A beamformer, for a differential microphone array (DMA) including a number M of microphones, is constructed based on a specified target directivity factor (DF) value for the DMA. An N order beampattern is generated for the DMA, wherein N is an integer and a first DF value corresponding to the N order beampattern is greater than the target DF value. An N−1 order beampattern is generated for the DMA, wherein a second DF value corresponding to the N−1 order beampattern is greater than the target DF value. A fractional order beampattern is generated for the DMA, wherein a third DF value corresponding to the fractional order beampattern matches the target DF value and the fractional order beampattern comprises a first fractional contribution from the N order beampattern and a second fractional contribution from the N−1 order beampattern.