本文提出一個可以用來錄製空間聲場以及回放的整合式陣列系統。此架構類似於離散時間訊號處理的分析以及合成濾波器系統，此陣列系統的運作包括兩個階段：在第一個階段，利用麥克風陣列分析以及將聲場「編碼」，將聲場簡化為僅由聲源方向以及訊號兩個物理量來表示，此麥克風陣列是利用多重訊號分類(Multiple Signal Classification)這種常用的到達方向（Direction of Arrival）方法去估計聲源的方位，並將各種不同的聲源訊號分離。第二個階段則是一個喇叭陣列，它可以「解碼」以及重現在第一階段中獲得的聲場資訊，其中包含聲源方位、訊號，在這個階段我們透過在重建範圍內設置大量的假想控制點，來對欲重建的聲場做取樣，進而由這些控制點來反推喇叭訊號。而實際上在重現聲場的時候，可能會因為環境反射的因素而降低喇叭內部重建區域的音質，因此本文也討論，如何同時有效地控制喇叭外部聲場的輻射，並維持重建聲場的品質。過程中的逆矩陣運算則主要是由截斷奇異值（Truncated Singular Value Decomposition）和最佳化（Convex Optimization）兩種方法求解。最後，本文也提出客觀與主觀的評估測試，來衡量此陣列系統對於聲場的分離以及重建之效果。

An integrated recording and reproduction array system for spatial audio is presented. The system has a generic framework akin to the analysis-synthesis filterbanks in discrete time signal processing. The architecture of the system consists of two stages. In the first stage, an analysis microphone array that “encodes” the sound field into sparse source components in the angle space. Direction of Arrival (DOA) of sound sources is estimated by MUltiple SIgnal Classification (MUSIC). The second stage is a field synthesis by loudspeaker array that “decodes”, or reproduces, the sound field on the basis of the source components obtained in the first stage. Specifically, this stage can be formulated as a deconvolution problem by matching the reproduced and target fields at numerous control points in the interior domain of the loudspeaker array, while minimizing the external radiation to mitigate the adverse effects of boundary reflections. The inverse problem is solved by Truncated Singular Value Decomposition (TSVD) or Convex Optimization (CVX) algorithms. Since the performance of sound field synthesis may be constrained by aliasing frequency, a hybrid method combing deconvolution and vector panning is proposed here for improving the reproduction. The result of source extraction and the performance of reproduction are also evaluated.

摘要 I
Abstract II
誌謝 III
Table of Contents IV
TABLE LIST V
FIGURE LIST VI
Chapter 1 INTRODUCTION 1
Chapter 2 SOUND FIELD ANALYSIS USING A MICROPHONE ARRAY 6
2.1 Source tracking 7
2.2 Source Extraction 8
Chapter 3 SOUND FIELD SYNTHESIS USING A LOUDSPEAKER ARRAY 11
3.1 Deconvolution-based sound field reproduction 12
3.2 Minimizing external radiation 14
3.3 Panning-based sound field reproduction 14
3.4 Hybrid approach 15
3.5 Integrated microphone and loudspeaker array 16
Chapter 4 NUMERICAL SIMULATIONS 17
4.1 Plane-wave decomposition using a microphone array 18
4.2 Reproduction by pressure matching 18
4.3 Binaural simulation for the synthesized sound field 20
4.4 Dark-zone control 21
Chapter 5 EXPERIMENTAL PERFORMANCE EVALUATIONS 23
5.1 Plane-wave decomposition using a microphone array 24
5.2 Performance evaluation of the loudspeaker array reproduction 24
Chapter 6 CONCLUSIONS 27
REFERENCES 29
APPENDIX 33

