No it doesn't work like that, 3D measurements for Spherical functions, 2D measurements need different functions. I'm sure Earl can explain more clearly what the specific differences are.
There was a good idea from Kees in the ASR thread to use an array of mems mics so a quarter of sphere can be captured in one go at each radial movement. The support frame can then be very thin as the mics themselves are so small so the interference from it is minimized. In Weinrich's paper the effect of the structure was shown, and his was already quite minimal.
I wonder if MATAA can be used to capture multiple microphones still with the ability to use a reference loopback channel to maintain timing?
REW's pro version has multiple mic functionality. I'm not sure about ARTA but I think not.
I am also curious about this aspect.
Referring to NTK's document part 2 here:
https://www.audiosciencereview.com/forum/index.php?attachments/part_2-pdf.39273/
It is said that the sound waves from a loudspeaker at any point in 3D space (parameterized by r, theta, phi in spherical coordinate system) at a given frequency 'omega' can be fully expressed as a linear combination of the spherical harmonics. The pressure field value at location (r, theta, phi) at frequency 'omega' given by below equation
and its 'N' term approximation given by
According to the coordinate system definition for measurement defined here: https://www.audiosciencereview.com/forum/index.php?attachments/part_1-pdf.39272/
All points in the plane containing the horizontal polars (assuming it is the xy plane) can also be obtained from the spherical coordinate system by setting theta = 90 degrees and by varying 'r' and 'phi'
In such a scenario, the pressure field values in the horizontal plane (xy plane) as shown in the equation above can also be obtained by setting 'theta = 90 degrees or pi/2 radians (in which ever way the equation is defined)'. To evaluate the values, we need to substitute 'theta = 90 degrees' in the right hand side Ynm (theta, phi) function also.
I dont see this creating a set of linearly dependent set of equations theoretically and it deson't seem impossible to use some method (like least squares) to determine the values of the pressure field at any point in xy plane using the coefficients (Amn, Bmn) evaluated (with theta = 90 degrees). However, it cannot be then used to determine the value of the pressure field at any point in 3D space (to construct the directivity baloon) which the original method permits.
Hence, other than the 2D reduction of the original method, which I outlined above being only able to capture/characterize much less data (values of the pressure field only along a plane) than what is possible (can construct the whole 3D directivity baloon), I dont see an impossibility in using the above equations to a 2D analysis, unless I missed something obvious in a quick look at the equations..
(Well, implementation-wise, there is also the problem of how the spherical harmonic function itself varies in the xy plane and whether it results in a set of linearly dependent set of equations in the above described case due to any sort of finite register-width approximation)
If I understand you, that is just what I did. See https://www.diyaudio.com/community/...d-scanner-on-a-shoestring.318151/post-7604604
I'm know thinking that we need a spherical harmonic equivalent for the 2D case.
Or maybe (and I just made this up while typing...) we can repeat the measurement of the horizontal plane above it and below it. Going from a point source to a line source. I don't know...
I'm know thinking that we need a spherical harmonic equivalent for the 2D case.
Or maybe (and I just made this up while typing...) we can repeat the measurement of the horizontal plane above it and below it. Going from a point source to a line source. I don't know...
For me the more important research question in the context of all this is the following:
It appears to me that the pressure field at any point in 3D space has a sparse representation (low values of N is sufficient to characterize the pressure field at any point pretty accurately) using the spherical harmonics as basis functions (for a loudspeaker with not impossibly complicated directivity patterns below 1kHz)
This brings the important question of whether we can solve for the entire thing using an underdetermined set of equations and recent ideas from compressive sensing including l1 norm minimization (from signal processing) rather than using an over determined system of equations and least squares kind of methods (l2 norm minimization).
If it is doable, the advantage would be a significant reduction in the number of measurements that would be needed to capture the pressure field and solve for the coefficients attached to the basis functions..
It appears to me that the pressure field at any point in 3D space has a sparse representation (low values of N is sufficient to characterize the pressure field at any point pretty accurately) using the spherical harmonics as basis functions (for a loudspeaker with not impossibly complicated directivity patterns below 1kHz)
This brings the important question of whether we can solve for the entire thing using an underdetermined set of equations and recent ideas from compressive sensing including l1 norm minimization (from signal processing) rather than using an over determined system of equations and least squares kind of methods (l2 norm minimization).
If it is doable, the advantage would be a significant reduction in the number of measurements that would be needed to capture the pressure field and solve for the coefficients attached to the basis functions..
