is a key difference - an electrical transmission line in terms of where the reflections are able to go is entirely a 1 dimensional device with a single operational axis.
Physically it might curve through 3d space if the cable is bent, and the electric/magnetic fields are orientated at right angles in 3d space, but as far as signal propagation goes the only way for a reflection to go is in the reverse direction back to the source. (Where it can reflect again if there is a mismatch at that end as well)
The wave is either going forwards or backwards, never in any other direction thus reflection is an appropriate term - the wave is literally being reflected back the way it came like a light beam at 90 degrees to a mirror.
Not so with baffle diffraction - it might travel from a tweeter in the middle of a baffle to the edge, as soon as it hits the edge it re-radiates in all directions in 3 dimensional space from that edge, not just back the way it came.
Still, I think we're probably just quibbling over the use of the word reflection, not the underlying mechanism... 🙂
Think of it this way:
Imagine a baffle that is a metre wide, the middle 50cm is flat and has a driver flush mounted in the middle of it. The outer 25cm on either side is tapered back at 45 degrees. Effectively we have a huge 25cm chamfer with two sharp 45 degree edges.
As the wave travels along the flat part and reaches the first sharp 45 degree angle the solid angle expands - not as much as a 90 degree bend but it expands all the same, thus some out-of-phase diffraction occurs at this point. It then keeps going and reaches the second 45 degree bend and expands even further - more out-of-phase diffraction is radiated at this second distance. Agreed ?
So what if instead of bending 45 degrees backwards at the first corner it bends 45 degrees forward. Surely the wave is now forced to compress rather than expand ? If expansion causes pressure drop thus out-of-phase radiation, compression must cause a pressure increase and result in an in-phase diffraction from this point ?
Of course if the cabinet is ultimately still a box just with the edges sloping the wrong way, the edge of the cabinet will now have a 135 degree bend causing a large amount of out-of-phase diffraction at this point - total diffraction will be much worse (and more complex) than a simple 90 degree bend.
I thought I did bring this up in attempting to explain why felt on the side of the cabinet wouldn't do much - the high frequencies that the felt would be good at absorbing wouldn't bend sharply enough around the corner to actually pass through the felt. Low frequencies would but wouldn't be effectively absorbed by the thickness of felt.
I'm not sure I understand how the distance a wave has travelled along a given surface affects how easily it can bend when it reaches the end of the path - but clearly this is the case because I've played around with wave simulators and a longer waveguide of the same angle provides less "spillover" at low frequencies than a shorter one - and we all know that a waveguide can only control directivity down to a frequency that is dictated by its size. Still, it seems a bit counter-intuitive.
Interesting observation that I've never thought about before, but it also makes sense. I guess that's also why a constant directivity waveguide is more or less conical with just a very short taper in the throat to expand the plannar wave to a spherical one and another one at the mouth to minimize diffraction at the mouth. Most of the path the wave travels is at the same angle, thus the same angle for both high and low frequencies. (Until the driver itself starts beaming)
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If it were placed up against a wall with the side flush to the wall, it would re-radiate, but as a positive signal back into 1-pi space, though. If we're going to try to differentiate reflection from diffraction, we have to first establish the frame of reference. This is where it appears to me that it's all diffraction, the only difference is frame of reference.
Yes, it's semantics. We're all used to calling in-phase re-radiation as reflections, such as wall, floor or ceiling reflections. That's just a form of diffraction the way I see it.
This is where I think that I differ. I don't believe that it's an issue of "bending around the corner". I've tested very thick side placement of felt (I have a lot to play with 🙂 ). The primary difference is very similar to the same amount of solid material, i.e. it looks like a wider baffle. This is support for the idea that the reason the side felt is ineffective is due to angle of incidence. The wave, even lower frequencies, do not readily pass into the felt. Rather, they primarily pass over the felt. This is, again, why I think that thin felt applications have little affect on baffle diffraction as well.
Dave
Maybe it is just semantic, but I would only apply the term diffraction to the act of waves bending around an obstacle to fill in the shadow area behind. I believe that is the most common and proper usage.
Reflection off of a hard surface (or even the negative reflection off of an impedance drop) are just that: reflections.
David S.
