# How to compute beam pattern given a delay-and-sum filter in spectral domain?

Given a two-mic system (the mic spacing $d$ is known), how can I compute the beam pattern (see the Figure below) over frequency and angle $g(f,\theta)$ for a pair of spectral filters ($H_0$ for channel 0, and $H_1$ for channel 1)?

Both $H_0$ and $H_1$ are complex vectors.

• If your $H$ are really just single complex numbers, then you have a very simple filter; it's just a multiplication with a constant. Do you mean something like "$H_i$ are complex tap delay line model vectors"? – Marcus Müller Aug 24 '17 at 7:45
• Use a steering vector for your array (see array signal processing literature) to generate directional signals from -90 to 90. Spatially filter you received signal with H. Compute the power of the signal. Repeat the process by varying f. – learner Aug 24 '17 at 9:05
• @MarcusMüller $H_{0}$ and $H_{1}$ are vectors. For example, if we use 512-point FFT, then $H_{0}$ has 257 dimensions – read Read Aug 24 '17 at 19:54

One of the method for calculating beam pattern could be, you simulate/capture audio from different directions on array and filter these captures with filters($H$'s) generated. the audio coming from direction of beam pattern will be passed as it is, but the audio coming from other directions will be attenuated. the amount of attenuation with respect to spatial location is nothing but the beam pattern .
• For a two-channel and n-point DFT, if I have $H_{0} = [a_{0}+jb_{0}, a_{1}+jb_{1}, ..., a_{n-1}+jb_{n-1}]$ and $H_{1}$. How would you represent an audio sample with frequency $f$ and angle $\theta$ in complex vector. – read Read Aug 25 '17 at 4:02