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.

摘要
ABSTRACT
誌謝
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
CHAPTER 1 INTRODUCTION
CHAPTER 2 SPHERICAL ARRAY FORMULATIONS
2.1 Plane wave expansion based on spherical harmonic
2.2 Arrays formulated in the modal domain
2.3 Arrays formulated in the space domain
2.4 Source localization and separation algorithms
CHAPTER 3 NUMERICAL SIMULATIONS
3.1 DAS beamformers in the modal domain and the space domain
3.2 MVDR beamformers in the modal domain and the space domain
3.3 Source localization and separation
3.4 Summary of numerical simulations
CHAPTER 4 SOURCE LOCALIZATION AND SEPARATION EXPERIMENTS
CHAPTER 5 CONCLUSIONS
REFERENCES
APPENDIX

1 J. Meyer and G. Elko, "A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield," IEEE International Conference on Audio Speech and Signal Processing (ICASSP), 2, 1781-1784, Orlando, FL, (2002) .
2 T. D. Abhayapala and D. B. Ward, “Theory and design of high order sound field microphones using spherical microphone array,” IEEE International Conference on Audio Speech and Signal Processing ICASSP, 2, 1949–1952, Orlando, FL (2002).
3 M. Park and B. Rafaely, “Sound-field analysis by plane wave decomposition using spherical microphone array,” J. Acoust. Soc. Am. 118(5), 3094–3103 (2005).
4 B. Rafaely, “Spatial aliasing in spherical microphone arrays,” IEEE Trans. Signal Process, 55(3), 1003-1010 (2007).
5 B. Rafaely, “The Spherical-Shell Microphone Array,” IEEE Trans. Audio, Speech, Lang. Process, 16(4), 740-747 (2008).
6 S. Yan, H. Sun, and X. Ma, “Optimal modal beamforming for spherical microphone array,” IEEE Trans. Audio, Speech, Lang. Process, 19(2), 361-371 (2011).
7 B. Rafaely, “Acoustic analysis by spherical microphone array processing of room impulse responses,” J. Acoust. Soc. Am. 132(1), 261-270 (2012).
8 N. Huleihel and B. Rafaely, “Spherical array processing for acoustic analysis using room impulse responses and time-domain smoothing,” J. Acoust. Soc. Am. 133(6), 3995-4007 (2013).
9 B. Rafaely, “Phase-mode versus delay-and-sum spherical microphone array processing,” IEEE Signal Process. Lett. 12(10), 713–716 (2005).
10 A. Koretz and B. Rafaely, “Dolph-Chebyshev beampattern design for spherical arrays,” IEEE Trans. Signal Processing, 57(6), 2417-2420 (2009)
11 H. Sun, S. Yan, and U. P. Svensson, “Space domain optimal beamforming for spherical microphone arrays,” IEEE International Conference on Audio Speech and Signal Processing (ICASSP), 117-120, Dallas, TX (2010).
12 R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas, Propagation. 34(3), 276-280 (1986).
13 G. F. Edelmann and C.F. Gaumond, “Beamforming using compressive sensing,” J. Acoust. Soc. Am. 130(4), EL232-237 (2011).
14 A. Xenaki and P. Gerstoft, “Compressive beamforming”, J. Acoust. Soc. Am.136(1), 260-271(2014).
15 M. R. Bai and C.H. Kuo, “Acoustic source localization and deconvolution-based separation”, J. Comp. Acous, 23, 1550008 (2015).
16 G. W .Elko, R. A. Kubli and J. M. Meyer. 2009. Audio system based on at least second-order eigenbeams. U.S. Patent No.7587054.
17 G. W .Elko, R. A. Kubli and J. M. Meyer. 2013. Audio system based on at least second-order eigenbeams. U.S. Patent No. 8433075.
18 ITU-T Recommendation P.862, “Perceptual evaluation of speech quality (PESQ): An objective method for end-to-end speech quality assessment of narrow-band telephone networks and speech codecs,” International Telecommunication Union, Geneva, Switzerland, 21pages (2001).
19 ITU-T Recommendation P.862.2, “Wideband extension to Recommendation P.862 for the assessment of wideband telephone networks and speech codecs,” International Telecommunication Union, Geneva, Switzerland, 4 pages (2007).
20 E. G. Williams, Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography, Academic Press, New York, Chap. 6 (1999).
21 B. Rafaely, Fundamentals of Spherical Array Processing, Springer Chap. 3 (2015).
22 M. R. Bai, J. G. Ih, and J. Benesty, Acoustic Array Systems: Theory, Implementation, and Application, Wiley Chap. 3-4. (2013).
23 M. R. Bai, Y. S. Hua and C. C. Kuo, An integrated recording and reproduction array system for spatial audio, 21th Int. Cong. On Sound and Vibration (ICSV 2014) 13-17 July 2014, Beijing.
24 S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press, New York, Chap. 1-7 (2004).
25 M. Grant and S. Boyd, cvx, Version 1.21 MATLAB software for disciplined convex programming available at http://cvxr.com/cvx (last viewed on June 14 ,2013).
26 L. Meirovitch and H. Baruh, “Robustness of the independent modal-space control method,” J. Guid. Control Dyn., 6(1), 20-25 (1983).
27 ITU-R Recommendation BS.1534-1, “Method for the subjective assessment of intermediate quality levels of coding systems,” International Telecommunication Union, Geneva, Switzerland (2003).