本計畫為了商業上的個人音效(personal audio)應用提出一種喇叭陣列技術來達到音場聚焦與控制(sound field focusing and control , SFC )。本論文提出了三種欠定多通道逆濾波器技術（underdetermined multichannel inverse pre-filters, UMIF）來實現聲場聚焦系統。本論文提出一種頻域欠定多通道逆濾波器技術(Frequency-domain Underdetermined Multichannel Inverse Filtering approach, FUMIF)。透過使用FUMIF的方法，從向量子空間與模型匹配框架的角度建立一種多通道控制方法。最小平方差無失真響應(Minimum Variance Distortionless Response)波束成形器和線性約束最小平方差(Linearly Constrained Minimum Variance) 波束成形器用於設計超指向性喇叭陣列系統。MVDR和LCMV不只最小化虛擬控制點的輸出能量來控制聲場聚焦的暗區聲場，同時精確的處理量測控制點的效果。
筆記型電腦在所提出的喇叭陣列演算法下得以實現個人音效。本論文比較了三種濾波器的波束圖形、聲學對比、語音音質和字錯率，並在建構實際的揚聲器系統時，優化揚聲器的數量與排列方式。從模擬結果和實驗結果表示，我們可以透過FUMIF實現音場聚焦與控制技術。

This thesis presents a loudspeaker array system to achieve sound field focusing and control (SFC) for personal audio applications. Three underdetermined multichannel inverse filtering (UMIF) formulations are proposed to implement the SFC system.
A frequency-domain underdetermined multichannel inverse filtering (FUMIF) approach is proposed in this thesis. By using the FUMIF approach, a multichannel control approach is formulated from the perspectives of vector subspaces and model-matching framework. The minimum variance distortionless response (MVDR) beamformer and the linear constrained minimum variance (LCMV) beamformer are employed to design the superdirective loudspeaker array system. The MVDR and LCMV method not only minimize the acoustic power on the fictitious control points but also achieve perfect reproduction performance on the measured control points.
A personal audio system is implemented for notebook computers on the basis of the proposed loudspeaker array algorithms. Three filtering approaches are compared in terms of beampatterns, acoustic contract, speech quality, and word error rate. The number or arrangement of loudspeakers is optimized when construct the practical loudspeaker array system. Results of simulations and experiments have demonstrated the efficacy of the FUMIF approaches for sound field focusing and control.

摘 要 ii
ABSTRACT iii
CONTENTS v
圖目錄 LIST OF FIGURES vi
表目錄 LIST OF TABLES vii
導論 INTRODUCTION 1
第一章 欠定多通道逆濾波器(Underdetermined Multichannel Inverse Filters) 3
1.1 單通道逆濾波器(Monochannel Inverse Filtering) 3
1.2 多通道逆濾波器(Multichannel Inverse Filtering) 5
1.3 聲場聚焦控制(Sound field focusing and control problem) 8
1.4 吉洪諾夫正規化應用於逆濾波器(Inverse filtering with Tikhonov regularization) 9
1.5 頻域欠定多通道逆濾波器(The Frequency-domain Underdetermined Multichannel Inverse Filtering Method) 9
第二章 揚聲器陣列波束成形術(Speaker Array Beamforming) 11
2.1 聲援陣列模型(Formulation of the Source Array Model) 11
2.2 基於能量的演算法(Energy-based Approaches) 12
2.3 最小平方差無失真響應(Minimum Variance Distortionless Response) 13
2.4 線性約束最小平方差(Linearly Constrained Minimum Variance) 14
第三章 模擬與實驗(Simulation and Experiment) 16
3.1 系統設置(System Settings) 17
3.2 模擬結果(Simulation Results) 19
3.2.1 筆電喇叭陣列模擬(Simulation of Notebook Speaker Array) 21
3.2.2 一般喇叭陣列模擬(Simulation of Normal Speaker Array) 26
3.3 實驗結果(Experiment Results) 32
3.3.1 筆電實驗結果(Experiment Results of Notebook) 35
3.3.2 一般喇叭陣列實驗結果(Experiment Results of Normal Speaker Array) 40
第四章 結論與展望(Conclusions and Future work) 49
參考文獻References 51

[1] T. Sporer, “Wave field synthesis - generation and reproduction of natural sound environments”, in Proc. of the 7th int. conference of digital audio effects, Naples, Italy, 2004.
