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I was following this article and I wanted to "borrow" their Idea for my own work.

The difference is that I am using a microphone tetrahedral array and not a binaural microphone. I have two different questions I guess:

First, I would love an intuitive explanation behind their pre-processing step. I could not figure out the intuition of going from a single dimension $\theta_{t,f}=\angle(X_{t,f}^{(0)},\overline{X_{t,f}^{(1)}})$ to two dimensions $\cos(\theta_{t,f}),\sin(\theta_{t,f})$ and back to a single dimension $\phi_{t,f}$ using PCA. What do these quantities represent?

Second, How can I apply a similar method for a tetrahedral microphone array? Is there a better\easier way? Is there a toolbox I can use?

The dataset I am working with contains 4 channels and can be downloaded here.

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