# How to generate a beam pattern from a beamformer on 3D

given a 3D microphone array with $$M$$ microphones, $$d(f,\Theta)\in \mathbb{R}^{f\times M}$$ is the steering vector for a given direction $$\Theta=(\varphi,\theta)$$, inclanation and azimuth respectively.

I have generated both delay and sum $$h_{DS}=\frac{d(f,\Theta)}{M}$$ and minimum variance distortionless response $$h_{MVDR}=\frac{\Phi_y^{-1}d(f,\Theta)}{d^H(f,\Theta)\Phi_y^{-1}d(f,\Theta)}$$.

I have a function that generates a plot given a beam pattern - 3 column table corresponding to $$(\varphi,\theta, A)$$, where $$A$$ is the amplitude in that direction.

How do I generate such a beam pattern from each filter? Is there any value in generating a beam pattern from the steering vector regardless of the filter?

• if I'm getting you correctly, you're interpreting your $h_{XYZ}$ as spatial filter (I like that!), right? – Marcus Müller Jan 1 at 13:27
• @MarcusMüller, What do you mean by spatial filter? As far as my understanding goes MVDR is trying to overcome directional interference, while the input is a ,multi-microphone array and the output is a single channel. Am I missing anything? – havakok Jan 1 at 14:18
• no, I was just confused because only in your last paragraph you introduced the term "for each filter", and now I'm wondering what your filters are. – Marcus Müller Jan 1 at 14:33
• DS filter and MVDR filter. – havakok Jan 1 at 15:15
• yeah, these "filter" in spatial domain, not in say, frequency domain, so we're on the same understanding. – Marcus Müller Jan 1 at 15:17