A frequency-domain method is proposed for designing directional patterns from arbitrary microphone arrays employing the complex Fourier series. A target directional pattern is defined and an optimal set of sensor weights is determined in a least-squares sense, adopting a continuous-wave approach. It is based on discrete measurements with high spatial sampling ratio, which mitigates the potential aliasing effect. Fourier analysis is a common method for audio signal decomposition; however in this approach a set of criteria is employed to define the optimal number of Fourier coefficients and microphones for the decomposition of the microphone array signals at each frequency band. Furthermore, the low-frequency robustness is increased by smoothing the target patterns at those bands. The performance of the algorithm is assessed by calculating the directivity index and the sensitivity. Applications, such as synthesizing virtual microphones, beamforming, binaural, and loudspeaker rendering are presented.
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