In some applications, the signal to noise raio improvement and desired beamwidth leads to the use of two microphones not being adequate. Three microphones may be utilized. If differential beamformers are deployed, the order will have to be second order purely based on the number of microphones. The topology could be linear or non linear.
Consider a three microphones non-linear array as shown in Figure 1 below:
Figure 1: Three microphone array
The DMA beamforming is an optimization problem to meet constraints for microphones. For three microphones, the constraints are:
where is the desired beam direction and are desired null directions. Given , the choice of will determine whether the spatial beam will be a dipole, cardioid, hypercardioid or supercardioid. Figure 2 below illustrates these 4 spatial beams.
Figure 2: Different spatial patterns
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