本文提出了一種具有時域欠定多通道逆預濾波器（time-domain underdetermined multichannel inverse pre-filters,TUMIF）的強健性雙耳音訊呈現系統。我們將過去關於反算問題的研究重新構造成更通用的多通道模型匹配環境並定義了時域欠定多通道逆預濾波器的公式。反算問題被假定為線性欠定方程組(linear underdetermined systems)。根據虛擬聲源和控制點的數量選擇系統的通道數，通過在再現區域中選擇多個控制點來實現系統的強健性，使其能有較寬的甜區。在滿秩條件下，逆濾波器的精確解決方案始終存在。然而通過使用Tikhonov正則化，預濾波器的增益在設計階段受到限制。我們在六個元件的線性揚聲器陣列上實現所提出的雙耳音頻系統，以TUMIF技術應用於三維音頻再現問題。在本論文中提出了串音消除，雙通道的聲源拓寬和五通道虛擬環繞音效來驗證該方法。模擬和實驗結果顯示TUMIF方法可以實現強健性的雙耳音效呈現。

Robust binaural audio rendering system with time-domain underdetermined multichannel inverse pre-filters (TUMIF) is presented in this thesis. We reformulate the celebrated multiple-input/output inverse theorem (MINT) into a more general multi-channel model matching formalism, with emphasis on the binaural audio rendering application. A model-matching problem is cast in the time domain as a linear underdetermined system. The number of channels is selected in relation to the numbers of image sources and control points. Robustness with a widen sweet spot is achieved by selecting multiple control points in the reproduction zones. Under full rank conditions, exact solutions of inverse filters always exist. However, the gains of prefilters are limited in the design stage by using the Tikhonov regularization. The proposed binaural audio system has been implemented on a six-element linear loudspeaker array. Binaural rendering problems, including cross-talk cancellation, source widening, and 5.1 virtual surround, are examined to validate the proposed TUMIF approach. Results of objective and subjective tests have demonstrated the efficacy of the TUMIF approach for robust binaural audio rendering.

1. C. Kyriakakis, “Fundamental and Technological Limitations of Immersive Audio Systems,” Proceedings of the IEEE 86(5), 941-951(1998).
2. R. Nicol, AES Monograph:Binaural Technology, Audio Engineering Society, Now York, (2010).
3. B. Gardner and K. Martin, “HRTF Measurements of KEMAR Dummy-Head Microphone,” MIT Media Lab, 1994, http://sound.media.mit.edu/KEMAR.html
4. B. B. Bauer, ‘‘Stereophonic earphones and binaural loudspeakers,’’ J. Audio Eng. Soc. 9(2), 148-151 (1961).
5. M. R. Schroeder and B. S. Atal, ‘‘Computer simulation of sound transmission in rooms,’’ IEEE Conv. Record. 7, 150-155 (1963).
6. P. Damaske and V. Mellert, ‘‘A procedure for generating directionally accurate sound images in the upper- half space using two loudspeakers,’’ Acustica 22, 154-162 (1969).
7. D. H. Cooper, “Calculator program for head-related transfer functions,” J. Audio Eng. Soc. 30, 34-38 (1982).
8. W. G. Gardner, “Transaural 3D audio,” MIT Media Laboratory Tech. Report 342 (1995).
9. D. H. Cooper and J. L. Bauck, “Prospects for transaural recording,” J. Audio Eng. Soc. 37(1/2), 3-19 (1989).
10. J. L. Bauck and D. H. Cooper, “Generalized transaural stereo and applications,” J. Audio Eng. Soc. 44(9), 683-705 (1996).
11. D. B. Ward and G. W. Elko, “Optimal loudspeaker spacing for robust crosstalk cancellation,” Proc. ICASSP 98 IEEE, Seattle, WA,3541-3544, (1998).
12. D. B. Ward and G. W. Elko, “Effect of loudspeaker position on the robustness of acoustic crosstalk cancellation,” IEEE Signal Process. Lett. 65, 106-108 (1999).
13. M. R. Bai, C. W. Tung, and C. C. Lee, “Optimal design of loudspeaker arrays for robust cross-talk cancellation using the Taguchi method and the genetic algorithm,” J. Acoust. Soc. Am. 117(5), 2802-2813 (2005).
14. T. Sporer, “Wave field synthesis—Generation and reproduction of natural sound environments,” in Proceedings of the 7th International Conference on Digital Audio Effects, Naples, Italy (2004).
15. S. Spors, R. Rabenstein, and J. Ahrens, “ The theory of wave field synthesis revisited,” in Audio Engineering Society Convention Paper, Amsterdam, the Netherlands (2008).
16. D. de Vries, AES Monograph: Wave Field Synthesis (Audio Engineering Society, New York, 2009), 95 pp.
17. F. M. Fazi, “ Sound field reproduction,” Ph.D. thesis, University of Southampton, 2010.
18. 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).
19. 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, 2625-2633 (1991).
20. M. Kolundzija, C. Faller, and M. Vetterli, “ Sound field reconstruction: An improved approach for wave field synthesis,” in Proceedings of the 126th AES Convention, Audio Engineering Society, Munich, Germany (2009).
21. M. Kolundzija, C. Faller, and M. Vetterli, “ Designing practical filters for sound field reconstruction,” in Proceedings of the 127th AES Convention, Audio Engineering Society, New York (2009).
22. M. A. Gerzon, “ Ambisonic in multichannel broadcasting and video,” J. Audio Eng. Soc. 33, 859-871 (1985).
23. O. Kirkeby, P. A. Nelson, and H. Hamada, “Fast Deconvolution of Multichannel Systems Using Regularization,” IEEE Trans. Speech and Audio Processing. 6, 189-195, 1998.
24. O. Kirkeby and P. A. Nelson, “Digital Filter Design for Inversion Problems in Sound Reproduction,” J. Audio Eng. Soc. 47, 583-595, 1999.
25. J. F. Claerbout, Earth Soundings Analysis: Processing versus Inversion (PVI). 1992
26. M. Miyoshi and Y. Kaneda, “Inverse filtering of room acoustics,” IEEE Trans. Acoust., Speech, Signal Process. 36(2), 145-152, 1988.
27. S. G. Norcross, G. A. Soulodre, and M. C. Lavoie, “Subjective Investigations of Inverse Filtering,” J. Audio Eng. Soc. 52, 1003-1028, 2004.
28. C.W Groetsch, “The theory of Tikhonov regularization for Fredholm equation of the first kind,” Pitman Advanced Pub.Program, Boston (1984)
29. C Dinu, C Andrei, "PEAQ – an Objective Method to Assess the Perceptual Quality of Audio Compressed Files", Proceedings of International Symposium on System Theory SINTES 12, 2005.
30. ITU-R Recommendation BS.1534-1, “Method for the Subjective Assessment of Intermediate Sound Quality (MUSHRA)”, International Telecommulications Union, Geneva, Switzerland, 2001.