Directivity pattern for a beamformed signal
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Finally, I got a signal y(1x5001) (delayed and summed output of the microphones).
How can I plot the directivity pattern(mesh-plot) of the above array? I have gone through many books which describe the pattern mostly for linear array geometries. If Iam not wrong, I should end up having my mainlobe at (30°,45°) for my wideband output signal 'y' (that would mean my beamformer is working).
How can I go about doing this using the signal y? What would be the steering vector in my case?
Please help.
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Honglei Chen
2011-12-30
In many literature, beam pattern is a narrow band concept so it is related to the steering vector. Since you are using time domain beamforming, I would do the following:
1. Simulate incoming signals for each direction you would like to calculate the beam pattern. It is the same as you simulate your source.
2. Process each signal using the SAME beamformer you use for your desired source, i.e., beamform each signal to (30, 45) degrees.
3. Now you get a beamformed signal for each direction and you can now compute the power or energy for those signals. You can then plot power or energy as a function of angle and it should match your beam pattern.
HTH
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Honglei Chen
2012-1-3
Let's say you have a signal sn. In your beamforming example, you first delay it as if it is come from (30,45) and then add delay corresponds to (30,45) to beamform it. What you need to do here is pretty much the same, just for different directions. For example, use (0,45) as the source direction. You will add delay to sn to make it look like coming from (0,45). Then you still beamform it using the delay corresponds to (30,45). This tells you how much energy you can get if the signal is at (0,45) while you beamform to (30,45). If you repeat this for all possible directions, you have a beam pattern for steering toward (30,45). HTH
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