In this paper, four delay-and-sum (DAS) beamformers formulated in the modal domain and the space domain for open and solid spherical apertures are examined through numerical simulations. The resulting beampatterns reveal that the mainlobe of the solid spherical DAS array is only slightly narrower than that of the open array, whereas the sidelobes of the modal domain array are more significant than those of the space domain array due to the discrete approximation of continuous spherical Fourier transformation. To verify the theory experimentally, a three-dimensionally printed spherical array on which 32 micro-electro-mechanical system microphones are mounted is utilized for localization and separation of sound sources. To overcome the basis mismatch problem in signal separation, source localization is first carried out using minimum variance distortionless response beamformer. Next, Tikhonov regularization (TIKR) and compressive sensing (CS) are employed to extract the source signal amplitudes. Simulations and experiments are conducted to validate the proposed spherical array system. Objective perceptual evaluation of speech quality test and a subjective listening test are undertaken in performance evaluation. The experimental results demonstrate better separation quality achieved by the CS approach than by the TIKR approach at the cost of computational complexity.

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