David,
Agree, but perhaps good to note that there are secondary effects of diffraction and reflection that are similar in nature and important: both lead to secondary wave fronts that will combine constructively or destructively with the original sound source. This can cause a raggedness in the FR that is impossible to correct through equalization. Good example is a tweeter that is not flush mounted with the baffle. The primary effect is diffraction around the tweeter faceplate, which shows up as peaks and valleys in the FR because of the secondary effect, i.e. the recombination of different wave fronts, or interference.
Diffraction and the interference it may cause are often just called 'diffraction', but this shorthand is semantically not correct.
vac
Vac
Agree, but perhaps good to note that there are secondary effects of diffraction and reflection that are similar in nature and important: both lead to secondary wave fronts that will combine constructively or destructively with the original sound source. This can cause a raggedness in the FR that is impossible to correct through equalization. Good example is a tweeter that is not flush mounted with the baffle. The primary effect is diffraction around the tweeter faceplate, which shows up as peaks and valleys in the FR because of the secondary effect, i.e. the recombination of different wave fronts, or interference.
Diffraction and the interference it may cause are often just called 'diffraction', but this shorthand is semantically not correct.
vac
Vac
While it is mostly semantic, I agree with DBMandrake, the forward facing wall does cause diffraction at its junction. Its the mechanism that counts, not what you call it. Clearly we don't all define terms the same way - thats not uncommon. I certainly do not consider diffraction "the act of waves bending around an obstacle to fill in the shadow area behind" - I have never defined it that way and in general physics does not either. Actually physicists would mostly use the term "scattered" which emcompasses all of this discussion. A wave hits an obstacle and gets "scattered" in many directions.
Indeed, which is why it's best to try to manage these acoustically. I'm working on a dipole midrange project right now, and encountered a surprising amount of scattering (a term I'll strive to adopt as it's simple and easy to understand) from the reverse mounted 2nd driver.
Rough testing jig:
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Closeup of driver mountings (flush mounted, but not yet relieved or felted)
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I had to relieve the cutout further and wrap the magnet with thick wool felt to suppress the scattering artifacts.
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You can see how thick the felt is (about 5/8") but it's carefully positioned to not obstruct the output "slots" any more than necessary. Smaller motor would be nice but these are the drivers I'm working with... since they're very sensitive and I had enough of them around to do the job 🙂
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If anyone cares, this is the network giving me a nice flat bandpass response, 2nd order, from about 300-1k.
Attachments
Sims say I can pick up a bit of sensitivity by omitting the second resistor, but yes, it's a very lossy filter. That's the nature of the minimalist dipole beast, you have a slope built-in that starts with the cancellation, about 800hz in this case. The big coil knocks it back to flat within the passband which is primarily within the cancellation region, and introduces the lowpass where the cancellation ceases.
You could, of course, use a bigger baffle, but smaller baffle=more cancellation=more consistent directivity within the cancellation range.
It's interesting to see the different viewpoints and understandings on diffraction, given how fundamental and influential it is in the operation of a speaker.
One thing I've noticed a lot when searching for information on diffraction - at least on the internet - is that most people/articles seem to treat it as a frequency domain problem, when really its not.
When I was searching the internet for the example image I posted above with the arrows showing how diffraction radiates in all directions from sharp edges, I really struggled to find an image. (In fact that was the only one I could find in a 15 minute search)
99% of the articles on diffraction that I could find focused either entirely or almost entirely on the frequency domain effect of diffraction, with plenty of frequency response diagrams for different shaped baffles, driver locations and so on, but little if any discussion on the true spatial / time domain nature of diffraction, (eg in/out of phase time delayed radiation at physically displaced locations from the drivers) the effect on the impulse response, the effects on the off axis response, diagrams showing the physical manifestation of diffraction (as in the image I posted) and so on.
I worry that this tendency to see it as only a frequency domain problem leads a lot of designers (DIY especially) to apply frequency domain fixes (EQ) that don't really solve the issue, or to believe that asymmetric driver offsets which lead to a flatter on axis response actually solve the root problems of diffraction when they don't.
Sure, the on axis response might measure flatter over a long enough time window with an offset driver but the re-radiated energy is still just as severe as before, just smeared around a bit differently in time.
