I'm going to try and create a couple of files that we can listen to, one with diffraction, another without. This is how it could be done:
1. Use Bagby's baffle simulator to come up with the frequency response with rounded edges, and then with sharp edges.
2. Export response to RePhase and generate convolution impulse with no changes.
3. Not clear on this part, but somehow pipe music through the convolved impulses and come up with modified and unmodified music files. Foobar has a convolution engine, but not sure at this time how to record the output. Should be doable.
4. Use Foobar's ABX comparator to do the blind testing.
Not sure if this will work. But it ought to capture the effect of a full baffle.
1. Use Bagby's baffle simulator to come up with the frequency response with rounded edges, and then with sharp edges.
2. Export response to RePhase and generate convolution impulse with no changes.
3. Not clear on this part, but somehow pipe music through the convolved impulses and come up with modified and unmodified music files. Foobar has a convolution engine, but not sure at this time how to record the output. Should be doable.
4. Use Foobar's ABX comparator to do the blind testing.
Not sure if this will work. But it ought to capture the effect of a full baffle.
The last part is easily done in Mathcad. I've done it often. My question would be how good is the diffraction model? I would think that a radius would be pretty difficult to do.
This is quite similar to what I did, almost exact actually, except that I simulated diffraction effects more directly rather than through a diffraction program.
This is quite similar to what I did, almost exact actually, except that I simulated diffraction effects more directly rather than through a diffraction program.
For #3, I think you could use ConvolverVST with any recording software that supports VST, Audacity, Reaper, etc. The two convolver plugins I've found for Foobar don't have much for options.
I have no idea how accurate it is. But on the page, it does say that the model has been verified with actual measurements. I have used it a few times, mostly for baffle step, and it's pretty accurate.
For the test, we must first prove diffraction is audible, right? For that, this method may be sufficient. Then we can see if the radius makes a difference.
BTW, I've read your paper, need to read it again to fully absorb.
For the test, we must first prove diffraction is audible, right? For that, this method may be sufficient. Then we can see if the radius makes a difference.
BTW, I've read your paper, need to read it again to fully absorb.
Diffraction was always audible to me since my first pair of custom made speakers back in 80's. But I never felt it was dominant enought to make it a deciding factor. I used some baffle simulators to help locate the driver to minimize the effect. Remember another thread that started out with an attempt to kill diffraction? Well, I don't think it ever materialized with a more satisfying speaker.
Diffraction is not a serious problem until you have gotten rid of the myriad of other problems in speaker design. But once you get power handling, frequency response and polar response under control then diffraction is an issue.
Is diffraction a minimum phase phenomenon? Can one really convert a measured or simulated frequency response to an impulse response and use that in a convolver to simulate diffraction?
If the delayed signal (in this case the diffraction from one or more edges) is lower in amplitude than the direct signal at all frequencies then at any given listening point the summed result has to be minimum phase.
So yes, diffraction is minimum phase at any given listening point unless you could artificially attenuate the direct signal sufficiently without attenuating the diffracted signal.
To prove it empirically measure and compare the excess group delay of a single driver mounted on a sharp edged box with lots of diffraction to the same driver mounted in a sphere. (or on an infinite baffle)
Assuming the driver itself is minimum phase (most conventional drivers are) then you'll see no excess group delay in either the diffracting or diffraction free measurement.
Of course diffraction will cause the frequency response at different listening points to vary wildly due to interference effects, but all the different responses are still individually minimum phase.
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Diffraction is a delayed signal that combines with the source. It causes the measurement to be non minimum phase simply because you capture the combination of the minimum phase signal and the delayed diffraction signal, thus, when you measure at different distances, the result will change. From a crossover design point of view, you can still consider it minimum phase under most situations.
The response being different at different measuring distances (because of the geometry of the direct and delayed signal paths) has nothing to do with whether its minimum phase or not. They're different responses but all minimum phase.
The delayed signal has to exceed the amplitude of the direct signal for there to be any possibility of a non minimum phase result.
You can consider it minimum phase under all practical circumstances, however just because its minimum phase doesn't necessarily mean you can correct for it with minimum phase EQ because the correction is only valid at one point in space. At most other points the correction would make things worse.
There are an infinite number of different minimum phase responses spread across the polar response of the speaker.
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Digital Filters, Filter Inversion, Minimum Phase and All That(go to page 2 for shortcut to the problem of minphase and inversion, in an attempt eliminate a reflection.
Thanks for finding that 🙂
Here's the relevant section from the article:
(my emphasis in bold)
Interesting that this text says "typically" minimum phase when the reflected sound is lower in level, another reference I've read claimed to offer a mathematical proof that its not possible for it to be non minimum phase provided the delayed signal is lower in level than the first arrival, but my maths is not good enough to be able to poke holes in (or confirm) that proof.
