Hi Marc,

Yes, as with SMAs, the aliasing frequency scales inversely with the radius.

But a small radius limits the low-frequency end: The smaller the radius is, the 
higher will be the frequencies above which a certain (higher) order can be 
deduced. The 0th order is always there. For an array with a very small radius 
the 1st order may only be available above a certain frequency (and up until the 
aliasing frequency) etc.

The radius of this particular prototype had a very different motivation:

We figured out that there existed only about half a dozen arrays in the world 
that use this equatorial layout, and all of them were experimental prototypes. 
The one that we used in the video was originally built for motion-tracked 
binaural where the array needs to have a radius similar to that of a human head 
so that a useful ITD is produced. Here are the details of the array: 
https://www2.ak.tu-berlin.de/~akgroup/ak_pub/abschlussarbeiten/2018/Fiedler_MasA.pdf
  Fortunately, this is indeed a size that allows for fitting all hardware into 
the scattering body.

It is certainly no coincidence that this same size works well also for SMAs 
that perform spherical harmonic decomposition for subsequent binaural 
rendering. Many authors concluded this. One author that I can remember off the 
top of my head is Benjamin Bernschütz. His PhD thesis contains a lot of 
information on this.

If it works well for SMAs, then it works well for EMAs!

It was indeed a bit of luck that we were able to get hold of a prototype that 
was ideal for our purposes. In the near future, we will look into how small the 
array can be before things break down.

Best regards,
Jens



On 1 Dec 2021, at 15:55, Marc Lavallée 
<[email protected]<mailto:[email protected]>> wrote:

Le 2021-12-01 à 09 h 20, Jens Ahrens a écrit :
I’m not sure if I understand your question correctly. I’ll do my best to be 
comprehensive so that my response covers what you are interested in:

For this type of array, the spatial aliasing frequency f_a is dependent on 
order N and radius R of the array in the exact same manner like with spherical 
microphone arrays (SMAs): N = (2 pi f_a / c) R

   N = 7
   R = 0.0875 m

So that

   f_a = 4.3 kHz

With a  bit of algebra, f_a = c  N / ( R 2 pi ).
So a smaller radius for the sphere would improve f_a?
Was 0.0875 m chosen in order to embed some hardware?

Marc
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