The driver is still not acting like a point source, but rather a point source surrounded by an interference producing rectangular line source at the cabinet edge. At treble frequencies this makes the apparent size of the sound source many times larger than the tweeter thus screwing up the directivity characteristics of what would otherwise be a small point source.
Meanwhile the driver offset will just push the response anomalies off axis, and result in asymmetric polar patterns etc, not a good thing in the horizontal plane at high frequencies if you want good imaging.
In years past I don't think I paid nearly enough attention to diffraction (or understood it well enough for that matter) but I now understand just how important it is, to the point where I think minimising the actual re-radiation effects of diffraction (rather than just trying to get a flat on axis response) is absolutely critical at high frequencies.
I think a speaker that has little or no diffraction at treble frequencies (thus allowing the tweeter to work as an actual point source) really does sound better than one where there is a lot of diffraction occurring, and you will also generally get a flatter response as part of the bargain, as diffraction is a major source of non-flatness in the treble response of many speakers.
There is something beyond just the frequency response though when listening to a low diffraction treble and a high diffraction treble. To me the low diffraction treble just sounds smoother, cleaner, more stable with movements off axis, and sounds more like the sound source location is floating behind the speakers and not coming from the speakers, whereas a speaker with a lot of diffraction at high frequencies I find tends to localize at the front of the speakers and sound like the sound source is the speaker.
It seems almost like diffraction (at least at high frequencies) could be one of the cues that gives away that we're hearing "speaker sound" rather than a real original sound source, especially when the same diffraction profile will be applied to all reproduced sounds.
The question is, how best to achieve a (close to) zero-diffraction point source at high frequencies ?
Absorption ? (EG dlr's tests)
Directivity ? (Wave-guides, large drivers that are starting to beam etc)
Cabinet contouring ? (Sculpted, very curved cabinets like the KEF blade rather than just an edge radius on a flat baffle, etc)
Combinations of the above ?
One thing I've noticed a lot when searching for information on diffraction - at least on the internet - is that most people/articles seem to treat it as a frequency domain problem, when really its not.
When I was searching the internet for the example image I posted above with the arrows showing how diffraction radiates in all directions from sharp edges, I really struggled to find an image. (In fact that was the only one I could find in a 15 minute search)
99% of the articles on diffraction that I could find focused either entirely or almost entirely on the frequency domain effect of diffraction, with plenty of frequency response diagrams for different shaped baffles, driver locations and so on, but little if any discussion on the true spatial / time domain nature of diffraction, (eg in/out of phase time delayed radiation at physically displaced locations from the drivers) the effect on the impulse response, the effects on the off axis response, diagrams showing the physical manifestation of diffraction (as in the image I posted) and so on.
I worry that this tendency to see it as only a frequency domain problem leads a lot of designers (DIY especially) to apply frequency domain fixes (EQ) that don't really solve the issue, or to believe that asymmetric driver offsets which lead to a flatter on axis response actually solve the root problems of diffraction when they don't.
Sure, the on axis response might measure flatter over a long enough time window with an offset driver but the re-radiated energy is still just as severe as before, just smeared around a bit differently in time.
The driver is still not acting like a point source, but rather a point source surrounded by an interference producing rectangular line source at the cabinet edge. At treble frequencies this makes the apparent size of the sound source many times larger than the tweeter thus screwing up the directivity characteristics of what would otherwise be a small point source.
Meanwhile the driver offset will just push the response anomalies off axis, and result in asymmetric polar patterns etc, not a good thing in the horizontal plane at high frequencies if you want good imaging.
In years past I don't think I paid nearly enough attention to diffraction (or understood it well enough for that matter) but I now understand just how important it is, to the point where I think minimising the actual re-radiation effects of diffraction (rather than just trying to get a flat on axis response) is absolutely critical at high frequencies.
I think a speaker that has little or no diffraction at treble frequencies (thus allowing the tweeter to work as an actual point source) really does sound better than one where there is a lot of diffraction occurring, and you will also generally get a flatter response as part of the bargain, as diffraction is a major source of non-flatness in the treble response of many speakers.
There is something beyond just the frequency response though when listening to a low diffraction treble and a high diffraction treble. To me the low diffraction treble just sounds smoother, cleaner, more stable with movements off axis, and sounds more like the sound source location is floating behind the speakers and not coming from the speakers, whereas a speaker with a lot of diffraction at high frequencies I find tends to localize at the front of the speakers and sound like the sound source is the speaker.
