在傳統聲場合成技術中多以無反射空間為前提條件，會造成在使用時，因環境反射的干擾而造成合成聲場品質下降、誤差提升的問題。為了解決傳統聲場合成技術中的此種問題，抗反射之聲場重建技術除了可用來解決傳統雙聲道音訊系統所固有的夾窄聆聽甜區特性，並且可用以達到減少反射音形成的雙重目的。而在這項技術中我們結合了兩種既有的聲場控制技術，一者為以等效聲源法為基礎之聲場重建技術，另一者則為聲學對比控制。將這類問題以最佳化之角度出發，使用凸面最佳化來設計喇叭陣列之濾波器，並且在設計時權衡了聲場所固有的兩個互相牴觸之特性，聲場重建效果以及聲學對比。
我們將控制點設於聲場暗區中的控制邊界上，用以限制聲音向外傳遞而造成反射音的形成。本研究中提供了兩種的不同邊界控制方式，聲壓控制法及聲壓與聲速控制法，分別控制在控制邊界上之聲音壓力及同時控制聲音壓力及速度。最佳化參數的選取方式也在本文中有詳細的描述。另外在設計目標函數時，也可以藉由選定不同的關聯範數而達到不同的所需要的聲場合成結果。除了上述的控制技術外，我們也提出了利用升階混音及虛擬麥克風內插技術提升喇叭陣列內部合成之聲場效果的另一項技術。我們利用兩種指標，分別是聲場匹配誤差及聲學對比度來對所使用的矩形麥克風陣列音訊系統進行效能的評估。此外，客觀的音訊品質感受度評估技術同時也被使用來對聲場進行聲音品值的估量。
研究中發現，升階混音及虛擬麥克風內插技術能夠有效的提升喇叭陣列內部之聲場重建的表現。而在兩種控制方式的比較中，相對於聲壓與聲速控制法，聲壓控制法可以用以提供較高的聲學對比，但也因而犧牲了聲場重建的效果。我們也發現了聲場的兩個重要特性，聲場合成效果及聲學對比，對於一個特定的音訊系統而言，兩者之間呈現了互相牴觸的關係。而在主觀聆聽測試中，我們發現聲壓與聲速控制法能夠比聲壓控制法提供較好的聽覺感受。此外，如果致力於提高聲學對比時，可以將較多的控制點佈置於聲學暗場之控制邊界上，或者是使用曼哈頓範數作為關連範數。

A reflection-resistive sound reconstruction system is proposed for audio reproduction with extended sweet spot and reduced boundary reflections. The method adopts a combined approach of equivalent source method (ESM)-based sound field synthesis (SFs) and acoustic contrast control (ACC). The conventional SFS that is based on the free-field assumptions suffer from synthesis error due to boundary reflections. To overcome the problem, the proposed system utilizes convex optimization in designing array filters to tradeoff reproduction performance and acoustic contrast. Upmixing and interpolation strategies are also proposed for the improvement of internal reproduction performance. Cost functions and constraints are defined, in conjunction with 1, 2 and infinity norms. Control points are deployed in the dark zone to minimize the sound field in the exterior region. Two approaches are employed to constrain the pressure and both pressure and velocity in the dark zone. Guidelines for choosing optimization parameter are summarized. Two performance measures, pressure matching error (PME) and acoustic contrast (AC), are adopted in simulations and experiments using a rectangular loudspeaker array. Perceptual Evaluation of Audio Quality (PEAQ) is also used in the objective of reproduction quality. The results show that the interpolation is available method for performance enhancement. The pressure-constrained (PC) method yields better acoustic contrast, but poorer reproduction performance than the pressure-velocity constrained (PVC) method. Two indices, acoustic contrast and reproduction performance, of a specific system are in tradeoff. Furthermore, the PVC method is the suitable method used for constrained method due to its better performance in auditory perception. High acoustic contrast can be achieved by deploying a large number of control points in the dark zone or choosing 1-norm as the conjunction in the cost function.

摘 要 I
ABSTRACT III
誌 謝 V
Table of Contents VI
List of Tables VIII
List of Figures IX
Chapter 1 INTROUCTION 1
Chapter 2 THEORETICAL BACKGROUND 5
2.1 Representation of Sound Fields 6
2.1.1 Equivalent Source Model 6
2.1.2 Basis Function Model 7
2.2 Sound Field Synthesis as an Optimization Problem 8
2.2.1 Performance metrics 8
2.2.2 Formulation of the optimization problem 9
2.2.3 Optimization approaches 10
Chapter 3 UPMIXING AND INTERPOLATION STRATEGIES 12
3.1 Optimization of Retreat Distance 13
3.2 Interpolation Techniques 14
3.2.1 The ESM-based Interpolation 15
3.2.2 The BFM-based Interpolation 16
3.2.3 The Hyper-ESM-based Interpolation 17
Chapter 4 SOUND FIELD SYNTHESIS WITH MINIMAL EXTERNAL RADIATION………………………………………………………………………23
4.1 Combined SFS-ACC Synthesis 24
4.2 Performance Metrics 24
4.3 Choice of Optimization Parameters and Norms 27
Chapter 5 SIMULATIONS AND EXPERIMENTS 31
5.1 Loudspeaker Arrangements 32
5.1.1 Uniform Rectangular Array 32
5.1.2 Automotive Spatial Sound 34
5.2 Numerical Simulations 34
5.3 Experimental Investigations 37
5.3.1 Objective Tests 39
5.3.2. Subjective Listening Tests 40
Chapter 6 CONCLUSIONS AND FUTURE WORK 78
REFERENCES 81