1 S. P. Thompson, “On the Function of the Two Ears in the Perception of Space,” Philos. Mag., vol. 13, 406-416, (1882).
2 H. A. M. Clark, G. F. Dutton and P. B. Vanderlyn, “The Stereosonic Recording and Reproduction System: A Two-Channel Systems for Domestic Tape Records,” J. Audio Eng. Soc. 6(2), 102-117, (1958).
3 H. Fletcher, “Auditory Perspective –Basic Requirements,” IEEE, 0095-9197 (1934).
4 J. C. Steinberg and W. B. Snow, “Auditory Perspective –Physical Factors,” IEEE, 0096-3860 (1934).
5 P. Scheiber, “Toward a More Accurate Spatial Environment,” J. Audio Eng. Soc. 17(6), 690-691, (1969).
6 P. Scheiber, “Analyzing Phase-Amplitude Matrices,” J. Audio Eng. Soc. 19(10), 835-839, (1971).
7 J. Hull, Surround Sound Past, Present, and Future – A History of Multichannel Audio From Mag Stripe to Dolby Digital, Dolby Laboratories Inc., San Francisco, (1999).
8 M. A. Gerzon, “Ambisonic in multichannel broadcasting and video,” J. Audio Eng. Soc. 33, 859–871, (1985).
9 C. Kyriakakis, “Fundamental and Technological Limitations of Immersive Audio Systems,” Proceedings of the IEEE 86(5), 941-951 (1998).
10 R. Nicol, AES Monograph: Binaural Technology, Audio Engineering Society, New York, (2010).
11 M. R. Bai and C. C. Lee, “Objective and subjective analysis of effects of loudspeaker span on crosstalk cancellation in spatial sound reproduction,” J. Acoust. Soc. Am. 120(4), 1976-1989, (2006).
12 T. Sporer, “Wave Field Synthesis – Generation and Reproduction of Natural Sound Environments,” Proc. of the7th Int. Conference on Digital Audio Effects, Naples, Italy, (2004).
13 S. Spors, R. Rabenstein and J. Ahrens, “The Theory of Wave Field Synthesis Revisited,” Audio Engineering Society Convention Paper, Amsterdam, the Netherlands, (2008).
14 D. de Vries, AES Monograph: Wave Field Synthesis, Audio Engineering Society, New York, 95 pages, (2009).
15 F. M. Fazi, “Sound Field Reproduction,” Ph.D. thesis, Faculty of Engineering, Science and Mathematics, University of Southampton, (2010).
16 J. B. Fahnline and G. H. Koopmann, “A numerical solution for the general radiation problem based on the combined methods of superposition and singular-value decomposition,” J. Acoust. Soc. Am. 90, 2808–2819 (1991).
17 L. Song, G. H. Koopmann, and J. B. Fahnline, “Numerical errors associated with the method of superposition for computing acoustic fields,” J. Acoust. Soc. Am. 89, 2626-2633 (1991).
18 M. Kolundzija, C. Faller, and M. Vetterli, “Sound Field Reconstruction: An improved approach for wave field synthesis,” Proceedings of the 126th AES Convention, Audio Engineering Society, Munich, Germany (2009).
19 M. Kolundzija, C. Faller, and M. Vetterli, “Designing Practical Filters For Sound Field Reconstruction,” Proceedings of the 127th AES Convention, Audio Engineering Society, New York (2009).
20 J. Ahrens, R. Rabenstein and S. Spors, “Sound Field Synthesis for Audio Presentation,” Acoustics Today, 10(2), 15-25 (2014).
21 M. R. Bai, J.-G. Ih, and J. Benesty, Acoustic Array Systems: Theory, Implementation, and Application, Wiley/IEEE Press, Singapore, Chaps. 3-4, (2013).
22 J. Capon, “High-Resolution Frequency-Wavenumber Spectrum Analysis,” Proceedings of the IEEE 57, 1408-1418, (1969).
23 R. O. Schmidt, “Multiple Emitter Location and Signal Parameter Estimation”, IEEE Trans. on Antenna Propag. AP-34, 276-280, (1986).
24 J. Gomes, J. Hald, P. Juhl and F. Jacobsen, “On the Applicability of the Spherical Wave Expansion with a Single Origin for Near-Field Acoustical Holography”, J. Acoust. Soc. Am. 125, 1529-1537, (2009).
25 S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press, New York, Chap. 1-7, (2004).
26 M. R. Bai and C. C. Chen, “Application of convex optimization to acoustical array signal processing,” J. Sound Vib., 332(25), 6596 – 6616.
27 Y.-H. Kim and J.-W. Choi, Sound Visualization and Manipulation, Wiley, Singapore, Chap. 6, (2013).
28 J.-W. Choi and Y.-H. Kim, “Generation of an acoustically bright zone with an illuminated region using multiple sources,” J. Acoust. Soc. Am. 111, 1695–1700, (2002).
29 A. J. Klockars, G. R. Hancock and M. J. McAweeney, “Power of Unweighted and Weighted Versions of Simultaneous and Sequential Multiple-Comparison Procedures,” Psychological Bulletin 118, 300-307, (1995).
30 M. Kutner, C. Nachtsheim and J. Neter, Applied Linear Regression Models, McGraw-Hill/Irwin, New York, 4 ed., 701 pages, (2004).
31 E. J. Candes, and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine, 25(2), 21-30, (2008).
32 E. J. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Communications on Pure and Applied Mathematics, 59(8), 1207-1223, (2006).
33 E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction form highly incomplete frequency information,” IEEE Transactions on Information Theory, 52(2), 489-509, (2006).
34 G. F. Edelmann, and C.F. Gaumond, “Beamforming using compressive sensing,” J. Acoust. Soc. Am. 130, EL232-237, (2011).
35 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).
36 ITU-R Recommendation BS.562, “Subjective assessment of sound quality,” International Telecommunications Union, Geneva, Switzerland, 8 pages (1986).
37 E. Tiana-Roig, F. Jacobsen and E. F. Grande, “Beamforming with a Circular Microphone Array for Localization of Environmental Noise Sources,” J. Acoust. Soc. Am. 128(6), 3535-3542 (2010).
38 M. Grant and S. Boyd, cvx, v.1.21 Matlab software for disciplined convex programming, http://cvxr.com/cvx (last viewed June 14, 2013).