傳統的立體音研究始於Blumlein，隨著時間的演進，人們追求虛擬實境系統和要求更好的聽覺環境，並使用多組揚聲器去建立一個完整多層面的環境，例如杜比數位或DTS環繞技術都是建立在多揚聲器的環境之上。
無論如何杜比數位和DTS，為了擁有一個好的聲場，他們對於多通的揚聲器的最佳位置在傾聽者和揚聲器之間都有要求特殊的角度範圍，但是如此的要求會產生一個問題：當環境限制造成這個最佳位置要求無法達成時，我們就無法擁有一個比較好的聲場。
本文的目的就是利用聲場重現的方式解決這個位置擺設的問題，首先我們利用時間差和強度差作為波場合成的原理，然後用虛擬揚聲器產生聲場並加以分析，接著我們獲得真實揚聲器的訊號，並且利用最小平方誤差產生與虛擬聲場近似的真實聲場，最後使用驗證工具，就是利用量測空間中訊號增益最大的方向來判斷虛擬揚聲器產生的位置，除了聲場重現之外，本文還提出揚聲器距離和角度的誤差修正方式，校正揚聲器擺放位置的誤差。

The traditional stereo research is first developed by Blumlein. As time goes by, people pursue a virtual reality stereo system and pay more attention to the auditory environment. The integrated and multi-level environment is thus established by means of placing several groups of loudspeakers. For example, the Dolby Digital or DTS surrounding technology are built upon this multi-speaker environment. However, both Dolby Digital and DTS require optimal placements of multi-channel loudspeakers which require specific angles between loudspeakers and listeners in order to achieve a better sound field. Problems arise when the optimal placement may not be available due to the inherent environment settings. The perceived sound field may degrade inherently.
This paper aims to solve the placement issue by means of sound field reappearance. The method is specified as follows. First, interaural time difference (ITD) and interaural intensity difference (IID) are employed using the principle of wave field synthesis. Then we analyze the sound field generated by virtual loudspeakers. Next step is to obtain sound signals of real loudspeakers that produce the sound field close to that of the virtual loudspeakers by means of minimizing least square errors. Lastly, verification tools are used to verify the location of the produced virtual loudspeakers by detection of signal magnitude.

[1] L. Rayleigh, "On our perception of sound direction," Philosophical Magazine, vol. 13, pp. 214–232, 1907.
[2] A. D. Blumlein, "Improvements in and relating to Sound-transmission, Sound-recording and Sound-reproducing Systems," U.K. Patent, 1931.
[3] H. Fletcher, "Auditory Perspective -Basic Requirements," American Institute of Electrical Engineers, Transactions of the, vol. 53, pp. 9-11, 1934.
[4] J. W. S. Rayleigh and R. B. Lindsay, The theory of sound: Dover, 1945.
[5] D. de Vries and M. M. Boone, "Wave field synthesis and analysis using array technology," in Applications of Signal Processing to Audio and Acoustics, 1999 IEEE Workshop on, 1999, pp. 15-18.
[6] S. Takane and T. Toshio, "A new theory for active suppression of reflected sound waves from the walls based on Kirchhoff-Helmholtz boundary integral equation," Acoust Sci Technol, vol. 25, 1, pp. 37-44(2004), 2004.
[7] J. Peifeng, et al., "Development of a Directional Loudspeaker System for Sound Reproduction," in Multimedia and Expo, 2007 IEEE International Conference on, 2007, pp. 591-594.
[8] M. Naoe, et al., "Performance Evaluation of 3D Sound Field Reproduction System Using a Few Loudspeakers and Wave Field Synthesis," in Universal Communication, 2008. ISUC '08. Second International Symposium on, 2008, pp. 36-41.
[9] K. C. K. Foo and M. O. J. Hawksford, "Three-dimensional sound positioning using a pair-wise loudspeaker paradigm," in Audio and Music Technology: The Challenge of Creative DSP (Ref. No. 1998/470), IEE Colloquium on, 1998, pp. 7/1-7/6.
[10] L. P. Huelsman, Basic circuit theory,Third Edition: Prentice Hall 1991.
[11] 白明憲, 工程聲學: 全華圖書股份有限公司, 2008.
[12] S.-C. Chang, "Study of Spatial Audio Modeling and its Digital Implementation," Master of Science, Electrical Engineering, National Cheng Kung University, 2002.
[13] J. Ahrens and S. Spors, "Reproduction of a plane-wave sound field using planar and linear arrays of loudspeakers," in Communications, Control and Signal Processing, 2008. ISCCSP 2008. 3rd International Symposium on, 2008, pp. 1486-1491.
[14] D. B. Ward and T. D. Abhayapala, "Performance bounds on sound field reproduction using a loudspeaker array," in Applications of Signal Processing to Audio and Acoustics, 2001 IEEE Workshop on the, 2001, pp. 187-190.
[15] O. Kirkeby, et al., "Local sound field reproduction using two closely spaced loudspeakers," The Journal of the Acoustical Society of America, vol. 104, pp. 1973-1981, 1998.
[16] E. Wenzel, et al., "Localization using nonindividualized head-related transfer functions," The Journal of the Acoustical Society of America, vol. 94, pp. 111-123, 1993.
[17] R. O. Duda, "Modeling head related transfer functions," in Signals, Systems and Computers, 1993. 1993 Conference Record of The Twenty-Seventh Asilomar Conference on, 1993, pp. 996-1000 vol.2.
[18] V. Larcher and J.-M. Jot, "Techniques d'interpolation de filtres audio-numériques: Application à la reproduction spatiale des sons sur écouteurs," presented at the Proc. of the 4th congress of the french Soc. of Acoust, 1997.
[19] A. J. Berkhout, et al., "Acoustic control by wave field synthesis," The Journal of the Acoustical Society of America, vol. 93, pp. 2764-2778, 1993.
[20] M. Zhang, et al., "HRTF measurement on KEMAR manikin," presented at the Proceedings of ACOUSTICS 2009, ACOUSTICS 2009.
[21] M. D. Burkhard, KEMAR Manikin Handbook.
[22] S. Boyd and L. Vandenbergh, Convex Optimization. UK: Cambridge University Press, 2004.