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BTW, it took me many years, just until recently, to mentally accept that reflections are minphase (execpt for that one special case). I had to prove it to myself with Audition. I modelled a single reflection by putting a lower amplitude Dirac after a full scale one. This gives a comb filter pattern, with finite "nulls". Then I approximated the freq response with a series of parametric filters and voilá, the same impulse pattern resulted when I sent a Dirac through that filter chain which for sure was minphase.
Now, when I see a set of close spaced resonances in a drivers freq response plot, I know its not "true resonances" but just a reflection bouncing back and forth, in the cone, or cabinet, or whatever. Well, actually it is both, a duality.
Somewhere in the Beyond the Ariel thread we had a discussion whether there was a dying multiple reflection (my guess) or a set of closely spaced resonances (JohnK's point) in what we saw in measured data. None of us was aware of the duality that is present (well, mabye some were but I did not get it at the time). I'll try find the section where this was discussed...
EDIT: Found. It all starts here : http://www.diyaudio.com/forums/multi-way/100392-beyond-ariel-139.html#post2258879
The discussion then spreads accross many, many pages...
Now, when I see a set of close spaced resonances in a drivers freq response plot, I know its not "true resonances" but just a reflection bouncing back and forth, in the cone, or cabinet, or whatever. Well, actually it is both, a duality.
Somewhere in the Beyond the Ariel thread we had a discussion whether there was a dying multiple reflection (my guess) or a set of closely spaced resonances (JohnK's point) in what we saw in measured data. None of us was aware of the duality that is present (well, mabye some were but I did not get it at the time). I'll try find the section where this was discussed...
EDIT: Found. It all starts here : http://www.diyaudio.com/forums/multi-way/100392-beyond-ariel-139.html#post2258879
The discussion then spreads accross many, many pages...
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Brilliant... thanks! I will try to get a test up over the weekend. Or at least a test method discussion 🙂
I played with Bagby's baffle sim yesterday. The radius smooths the response quite a bit. But again, if you start overlaying off-axis angles, even as small as 5, 10 and 15 deg, it all smooths out even without the radius. I was getting less than +-1db variation with just four averages.
Question for Earl on his paper. The filter response applied in your paper is (a) +2, +4 or +6 db above the main level, and (b) the delay is a single number. In diffraction, I'm guessing that the reflected sound is not higher in level than the direct sound. If anything, it should be lower. Also, a rectangular baffle has diffraction from all edges, the combined effect should be considered, right? Adding a single delay does not seem to be replicating the effect of diffraction. You may be testing for something else, but it may not directly apply to diffraction.
If you look at Edge or the Bagby simulator, the diffraction of the entire baffle is reflected (pun not intended) in the frequency response. If we are testing for the audibility of diffraction, shouldn't such a combined response be used?
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It is non intuitive and took me a while to accept too, especially when there is a lot of debate about whether cabinet diffraction results in a minimum phase response or not.
My empirical testing after reading about this proof was to look at the measured excess group delay of various drivers in a cabinet under different conditions. ARTA does a particularly good job of measuring excess group delay, and is what I used.
The beauty of excess group delay is that its group delay that results only from excess phase, so that the group delay from the minimum phase part of the signal is eliminated from the measurement.
Any minimum phase response will look like a horizontal flat line on an excess group delay graph regardless of any frequency response variations, with the vertical position of the line representing the relative path delay.
What I found is that any minimum phase driver mounted on any sort of baffle always measured completely minimum phase despite the obvious diffraction effects in the amplitude response.
I even went back to old measurements taken over a couple of years and it was the same every time. As long as the measurement was gated to exclude room reflections that is.
On measurements taken with long gate times which include room reflections, at some distance from the speaker (typically more than about a metre) the measurement would start to become non minimum phase at certain frequencies.
This is because either (a) the direct signal is being notched out by a boundary cancellation (for example from the front wall behind the speaker) leaving the other delayed reflections larger in amplitude than what was left of the direct signal, or (b) multiple reflections from different room boundaries were all arriving in phase at that frequency such that the combined amplitude of the delayed reflections was greater than the direct path signal.
But with room reflections gated out I never saw a single measurement of a single driver on a baffle that was not minimum phase.
So in summary - baffle diffraction is always minimum phase in any realistic situation, (put a pillow in front of the driver to attenuate the direct signal but not the diffracted signal and then maybe not) while room reflections can easily be non minimum phase depending on the circumstances and how far you are from the speaker.
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How does one convert .FRD files to .WAV or headerless PCM (.DBL)? I want to play with the Bagsby simulator as well...
Convolution does not require a minimum phase impulse response. So the answer is yes, on can do that, no matter what the diffraction is like MP or not.