Earl do you have any idea of how nearfield the measurements can be made in practice for the modal analysis to extrapolate the far field data?
I wonder if there is the possibility to use a two microphone setup with compensation, like the AudioChiemgau mode compensator
https://www.audiosciencereview.com/...move-room-modes-from-bass-measurements.49892/
Use that to take polar nearfield measurements and then use modal analysis to extrapolate the data back to far field.
The idea being that the reflections can be cancelled with the dual mic setup in the lower frequencies to overcome the gate resolution, and get the modal analysis to overcome the fact that the data is neither truly nearfield like at the dust cap nor far field and therefore not truly representative of either.
If the mic signals are recorded separately and processed afterwards (rather than using an analogue hardware compensation) the data from one mic alone could be used separately to avoid the comb filtering from the dual mic setup at high frequencies.
My guess would be the radius of that sphere which can completely encompass the source. Closer than that and things get dicey. Ideally one should move back at higher frequencies. Do this once ? twice? Don't know the answer to that one.
Again, my bet would be on numerical extension of the impulse response. I figured that would work quiet well and word from the street has it that it did in Bill's software.
I was wondering in general how this would fit to the entire equation?
As far I am aware everything just below the bafflestep can basically just measured with nearfield measurements and be extrapolated to a farfield response?
I think Klippel does this at least to some extend as well.
I wonder what putting a mic on a rail and doing a continuous step, analyze, maybe average blocks in time or maybe frequency, step again. I remember an AES paper where the authors claim that the polar response could be predicted from the near field axial response. Now that would be an easy implementation.
A more general answer to the question of how close - the subject of Nearfield Acoustic Holography (NAH) is about this. There are books on the subject, but that's a whole lot of mics and signal processing - but again, it works.
That is what I feared. The dual mic mode compensation gets progressively less useful the further back you go and by the time you get to something the whole source can fit in it will be next to useless.
I don't think Bill's software is even still available it was a long time ago.
This is the article he wrote
http://www.libinst.com/cepst.htm
Bill refers to Keith Holland's work on cepstral analysis, radio silence from then on.
I have found an old thesis where there is the claim to have been able to successfully lifter out a reflection
2.3.8 in this document which also has good references to understanding the technique.
https://vtechworks.lib.vt.edu/serve.../429fc058-6150-4007-99e2-1040bb05dea4/content
Tom tried to blank out a reflection a while ago, I don't remember it working that well.
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In a 2D system, if the measurements could be made in the very nearfield and then extrapolated back to the far field, reflections are much supressed so there would be less or no need for gating and the reduction in frequency resolution of the base measurements.
If the measurements are in the nearfield but not very close up we go back to only a small benefit from a slightly longer gate time.
I am not aware of any method available to compensate for cabinet diffraction with nearfield polar measurements. Most use a single axial nearfield measurement and any directivity is simulated based on piston size.
At these lower frequencies (just below bafflestep), there are no or very little diffraction effects?
Btw, I am very much aware what most people use 😉
That would depend on what you consider to be below the baffle step. What frequencies that affects will then depend on the speakers size.
There are some directivity effects in the 150Hz range and up that are not included when a simple baffle step compensation is used.
Of course there is an argument as to whether these matter much, are swamped out by room modes etc. There shouldn't be any argument that they are there and can be measured or simulated.
There are some directivity effects in the 150Hz range and up that are not included when a simple baffle step compensation is used.
Of course there is an argument as to whether these matter much, are swamped out by room modes etc. There shouldn't be any argument that they are there and can be measured or simulated.
The condition number of a matrix is the ratio of its largest singular value to its smallest singular value.
We take the SVD of a matrix to find the singular values and then take the ratio of the largest to the smallest one.
I am pretty sure that these days, there would be built-in functions in all good scientific computing packages, which compute & return the condition number of a matrix once we give the matrix as an argument to the function. For example, Matlab uses this: https://in.mathworks.com/help/symbolic/cond.html
For context, the matrix that I was talking about was the one we use for solving for the scaling coefficients for the basis functions
As per an example in part 2 of NTK's document, the matrix looks like below for N=1
As the value of N increases the size of this matrix is going to increase significantly.
The reason why I was interested in finding out the condition number is the following. The matrix needs to be well-conditioned (condition number closer to 1) for us to be able to solve the system of equations properly. This happens when the rows/columns of the matrix are linearly independent, meaning one row/column cannot be obtained using a linear combination of other rows/columns.
Now when we look at the measurement locations distributed in a circle as in your earlier plot shown below, since all the measurement are at the same distance from the source (radius of the circle), the values of the spherical hankel functions (h_n (kr)) which determine the radial dependency will evluate out to be the same. This becomes similar to the rank deficient scenario explained in NTK's document part-2 pages 3 & 4. It won't help us solve the equation.
