Conventional delay and sum beamformers are additive in nature. Another approach to forming a super directive beam in a specific direction is by the use of differential beamformers, distinctive from additive beamforming. The number of microphones available limits the order of the differential microphone array (DMA) beamforming. For N microphones, an N-1 order differential microphone beamforming is realized. Thus, for a first order DMA beamforming, two microphones are required. An advantage of using DMA beamforming is that the amplitude response tends to be flat.
Consider a two microphones array as shown in Figure 1:
Figure 1: Two microphone array
The DMA beamforming is an optimization problem to meet constraints for N microphones. For two microphones, the constrainst are:
where is the desired beam direction and is a desired null direction. Given , the choice of will determine whether the spatial beam will be a dipole, cardiod, hypercardiod or supercardiod. Figure 2 below illustrates these 4 spatial beams.
Figure 2: Different spatial patterns
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