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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?

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    $\begingroup$ if I'm getting you correctly, you're interpreting your $h_{XYZ}$ as spatial filter (I like that!), right? $\endgroup$ – Marcus Müller Jan 1 at 13:27
  • $\begingroup$ @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? $\endgroup$ – havakok Jan 1 at 14:18
  • $\begingroup$ 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. $\endgroup$ – Marcus Müller Jan 1 at 14:33
  • $\begingroup$ DS filter and MVDR filter. $\endgroup$ – havakok Jan 1 at 15:15
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    $\begingroup$ yeah, these "filter" in spatial domain, not in say, frequency domain, so we're on the same understanding. $\endgroup$ – Marcus Müller Jan 1 at 15:17

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