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Yes this is exactly what I meant. Sorry, it seems like I missed many posts in between in this thread.. Let me read the recent posts once again
Ideally, that would be the better way to go forward I guess..
The problem we have will be linear dependency in the set of equations that we create for solving the coefficients, which is also dependent on how the spherical harmonics function values vary at the measurement points..
But I think what you are saying is definitely worth trying out (atleast in code/simulation with synthetic data) to see how well/bad it works.
Edit: One good way to check whether we will be able to solve such a system of equations properly with l2 norm minimization (least squares) is to check the matrix condition number (ratio of largest eigen value to smallest eigen value). If it is not low enough, it might get difficult to proceed..
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I believe from the earlier discussion they are radial Hankel and Bessel functions (instead of spherical) and legendre polynomials were mentioned.
Beyond the names I can't help.
You can record multiple channels no problem, I do that all the time when making music and recording instruments.
Since we don't need any results immediately on the fly, a two or multiple mic recording is very easy to implement.
Mechanically speaking, it will even keep that moving beam better in balance as well 🙂😎
Use one or fewer mics, move them in space and combine the results is exactly the same thing of course 😉
In a book from university on partial differential equations I found a section on "Harmonic Functions in the Plane" "Polar Coordinates". Harmonic functions are the solution to the laplace formula (as far as I understand).
In order not to infringe (?) any copyright I searched the internet and found the document attached in which the same formula is present:
p. 166, equation 8
ps. The book is in a mint condition. Probably not a good sign...
Lol 😂
You know what I meant.
Although, using less then one mic makes the math extremely simple all of a sudden 😉😃
Sure but I couldn't miss that opportunity
Even for a single mic there is some value in considering a MEMS mic as they are so small the apparatus to move one or more could be much less bulky.
Weinrich used two small knowles capsules that would have been somewhat equivalent in the 80's.
Getting MEMS calibrated can be a bit of a challenge.
On paper it works great, in practice there are not many of the shelf variants available for users.
Multiple mic setup, especially an array, will also become expensive very quickly.
@Tom Kamphuys: If possible, can you check the condition number of the matrices in your two examples (the random-looking distribution of measurement points vs the circular distribution of points) here: https://www.diyaudio.com/community/...d-scanner-on-a-shoestring.318151/post-7604604
Also, in the random-looking setup, was it a uniform random sampling of points within a bounded region in the xy plane?
Also, in the random-looking setup, was it a uniform random sampling of points within a bounded region in the xy plane?
Circumvent what? If you are doing sound field separation then no its not enough to just do a circle. It has to be a full sphere.
I never did sound field separation, only high polar resolution with a minimum of points. If you want to take data every 2 degrees then what I have is not much, if any, improvement. The LF stuff I just did with near field.
Multichannel Audio interface makes this possible. And the more mics, the faster the point cloud of measurements. Disparate positions I would think both vertically and in depth away from the DUY.
I like the arc of microphones. but that would require a flexible array, or it would be too limited in loudspeaker size. A number of methods to accomplish this.
I understand I need a full sphere for SFS. NTK can also do full sphere without SFS.
I would love to have what you did available: 2D without SFS. I think it could be an intermittent goal. It shares parts/capabilities with the full blown diy Klippel: automated measurements, something rotates, translation of measurements to coefficients, evaluation on a denser grid, ...
The problem is, I don't know what you did. Especially the math. I think, however, together we have enough knowledge and capabilities in this thread to (re)create it. But that depends a lot on you. You need to be willing to share that, you need to educate us. And whether or not you want that is, of course, totally up to you.
How much smoothing of the measurements will this introduce is the question an engineer will need to know. I am not a great mathematician, but I understand your clear explanations and appreciate it! The resolution that we are looking at is down to 1/24th octave. That is where we see the beginnings of harmonics and nulls and peaks in the reproduction of the music, or the test signals.For me the more important research question in the context of all this is the following:
It appears to me that the pressure field at any point in 3D space has a sparse representation (low values of N is sufficient to characterize the pressure field at any point pretty accurately) using the spherical harmonics as basis functions (for a loudspeaker with not impossibly complicated directivity patterns below 1kHz)
This brings the important question of whether we can solve for the entire thing using an underdetermined set of equations and recent ideas from compressive sensing including l1 norm minimization (from signal processing) rather than using an over determined system of equations and least squares kind of methods (l2 norm minimization).
If it is doable, the advantage would be a significant reduction in the number of measurements that would be needed to capture the pressure field and solve for the coefficients attached to the basis functions..
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I like them to, but my wallet doesn't.
I guess with delays on each mic, you can make any shape array you want