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Polar chart visualization for coincident techniques
Old 4th August 2020
Homework in 3D

Originally Posted by lukedamrosch View Post
A few months back I was messing around with some of the various MatLab-like visualization tools for 3-dimensional graphing etc. I was hoping to do something similar to your chart, but visualizing microphone directivity (and coincident combinations) in three dimensions at various frequencies.

Any ideas/tips/shortcuts? I certainly don't want to reinvent the wheel if something like this is out there in open source land and can perhaps be tweaked for these purposes.
I'll table the frequency-dependence part of your question, since it's not accounted for in the simple trig models used for polar patterns.

There are a couple main tricks:

First, extend the printed polar patterns as figures of rotation around the mic axis. (This is valid for pencil mics, anyway.) The normalized polar sensitivity then becomes:

S = (1-B) + B * cos(a) * cos(b)

where a and b are azimuthal and elevational angles measured from the microphone axis.

Next, you have to express the source location in coordinates relative to the microphone position(s), transform to the (non-standard) polar coordinates above, and adjust the angles for the fact that the microphones might be rotated.

Dot products and normalized direction vectors make this all a bit easier.

Once you've figured it all out, you might as well go the rest of the way and compute the inter-channel time delay for the non-coincident case. Then choose your favorite ILD and ITD functions and predict the virtual source position on playback.

Yes, lots of people have done this before. You might find the code in someone's master's thesis.

David L. Rick
Old 6th August 2020
Lives for gear
lukedamrosch's Avatar

Thanks for this David, I appreciate it!
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