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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.

Circular microphone arrays (CMAs) are sufficient in many immersive audio applications because azimuthal angles of sources are considered more important than the elevation angles in those occasions. However, the fact that CMAs do not resolve the elevation angle well can be a limitation for some applications which involves three-dimensional sound images. This paper proposes a 2.5-dimensional (2.5-D) CMA comprised of a CMA and a vertical logarithmic-spacing linear array (LLA) on the top. In the localization stage, two delay-and-sum beamformers are applied to the CMA and the LLA, respectively. The direction of arrival (DOA) is estimated from the product of two array output signals. In the separation stage, Tikhonov regularization and convex optimization are employed to extract the source amplitudes on the basis of the estimated DOA. The extracted signals from two arrays are further processed by the normalized least-mean-square algorithm with the internal iteration to yield the source signal with improved quality. To validate the 2.5-D CMA experimentally, a three-dimensionally printed circular array comprised of a 24-element CMA and an eight-element LLA is constructed. Objective perceptual evaluation of speech quality test and a subjective listening test are also undertaken.