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.

摘要 I
ABSTRACT II
誌謝 III
TABLE OF CONTENTS IV
LIST OF FIGURES V
LIST OF TABLES VIII
Chapter 1 INTRODUCTION 1
Chapter 2 THE TIME-DOMAIN UNDERDETERMINED MULTICHANNEL INVERSE FILTERING 4
2.1 The time-domain matrix formulation of convolution 4
2.2 Formulation of TUMIF 5
2.2.1 The TUMIF-based binaural audio reproduction 7
2.2.2 The matching model 9
2.2.3 Inverse filtering with Tikhonov regularization 10
Chapter 3 APPLICATION SCENARIOS 11
3.1 Cross-talk cancellation 12
3.2 Source widening 13
3.3 The 5.1 virtual surround audio 14
Chapter 4 CONCLUSIONS 16
REFERENCES 17

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