1. 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).
2. 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 NY, USA (2009).
3. J. Rose, P. Nelson, B. Rafaely, and T. Takeuchi, “Sweet spot size of virtual acoustic imaging systems at asymmetric listener locations,” J. Acoust. Soc. Am. 112, 1992–2002 (2002).
4. J.-H. Chang, C.-H. Lee, J.-Y. Park, and Y.-H. Kim, “A realization of sound focused personal audio system using acoustic contrast control,” J. Acoust. Soc. Am. 125, 2091-2097 (2009).
5. S. J. Elliott, J. Cheer and J.-W. Choi, “Robustness and regularization of personal audio systems,” IEEE Trans. Audio, Speech, Lang. Process. 20, 2123-2133 (2012).
6. M. Shin, S. Q. Lee, F. M. Fazi, P. A. Nelson, D. Kim, S. Wang, K. H. Park, and J. Seo, “Maximization of acoustic energy difference between two spaces,” J. Acoust. Soc. Am. 128, 121-131 (2010).
7. J.-H. Chang, C.-H. Lee, J.-Y. Park, and Y.-H. Kim, “A realization of sound focused personal audio system using acoustic contrast control” J. Acoust. Soc. Am. 125, 2091-2097 (2009).
8. J.-H. Chang and F. Jacobsen, “Sound field control with a circular double-layer array of loudspeakers,” J. Acoust. Soc. Am. 131, 4518-4525 (2012).
9. D. de Vries, Wave field synthesis. AES Monograph. 95 pages (New York, 2009).
10. S. Spors, R. Rabenstein, and J. Ahrens, “The theory of wave field synthesis revisited,” Proceedings of the 124th AES Convention, Audio Engineering Society Convention, Amsterdam, The Netherlands (2008).
11. A. J. Berkhout, D. de Vries, and P. Vogel, “Acoustic control by wave field synthesis,” J. Acoust. Soc. Am. 93, 2764-2778 (1993).
12. M. M. Boone, E. N. G. Verheijen, and P. F. van Tol, “Spatial sound field reproduction by wave field synthesis,” J. Audio Eng. Soc., 43, 1003-1012 (1995).
13. 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).
14. 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).
15. M. R. Bai and J. H. Lin, “Source identification system based on the time-domain nearfield equivalence source imaging: Fundamental theory and implementation,” J. Sound Vib., 307, 202 – 225 (2007).
16. A. Sarkissian, “Extension of measurement surface in near-field acoustic holography,” J. Acoust. Soc. Am. 115, 1593–1596 (2004).
17. A. Sarkissian, “Method of superposition applied to patch near-field acoustic holography,” J. Acoust. Soc. Am. 118, 671–678 (2005).
18. M. Grant and S. Boyd, cvx, Version 1.21 MATLAB software for disciplined convex programming available at http://cvxr.com/cvx (last viewed February 14, 2012).
19. E. G. Williams, Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography (Academic Press, San Diego, 1999), pp. 26–28.
20. M. R. Bai and C. C. Chen, “On optimal retreat distance for the equivalent source method-based nearfield acoustical holography,” J. Acoust. Soc. Am. 129, 1407–1416 (2011)
21. R. P. Brent, Algorithms for Minimization without Derivatives (Prentice-Hall, Englewood Cliffs, NJ, 1973), pp. 48–75.
22. J.-H. Chang and F. Jacobsen, “Experimental validation of sound field control with a circular double-layer array of loudspeakers,” J. Acoust. Soc. Am. 133, 2046-2054 (2013).
23. http://www.bmw.com.tw/ (last viewed: July 2, 2013)
24. ITU-R Recommendation BS.1387-1, “Method for objective measurements of perceived audio quality,” International Telecommunications Union, Geneva, Switzerland, 100 pages (1998).
25. ITU-R Recommendation BS.562, “Subjective assessment of sound quality,” International Telecommunications Union, Geneva, Switzerland, 8 pages (1986).
26. ITU-R Recommendation BS.1534-1, “Method for the subjective assessment of intermediate quality level of coding systems,” International Telecommunications Union, Geneva, Switzerland, 18 pages (2001).