[2] S. Spors, R. Rabenstein, J. Ahrens, “The theory of wave field synthesis revisited”, Proc. AES 124th Conv. Audio Eng. Soc., 2008-May.
[3] D. de Vries, Wave Field Synthesis, AES Monograph, AES, New York, 2009.
[4] F. M. Fazi, “Sound field reproduction”, Ph.D. dissertation, University of Southampton, 2010.
[5] M. Kolundzija, C. Faller, and M. Vetterli, “Sound field reconstruction: An improved approach for wave field synthesi”, in Proc. 126th Conv. Audio Eng. Soc., Munich, Germany, 2009.
[6] M. Kolundzija, C. Faller, and M. Vetterli, “ Designing practical filters for sound field reconstruction,” in Proc. 127th Conv. Audio Eng. Soc., New York, 2009.
[7] M. A. Gerzon, “Ambisonic in multichannel broadcasting and video”, J. Audio Eng. Soc., vol. 33, pp. 859-871, 1985.
[8] B. B. Bauer, ‘‘Stereophonic earphones and binaural loudspeakers’’, J. Audio Eng. Soc., vol. 9, pp. 148-151, 1961.
[9] W. F. Druyvesteyn and J. Garas, “Personal sound”, J. Audio Eng. Soc., vol. 45, pp. 685–701, 1997.
[10] C. Kyriakakis, “Fundamental and technological limitations of immersive audio systems”, IEEE Proceedings, vol. 86, pp. 941-951, 1998.
[11] R. Nicol, “Binaural Technology”, AES Monograph, Now York, 2010.
[12] B. Gardner, K. Martin, HRTF measurements of KEMAR dummy-head microphone, 1994.
[13] 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’’, JASA, Vol. 125, No. 4, 2009, p. 2091-2097.
[14] M.F. Simón-Gálvez, S.J. Elliott, J. Cheer, "Time domain optimization of filters used in a loudspeaker array for personal audio", IEEE/ACM Trans. Audio Speech Lang. Process., vol. 23, no. 11, pp. 1869-1878, Nov. 2015.
[15] P. Coleman, P. J. B. Jackson, M. Olik, M. Mller, M. Olsen, J. Abildgaard Pedersen, "Acoustic contrast planarity and robustness of sound zone methods using a circular loudspeaker array", J. Acoust. Soc. Amer., vol. 135, no. 4, pp. 1929-1940, 2014.
[16] M. F. Simón Gálvez, S. J. Elliott, J. Cheer, "Personal audio loudspeaker array as a complementary TV sound system for the hard of hearing", IEICE Trans. Fundamentals, vol. E97, no. 9, pp. 1824-1831, 2014.
[17] O. Kirkeby, P. A. Nelson, H. Hamada, “Fast deconvolution of multichannel systems using regularization”, IEEE Trans. Speech Audio Processing, vol. 6, pp. 189-195, Mar. 1998.
[18] O. Kirkeby and P. A. Nelson, “Digital Filter Design for Inversion Problems in Sound Reproduction”, J. Audio Eng. Soc., vol. 47, no. 7/8, pp. 583-595, Aug. 1999.
[19] J. F. Claerbout, Earth Soundings Analysis: Processing versus Inversion (PVI), 1992.
[20] M. Miyoshi and Y. Kaneda, “Inverse filtering of room acoustics”, IEEE Trans. Acoust. Speech Signal Processing, vol. 36, pp. 145-152, 1988.
[21] M.R. Bai, H.Y. Chen, and L. Yang, “A novel approach for feedforward control of noise in ducts using simplified multichannel inverse filters,” in Proceeding of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Briton, UK, pp. 8469-8473, May, 2019.
[22] M.R. Bai, H.Y. Chen, and L. Yang, “A novel approach for feedforward control of noise in ducts using simplified multichannel inverse filters,” in Proceeding of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Briton, UK, pp. 8469-8473, May, 2019.
[23] M.R. Bai, Y.W. Chen, Y.C. Hsu, T.S. Wu, “Robust binaural rendering with the time-domain underdetermined multichannel inverse prefilters”, The Journal of the Acoustical Society of America 146, 1302 (2019).
[24] A.N. Tikhonov, “Solution of nonlinear integral equations of the first kind,” Soviet Math. Dokl, vol. 5, pp. 835-838, 1964.
[25] M. Bertero, T. A. Poggio, and V. Torre, “Ill-posed problems in early vision,” in Proceedings of the IEEE, vol. 76, no. 8, pp. 869-889, Aug. 1988.