By randomizing the measurement locations, you are sort of removing this radial dependency and giving more chances for the system of equations to be linearly independent and become more solvable
Atleast, the above was my suspicion about the issue..
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Methods that try to clean up the impulse and get rid of the room signature might probably be employing some sort of deconvolution/denoising kind of algorithms I guess. That in turn might usually involve some sort of adaptive filtering/inversion/pseudo inverse computation. In wireless communications, multipath propagation of signals (through the wireless channel) causes very similar kind of issues that sound signals undergo when they propagate inside rooms. We use different techniques to compensate for these issues therr. Similar techniques might be applicable in the case of sound also..
Anyway, I need to look up the literature to see how well these methods can be used. I also need to look into the power cepstrum analysis literature that @fluid posted above
I feel that these kind of explorations can happen in parallel while this thread moves on with its investigation of the 2D/3D klippel like methods as per NTK's documentation.. Most important part of it is that we have got the math for it worked out to a good extent. What remains is implementation of (especially) the robotics part of it.
If we get something promising from exploratory ideas in between, it can always be integrated into the mix. Otherwise we will lose track of the goal very easily and be left with no working method in the end..
Anyway, I need to look up the literature to see how well these methods can be used. I also need to look into the power cepstrum analysis literature that @fluid posted above
I feel that these kind of explorations can happen in parallel while this thread moves on with its investigation of the 2D/3D klippel like methods as per NTK's documentation.. Most important part of it is that we have got the math for it worked out to a good extent. What remains is implementation of (especially) the robotics part of it.
If we get something promising from exploratory ideas in between, it can always be integrated into the mix. Otherwise we will lose track of the goal very easily and be left with no working method in the end..
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Just for avoiding confusion, the matrix that I was referring to in above posts is the one just to the right of the "=" sign and contains terms of the form hn(kr)Y^m_n(theta, phi)
Now THAT sounds interesting! Can you shine some light on the theory you mentioned?
Oh, cepstral analysis and lifering. Been there, done that. It's a cool idea, but it didn't work great for me with real world data. For reference, I used some measurements taken outdoors on a tower that were anechoic down to about 70 Hz. I compared them to indoor measurements of the same speaker that needed gating to 300 Hz. I tried improving the frequency resolution of the indoor measurements using the cepstrum liftering method to replicate the outdoor/anechoic measurement. The issue was that the cepstra didn't nearly look as simple as what you see in the examples mentioned above. These demonstration examples show some clear spikes corresponding to a few and well resolved echoes, so it's relatively easy to identify and remove them from the data. In contrast, my real-world data showed many small spikes, and the echoes were not clearly resolved from the noise. It took a lot of subjective judgement to get the liftering right in a way such that the result resembled the anechoic reference.
So yes, cepstral liftering works, and it's not difficult to implement in software (MATAA has everything you need). However, for a reliable result you need anechoic data to confirm you got the liftering right. Once you're there, you can just use the anechoic data itself... If the cepstrum idea would be a practical cure-it-all tool, it would be used all the time. It is not.
I was hoping @gedlee had some other theory in mind that would be more useful in practical work.
So yes, cepstral liftering works, and it's not difficult to implement in software (MATAA has everything you need). However, for a reliable result you need anechoic data to confirm you got the liftering right. Once you're there, you can just use the anechoic data itself... If the cepstrum idea would be a practical cure-it-all tool, it would be used all the time. It is not.
I was hoping @gedlee had some other theory in mind that would be more useful in practical work.
Indeed the textbook examples make it seem so simple, there is the echo, just delete it. But of course it is not so simple.
There is some good information in the Keith Holland paper where he describes methods for cutting through the noise to get a clearer picture. Compensating for bandwidth limitations and some other techniques.
https://pearl-hifi.com/06_Lit_Archi...Keith/Cepstral_Analysis/Cepstral_Analysis.pdf
Better late than neverWell, fluid, at least you got me on board in this thread after 2 years.
I assume you know what diffraction is?
Frequencies that low are to big to have any diffraction effects.
There can be directivity effects, that's totally true. But that's not the same thing as diffraction.
When diffraction is the reason for the directivity it's hard to separate cause and effect.
It's not hard, because we know that those wavelengths are to big to cause any diffraction effects to begin with.
So with deduction of reasoning we can cancel that option out.
In fact, below say around 300Hz there aren't many disturbances or resonances left.
Unless you build a very tall speaker or have a very big woofer.
We are in full piston range at that point.
Which is great, because it makes everything very predictable.