Abstract: An Nth order linear differential microphone array (LDMA) including at most M microphones, where M is greater than N, is constructed by identifying a number K of combinations of at least (N+1) of the M microphones. A target cost function is specified based on at least one of a directivity factor, a beampattern, or a white noise gain associated with the LDMA. For each frequency band of a plurality of frequency bands: an optimal combination of microphones, from the K combinations, is determined based on an evaluation of the target cost function for the band and beamforming is performed using the determined optimal combination for the band. A union of the optimal combinations of microphones for the plurality of bands may be determined and the LDMA may be constructed, using microphones in the union, based on an evaluation of the target cost function across the plurality of bands.