本論文採用麥克風陣列信號處來取代假人頭錄音來達到雙聲道立體聲的效果。首先我們採用了波束成型的各個方法，包含了延遲相加(Delay And Sum (DAS)), 最小能量無失真響應(Minimum Power Distortionless Response, MPDR) 和 最小變異數無失真響應(Minimum Variance Distortionless Response, MVDR)來去做音訊的定位分離，此外還採用多重訊號分類(Multiple Signal Classification, MUSIC)做音訊的定位，在上述定位的比較中，多重訊號分類能同時偵測多個訊源、表現比較穩健。在分離的部分，我們額外採用提可諾夫正規化(Tikhonov Regularization, TIKR)，其結果為有相較於其他方法，更好的音質與更少的干擾。在最後一部分，我們會添加HRTF渲染，來達成雙聲道立體聲的效果。
另一種方式達成雙聲道立體聲效果方法多通道輸入輸出反函數定理(Multiple-Input/Output Inverse Theorem, MINT)，經由這個模型我們可以藉由設計出來的反向濾波器，進而直接達到渲染HRTF的效果。我們採用數種方法來設計濾波器，包含提可諾夫正規化與最小絕對收斂與選擇算子(least absolute shrinkage and selection operator, LASSO)。最後，由聆聽測試來證明出所有的演算法皆有明顯 HRTF效果，其中TIKR-HRTF的所有指標表現得最好。
關鍵詞:雙聲道立體聲、聲學陣列、多通道反向濾波器設計

A binaural rendering system is implemented for entertainment devices, which can emulate spatial audio effects. Traditionally, the binaural audio recording, also known as dummy head recording, is an expensive approach. This thesis proposes an array signal processing-based system to produce binaural outputs in place of costly dummy head recording. Microphone array can be applied to source separation and localization. Beamforming approaches used in this thesis are Delay And Sum (DAS), Minimum Power Distortionless Response (MPDR), and Minimum Variance Distortionless Response (MVDR). Another localization approach named the Multiple Signal Classification (MUSIC) algorithm can detect multiple source signals robustly. Source separation is achieved by the Tikhonov Regularization (TIKR) algorithm. This approach yields good sound quality and separation performance with low computation complexity. The last stage consists of convolving each separated source signal with the respective Head-Related Transfer Function (HRTF) to produce the outputs. Yet, another way of binaural rendering is Multiple-Input/Output Inverse Theorem (MINT) approach, where inverse filters need to be designed. Time-domain underdetermined multiple inverse filter (TUMIF) and frequency domain underdetermined multiple inverse filter (FUMIF) can be employed to design the inverse filters. Least-square Tikhonov Regularization (TIKR) and least absolute shrinkage and selection operator (LASSO) in sparse coding can be utilized to obtain the inverse filters. Listening tests demonstrated that the presented binaural rendering techniques delivered the binaural effects with different degrees, among which the TIKR-HRTF performed the best.

Index Terms: Binaural, Acoustic array, Multiple inverse filter design

TABLE OF CONTENTS
ABSTRACT III
致謝 IV
LIST OF FIGURE VI
LIST OF TABLES VII
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 THEORY OF MICROPHONE ARRAY 4
2.1 FARFIELD ARRAY MODEL 4
2.1.1 The steering matrix design of the uniform circular array 5
2.2 SOURCE LOCATION AND SOUND SEPARATION ALGORITHM 7
2.2.1 Minimum power distortionless response (MPDR) 7
2.2.2 Minimum variance distortionless Regularization (MVDR) 9
2.2.3 Multiple signal classification (MUSIC) 9
2.2.4 Tikhonov regularization (TIKR) 11
2.3 COMPRESSED SENSING (CS) 12
2.3.1 Least absolute shrinkage and selection operator gradient descent (LASSO-GD) 12
2.4 TIME-FREQUENCY MASK (TFM) 17
2.5 HEAD RELATED TRANSFER FUNCTIONS (HRTF) 21
CHAPTER 3 MODEL MATCHING METHOD 22
3.1 FREQUENCY-DOMAIN UNDERDETERMINED MULTICHANNEL INVERSE FILTERING (FUMIF) 24
3.2 TIME-DOMAIN UNDERDETERMINED MULTICHANNEL INVERSE FILTERING (TUMIF) 26
3.3 TUMIF-LASSO 27
CHAPTER 4 RESULTS AND DISCUSSION 28
4.1 BINAURAL RENDERING BY SEPARATION AND LOCALIZATION 28
4.1.1 Localization 29
4.1.2 Separation 31
4.1.3 Discussion 33
4.2 MODEL MATCHING 35
4.3 LISTENING TEST 35
CHAPTER 5 CONCLUSION 69
REFERENCES 70

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