[26] 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(4), 1695–1700 (2002).
[27] M.R. Bai, J.G. Ih, and J. Benesty, Acoustic Array Systems: Theory, Implementation, and Application, Wiley, Singapore, 536 pages (2013).
[28] M. Brandstein and D. Ward, Microphone Arrays: Signal Processing Techniques and Applications, Springer, Berlin, 398 pages (2001).
[29] H.L. Van Trees, Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory, Wiley, Singapore, 1472 pages (2004).
[30] J. Benesty, J. Chen, and Y. Huang, Microphone Array Signal Processing, Springer, Berlin, 250 pages (2008).
[31] S.J. Elliott, J. Cheer, J.W. Choi and Y.H. Kim, “Robustness and Regularization of personal audio systems,” IEEE Trans. Audio, Speech, Lang. Process. 20(7), 2123-2133 (2012).
[32] J.Cheer, S.J. Elliott, Y. Kim, and J.W. Choi, “Practical implementation of personal audio in a mobile device,” J. Audio Eng. Soc. 61(5), 290-300 (2013).
[33] M.M. Boone, W.H. Cho, and J.G. Ih, “Design of a highly directional endfire loudspeaker array,” J. Audio Eng. Soc. 57(5), 309-325 (2009)
[34] M.F. S. Gálvez, S.J. Elliott, and J. Cheer, “A superdirective array of phase shift sources,” J. Acoust. Soc. Am. 132(2), 746-756 (2012).
[35] M.R. Bai, Y.H. Hsieh, Point focusing using loudspeaker arrays from the perspective of optimal beamforming. J. Acoust. Soc. Am. 2015, 137, 3393–3410.
[36] F. Olivieri, F.M. Fazi, P.A. Nelson, M. Shin, S. Fontana, and L. Yue, “Theoretical and experimental comparative analysis of beamforming methods for loudspeaker arrays under given performance constraints”, J. Sound Vib., vol. 373, pp. 302-324, Jul. 2016.
[37] O. Kirkeby and P.A. Nelson, “Reproduction of plane wave sound fields,” J. Acoust. Soc. Amer., vol. 94, pp. 2992–3000, Nov. 1993.
[38] J.H. Chang and F. Jacobsen, “Sound field control with a circular doublelayer array of loudspeakers,” J. Acoust. Soc. Amer., vol. 131, no. 6, pp. 4518–4525, Jun. 2012.
[39] S.J. Elliott, J. Cheer, J.W. Choi, and Y. Kim, “Robustness and Regularization of Personal Audio Systems”, IEEE Transactions on Audio, Speech, and Language Processing, vol. 20, no. 7, pp. 2123-2133, May, 2012.
[40] P.N. Samarasinghe, M.A. Poletti, S.M.A. Salehin, T.D. Abhayapala, and F.M. Fazi, “3D soundfield reproduction using higher order loudspeakers”, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 306-310, Oct., 2013.
[41] M. F. S. G´alvez, S.J. Elliott, and J. Cheer, “A superdirective array of phase shift sources,” J. Acoust. Soc. Amer., vol. 132, pp. 746–56, May 2013.
[42] M. Shin, F.M. Fazi, P.A. Nelson, and F.C. Hirono, “Controlled sound field with a dual layer loudspeaker array,” J. Sound Vib., vol. 333, no. 16, pp. 3794–3817, Aug. 2014.
[43] P. Coleman, P.J.B. Jackson, M. Olik, M. Møller, M. Olsen, and J.A. Pedersen, “Acoustic contrast, planarity and robustness of sound zone methods using a circular loudspeaker array,” J. Acoust. Soc. Amer., vol. 135, no. 4, pp. 1929–1940, May, 2014.
[44] M.F.S. Gálvez, S.J. Elliott, and J. Cheer, “Time Domain Optimization of Filters Used in a Loudspeaker Array for Personal Audio”, IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 23, no. 11, pp. 1869-1878, July, 2015.
[45] Y. Maeno, Y. Mitsufuji, and T.D. Abhayapala, “Mode Domain Spatial Active Noise Control Using Sparse Signal Representation”, Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (ICASSP), pp. 211-215, Sep., 2018.
[46] F. Ma, W. Zhang, and T.D. Abhayapala, “Active Control of Outgoing Broadband Noise Fields in Rooms”, IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 28, pp. 529-539, Dec., 2019.