It seems almost like diffraction (at least at high frequencies) could be one of the cues that gives away that we're hearing "speaker sound" rather than a real original sound source, especially when the same diffraction profile will be applied to all reproduced sounds.
The question is, how best to achieve a (close to) zero-diffraction point source at high frequencies ?
Absorption ? (EG dlr's tests)
Directivity ? (Wave-guides, large drivers that are starting to beam etc)
Cabinet contouring ? (Sculpted, very curved cabinets like the KEF blade rather than just an edge radius on a flat baffle, etc)
Combinations of the above ?
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My guess is it might be better to omit the second resistor and recalculate the filter for the resulting higher impedance.
Hi Simon,
I wouldn't worry too much about whether the issue should be viewed as a time domain or a frequency domain issue. As you know, the two are inseperable.
I played once with balancing a grille side reflection against a cabinet edge (negative) reflection. It was easy to get the timings to equal and the levels to balance out. You could see this in the frequency domain or the time domain, which both improved. Was it a good solution? No, because it only worked well at a particular point in space where the path lengths were the same.
I can't see a good designer trying to fix the comb filtering with higher order EQ. This will always be an unsatisfactory answer since the problem varies so much with angle. Generally our diffraction/reflection issues are exacerbated by symmetry. As such they can be worse on axis and tend to fade off axis. A perfect EQ on axis adds a complimentary error off axis. Only well rounded edges or significant dampings (such as in DLR's examples) provides a cure that is improves all angles. Clearly that makes treatment at the source (the cabinet edge) the better solution.
David S.
I wouldn't worry too much about whether the issue should be viewed as a time domain or a frequency domain issue. As you know, the two are inseperable.
I played once with balancing a grille side reflection against a cabinet edge (negative) reflection. It was easy to get the timings to equal and the levels to balance out. You could see this in the frequency domain or the time domain, which both improved. Was it a good solution? No, because it only worked well at a particular point in space where the path lengths were the same.
I can't see a good designer trying to fix the comb filtering with higher order EQ. This will always be an unsatisfactory answer since the problem varies so much with angle. Generally our diffraction/reflection issues are exacerbated by symmetry. As such they can be worse on axis and tend to fade off axis. A perfect EQ on axis adds a complimentary error off axis. Only well rounded edges or significant dampings (such as in DLR's examples) provides a cure that is improves all angles. Clearly that makes treatment at the source (the cabinet edge) the better solution.
David S.
the sims say (and pcd is accurate thus far in my use) that the shaping is barely affected by the second resistor, it's pure loss. Hence, gonna pull it out in the next round of testing.
At risk of exposing my ignorance on the subject, is this really true ?
As far as I understand, the transformation from impulse response to frequency response is a many to 1 mapping not a 1 to 1 mapping.
In other words a given impulse response transformed into a frequency response will always give the same result, (there is only one possible frequency response resulting from that impulse response) however a given frequency response can potentially be the result of an infinite number of different impulse responses - in other words there is no unique relationship in the reverse direction, so that we cannot derive the impulse response from the frequency response alone. (I'm not so sure if this is still the case if we consider both frequency/phase response together, but even then I think its not possible)
That means that if frequency response (on axis at least) was our only target, there are a multitude of different impulse responses that might meet that goal.
Diffraction is a pretty obvious example of this I think - the re-radiated sound is often delayed enough that it will show up as a separate impulse, and if the measuring window is long enough to capture both it will affect the frequency response.
If I had a 2dB 1/3rd octave dip at 6Khz as a result of diffraction, and I carefully EQ that out so that the on axis frequency response is the same as the same tweeter in an infinite baffle, is the impulse response the same ? No, because you still have a time delayed impulse from the diffraction that shouldn't be there.
So in that sense looking at it as a frequency domain problem or a time domain problem is not the same. The frequency domain view is to do whatever is necessary to restore the frequency response. The time domain view is to realise that no matter what you do with EQ the time delayed impulse from the diffraction will always be present and needs to be eliminated at the source.
That's what I was getting at. It's two different perspectives on the problem.
