本論文提出了一種用於前饋式主動噪音控制的欠定多通道逆濾波技術(Underdetermined Multichannel Inverse Filtering approach, UMIF)。主動式噪音控制技術目前應用最廣泛的產品為耳機等通訊產品 ，而此類型產品因為控制區域都在使用者的耳道等一維系統，於是本論文應用時域之欠定多通道逆濾波技術(Time-domain Underdetermined Multichannel Inverse Filtering approach, UMIF)於一維系統，並提出一種基於原系統之共變異數矩陣去做為權重參數，做為稀疏編碼技術的最佳化控制器設計基礎。延伸一維系統至三維系統 ，由於三維前饋式主動噪音控制系統是一多輸入及多輸出系統，在設計時域控制器會有硬體設備之限制，故本論文延伸TUMIF，並應用頻域之欠定多通道逆濾波技術(Frequency-domain Underdetermined Multichannel Inverse Filtering approach, FUMIF)於三維系統。
單通道前饋控制是主動噪音控制（Active Noise Control, ANC）領域常用方法之一。傳統上，前饋式主動噪音控制的問題可以被視為一個過定逆濾波問題，其通常導致非零殘差，也就是一定會有無法消除的殘餘噪音。所以我們利用TUMIF，從向量空間和模型匹配的角度提出了一種多通道控制方法。利用額外的多控制聲源，可以將問題轉換為具有無限多組精確解和零殘差的欠定逆濾波問題。本論文提出，線性約束最小方差方法（Linearly Constrained Minimum Variance method, LCMV）應用於喇叭陣列之控制器設計，以最小化虛擬控制點的輸出能量來控制噪音聲場。使用最小平方法（Least Square approach, LS）和LCMV方法所得出的有限脈衝響應（Finite Impulse Response, FIR）控制器，往往因為控制器係數太長而不能應用。為了解決這個問題，我們使用稀疏編碼技術，最小絕對值收斂和選擇運算子（Least Absolute Shrinkage and Selection Operator, LASSO）算法來減少控制器長度。由數位信號處理器得到的模擬和實驗結果會比較以TUMIF為基礎的方法會與基準方法-濾波x最小均方算法（Filtered-x Least Mean Squared algorithm）在無響環境的一維管路系統。除此之外，我們將一維ANC系統延伸到三維ANC系統，透過延伸TUMIF，在頻域應用FUMIF來設計控制器，解決在時域設計控制器所遇到的問題，。
在三維主動式降噪控制系統，誤差麥克風在三維空間中是離散分布的，造成在非誤差麥克風所在的位置會有噪音放大的效果。 LCMV方法克服了區域中不連續的降噪性能，通過設計虛擬誤差麥克風在真實的誤差麥克風附近，使得LCMV可以達到更連續的降噪效果。模擬與實驗結果表示，LCMV方法可以明顯改善三維系統中區域不連續的降噪效果。

This thesis proposes an underdetermined multichannel inverse filtering (UMIF) approach in one-dimensional (1D) and three-dimensional (3D) feedforward active control system. In recent years, the earphone with active noise control (ANC) is widely used. The active area is the ear canal that could be seemed as a 1D system. Therefore, this thesis use a time-domain underdetermined multichannel inverse filtering (TUMIF) approach and the sparse coding technique to design filters in 1D ANC system.
Single-channel feedforward control is a commonly used approach for ANC. Traditionally, feedforward active control is formulated as an overdetermined inverse filtering problem which generally leads to non-zero residual noise. By using the TUMIF approach, a multichannel control approach is presented from the perspectives of vector subspaces and model-matching framework. With the additional secondary sources, the problem can be converted into an underdetermined system, which has infinite number of exact solutions with zero residual noise. This thesis proposes and examines the linear constrained minimum variance (LCMV) approach in a loudspeaker array system. The LCMV method is not only minimize the acoustic power on virtual error microphones (fictitious control points) but also achieving perfect performance on the real error microphones (measured control points). However, the TUMIF-based finite impulse response (FIR) filters obtained using the least-square (LS) method and the LCMV approach tend to be too long to implement in real-time. In order to solve this problem, a sparse coding technique, the least absolute shrinkage and selection operator (LASSO) algorithm, is exploited to reduce the controller orders. The TUMIF-based approaches will compare to the benchmarking method, the filtered-x least-mean-squares (FxLMS) algorithm, in a two-channel duct system in the anechoic room. Simulation and experiment results obtained using a digital signal processor are demonstrated in the 1D ANC system.
For 3D ANC system, this thesis extends the TUMIF approach into a frequency-domain underdetermined multichannel inverse filtering (FUMIF) approach due to memory storage limit. In 3D ANC system, the common difficulty is the discrete distribution of error microphones. Between the spaces of error microphones, the noise reduction performance may achieve an adverse effect. The LCMV approach broadens the controlled area. With arranging arbitrary number of fictitious control point, LCMV approach achieve a more global and general noise reduction performance. Simulation and experiment results have verified that the proposed approach, the LCMV approach, has achieved a global noise reduction performance in the anechoic room and the listening room.

摘 要 ii
ABSTRACT iv
致 謝 vi
CONTENTS viii
LIST OF FIGURES x
LIST OF TABLES xiii
INTRODUCTION 1
Chapter 1 UNDERDETERMINED MULTICHANNEL INVERSE FILTERS 5
1.1 Monochannel Inverse Filtering 5
1.2 Multichannel Inverse Filtering 10
1.3 Order Reduction of the Inverse Filters 15
1.3.1 The Orthogonal Matching Pursuit Algorithm 16
1.3.2 The Least Absolute Shrinkage and Selection Operator Algorithm 18
1.4 The Frequency-domain Underdetermined Multichannel Inverse Filtering Method 21
1.5 Pressure Matching Algorithm 24
1.5.1 Difference of the UMIF Method and the Energy-based Approach 26
Chapter 2 ONE-DIMENSIONAL ACTIVE NOISE CONTROL IN DUCT 27
2.1 System Architecture 27
2.2 Simulation and Experiment Results 35
2.3 Experiment Results 39
2.4 Discussions 44
Chapter 3 THREE-DIMENSIONAL ACTIVE NOISE CONTROL 44
3.1 System Architecture. 45
3.2 Simulation Results 55
3.3 Experiment Results 64
3.3.1 Anechoic Room 66
3.3.2 Listening Room 73
3.4 Discussions 81
Chapter 4 CONCLUSIONS AND FUTURE WORK 82
Appendix A 85
Optimal coefficient vector of the FUMIF-LCMV approach 85
REFERENCES 86

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