在本文中，波束成型分別在空間域及模態域下計算，並使用空心球或實心球陣列來實現。波束成型圖顯示出延遲疊加法波束成型在實心球型陣列上的指向性只比空心球上的指向性略高一些而已，而模態域波束成型的旁瓣大小會比空間域的大得多是因為將訊號用球型傅立葉轉換到模態域時會產生誤差。因此，我們使用實心球空間域波束成型來做聲源的定位和分離。使用3D印表機製作實驗模型，並在上面焊上32個微型麥克風。為了解決聲源分離時角度不匹配的問題，先使用最小方差無失真響應波束成型和多種訊號分類法來得出聲源的位置，再針對該角度使用梯克諾夫正規化法及壓縮傳感法來作聲源的分離。我們使用模擬和實驗來驗證這些演算法。聲源分離的結果使用客觀的聲音品質感測評估和主觀的聆聽測試來作評分。評分結果顯示出壓縮傳感法有較好的分離效果，但其聲音會失真得較嚴重。

In this work, four delay-and-sum (DAS) beamformers formulated in the modal domain and the space domain for open and solid spherical apertures are examined via 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 significantly higher than 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 systems (MEMS) microphones are mounted is chosen 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 (MVDR) beamformer or multiple signal classification (MUSIC) algorithm. Next, Tikhonov regularization (TIKR) and compressive sensing (CS) methods are used to extract the source signal amplitudes. Simulations and experiments are conducted to validate the proposed spherical array system. In particular, the experimental investigations include an objective Perceptual Evaluation of Speech Quality (PESQ) test and a subjective listening test. The experimental results demonstrate better sense of separation achieved by the CS approach than by the TIKR approach at the cost of slight distortion.

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