The difference here is that you're cancelling the reflection with an equally delayed but opposite phase reflection, which is different to trying to correct the frequency domain with EQ.
Comb filtering might be too strong a word. Although technically its comb filtering as its a delayed signal, the baffle dimensions and driver directivity usually conspire to limit the range where diffraction is a problem to an octave or so, so for example a 100mm face plate tweeter might have a dip around 5-6Khz, a small rise below that and not much else.
So no speaker designs put a small notch here, a small bit of boost there in their networks to compensate for left over diffraction effects ? I'm sure many do, even if they don't realise that diffraction is the root cause of the bumps/dips.
Yes, but a lot of speaker designs don't bother. They just pay lip service to diffraction by flush mounting a wide dispersion tweeter and radius-ing the edge of the flat baffle a bit. Better than nothing, but not enough on its own to solve the problem.
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Time domain or frequency domain are just two different ways of looking at the same phenomenon. When it comes to diffraction/interference and the raggedness it causes in the frequency response, this is easier to analyze by looking in the frequency domain. But your measuring microphone picks up the signal in the time domain, which then can be Fourier transformed into the frequency domain.
Impulse response has very little to do with this (apart from the fact that an impulse can sometimes be used as a handy measuring signal).
Just to throw an interesting fact around: the ears performs an instant hardware based Fourier transform of incoming sound, and is the only 'microphone' I know that works in this way. It transmits auditory information in the frequency domain. All audio technology, with perhaps the exception of FM synthesizers as used in electronic organs, works stricktly in the time domain. Digital is no exception.
vac
Impulse response has very little to do with this (apart from the fact that an impulse can sometimes be used as a handy measuring signal).
Just to throw an interesting fact around: the ears performs an instant hardware based Fourier transform of incoming sound, and is the only 'microphone' I know that works in this way. It transmits auditory information in the frequency domain. All audio technology, with perhaps the exception of FM synthesizers as used in electronic organs, works stricktly in the time domain. Digital is no exception.
vac
Absolutely.
No. If you perform an FFT on the impulse response IR you get the FR. The IR contains both FR and phase data. You can just as easily perform an iFFT (inverse FFT) on the FR and get the impulse response.
What I think you may be thinking about that is confusing you is the relationship between frequency response and phase that depends on the FR being causal, minimum-phase. If the FR is minimum-phase (M-P) we can derive FR from phase and vice-versa, but not if it is not M-P.
Time domain and frequency domain are inextricably related. They are simply two ways to show the same thing.
But you've changed the signal applied in this instance, not the diffraction signature. It changes nothing about how the diffraction signature affects any given signal.
This is a separate issue, not related to time/frequency relationship. Rather it's an argument about how one may correct diffraction and the impact in the polar response. It's almost always possible to correct diffraction on a single axis with EQ, but that will not address the polar response. If a single axis were all that is at issue, EQ would probably suffice, if not perfect.
I'd say it's two different issues.
Dave
The others have jumped in and pretty well answered this so I'll just add a little to clarify.
That the frequency domain and time domain response of a system are 1 to 1 correspondences is just something we accept from the Fourier Math. It is assumed both for the Fourier transform and the DFT or Discrete Fourier Transform. If you have magnitude and phase then only one impulse response will cause that.
What you are getting a little hung up on is with frequency responses that look "about the same". For example, using a 1/3rd Octave EQ to fill in the wiggles from the cabinet edge reflection (trying hard not to say diffraction any more, my own stubborness!). The end result can be fairly flat and may look like the same frequency response as if the edge reflection never happened, but it would not be the same.
I'm sure you've heard of minimum phase systems. We had a thread kicking them around last year. There are multiple definitions such as having the zeros in the left half plane, or having a phase response matching the Hilbert transform response. Just think of them as the simplest system that would have a particular amplitude frequency response (not phase response). Non-minimum phase sysems with the same amplitude response must be the combination of the minimumphse counterpart and additional all-passes.
Well, the notion is that a minimum phase system with non flat response can be corrected with a minimum phase EQ and the result is a perfect system, flat response and flat phase.
Your example of using 1/3rd Octave EQ to fix an edge reflection is distinctly the case of fixing a non-minimum phse sytem. The response may end up flat but the phase must reveal the non-minimum phase nature of the starting system. So the impulse response won't be perfectly corrected.
In fact it is difficult to fix reflections with an EQ of either the frequency domain or time domain. A good example is inter-aural crosstalk cancellation. If we have the left ear hearing the left speaker and also some crosstalk from the right speaker, lets cancel the sound of the right speaker by adding a complimentary delayed impulse of the opposite polarity. Except now we've added a reflection that also crosstalks at double the time delay, so add a second correction for that. It goes on and on.
Since minimum phase correction can never perfectly correct (amplitude and phase) a non-minimum phase system we are left with the possibility that many flat looking systems have different impulse responses and they must all be different forms of all-passes. This doesn't violate the 1 to 1 correspondence requirement because they will have different phase responses.
By comb filtering I only mean a response phenomenon that is periodic in frequency, i.e. has repeating wiggles.
David S.
Ok let me see if I have this straight. A frequency response on its own (without phase data) is not enough information to derive an impulse response, because without measured phase we can only calculate minimum phase, meaning if the system is not minimum phase the result will be wrong.
But if we have both frequency response and measured (total) phase, that's all we need to derive the impulse response ?
But in what way is it not the same ? The excess phase is different ?
I thought I had a pretty good idea of minimum phase and excess phase, at least in terms of linear filters and the all pass nature of a multiway speaker system.
Where I'm struggling a bit is understanding how that relates to systems where there are discrete reflections or echos with significant delays, as in the case of baffle diffraction arriving say 1ms after the main impulse.
Right. Well my example was to point out that I didn't think EQ, at least minimum phase EQ could correct it, so at least I got that right. 😛
So what you are saying is that the delayed reflection automatically makes the system non minimum phase ?
I can see how it would be possible to correct the impulse response (at one point in space) using DSP processing, since we can apply the necessary time delayed opposite phase impulses, much like inter-aural crosstalk cancellation. As you point out that would cause a cascading series of corrections to correct the corrections etc... but since the diffraction effect is significantly lower in amplitude than the direct signal the necessary corrections to correct a single impulse would eventually die out. In principle it should be easy to do in DSP.
What I'm struggling with is the concept that a significantly time delayed impulse from a reflection simply results in making the system non minimum phase, and that it could somehow be represented just by a minimum phase response and some amount of excess phase (all pass) characteristic, and be correctable with the right all pass response.
If the time delay was several ms, the original impulse could have been and gone well before the reflection ever arrives, what would this do to excess phase ? Is it a type of group delay, when only a narrow frequency range is being re-radiated by the baffle diffraction ?
Again, I struggle to see how group delay could entirely describe the situation, because group delay would normally mean that certain frequency ranges in the original impulse are being delayed more than others, but in the case of diffraction you have an original impulse containing all frequencies with (potentially) little or no group delay, followed by a second impulse containing a band limited set of frequencies of opposite phase.
This second impulse if integrated in the same time window as the first will cause a dip in the frequency response and presumably make the system non-minimum phase, but if it were windowed out the effect would be excluded.
Am I over-thinking the situation ?
One other concern I have is that I've taken quite a lot of excess phase measurements with ARTA, and I've never seen any excess phase in the measurement from diffraction effects, even though the window length is clearly long enough to encompass the delayed impulses.
Surely if the delayed diffraction impulse made the system non minimum phase, I should immediately see this in an excess phase measurement ?
😕
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I disagree. Baffle diffraction is, surprisingly, M-P. Some time ago feyz went through the math to show it. But more obvious than that, were a drivers response with diffraction not M-P, then M-P EQ (i.e. a crossover) would not be able to correct the combined response. All evidence shows that it can be corrected with a crossover. We do it all the time, largely with tweeters in the 2-5K area and the diffraction peaks that usually are in the crossover area of a tweeter. This, of course, is only going to be corrected on the specific axis, but that's another issue.
No, not correct.
I believe that what feyz showed was that as long as the diffraction signature is lower in the level than the direct signal (as it must be in this case), then the result is M-P. This is fully supported, again, through empirical testing. I've never encountered any diffraction that could not be corrected on a specific axis using M-P filters.
Dave
p.s. This is also supported by the fact that the response of driver w/diffraction and subsequent EQ is fully predictable with design software.
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