本論文討論了在聲場分析中兩個重要的議題：聲源定位及分離。演算法基於以平面波分解的基礎來實現定位與分離聲源訊號的目的。在定位的階段，以最小變異無失真響應法(Minimum Variance Distortionless Response, MVDR)與多重信號分類法(multiple signal classification, MUSIC)來測定平面波的方向。對於寬頻的訊號的應用上，同調(coherent)與非同調(incoherent)的技術被應用在定位處理上。在聲源分離階段，使用過定與未定設置的兩個方法被使用。過定的方法，使用Tikhonov正規化來實現聲源訊號的重建；而在未定的狀況下，轉向(steering)矩陣以定位出之方位再做增廣。因此，分離問題可以壓縮感知(compressive sensing, CS)的問題來表示且可以有效地以凸集合最佳化來求解。數值模擬與實驗以一24顆麥克風所組成的環形陣列來實現。客觀的語音品質感知試驗以及主觀的聆聽測試比較原始混雜訊號與分離出之訊號在語音品質上的提升。

This thesis examines two fundamental issues in sound field analysis: acoustic sources localization and separation. Algorithms are developed to locate and separate acoustic signals on the basis of plane-wave decomposition. In the localization stage, directions of plane waves are determined using either minimum variance distortionless response (MVDR) method or multiple signal classification (MUSIC) method. For broadband scenarios, coherent and incoherent techniques are utilized in the localization procedure. In the separation stage, two approaches with overdetermined and underdetermined settings can be employed. In the overdetermined approach, Tikhonov regularization (TIKR) is utilized to recover the source signals. In the underdetermined approach, the steering matrix is augmented by including the directions that have been determined in the localization stage. Hence, the separation problem is formulated into a compressive sensing (CS) problem which can be effectively solved by using convex (CVX) optimization. Simulation and experiments are conducted for a 24-element circular array. Sources Objective tests using perceptual evaluation of speech quality (PESQ) tests and subjective listening tests demonstrate that the proposed methods yield speech signals with well separated and improved quality, as compared to the mixed signals.

摘 要 i
ABSTRACT ii
誌 謝 iii
TABLE OF CONTENTS iv
LIST OF TABLES vi
LIST OF FIGURES vii
Chapter 1 INTRODUCTION 1
Chapter 2 ARRAY SIGNAL PROCESSING 3
2.1 Farfield array model 3
2.2 Choice of farfield array parameters 4
2.3 Spatial correlation matrix 5
Chapter 3 DOA ESTIMATION ALGORITHMS 7
3.1 MVDR algorithm 7
3.2 MUSIC algorithm 8
3.3 Wideband coherent processing 9
3.4 Neyman-Pearson detector 10
Chapter 4 ACOUSTIC SOURCE SEPARATION 12
4.1 Beamforming method 12
4.1.1 Beamformer design 12
4.1.2 Superdirective array (SDA) beamformer 13
4.2 Deconvolution-based method 14
4.2.1 TIKR method 14
4.2.2 CS method 15
4.3 Strategies of deconvolution-based source separation 16
Chapter 5 PERFORMANCE EVALUATION 23
5.1 Numerical simulation 23
5.2 Experimental investigation: anechoic room 25
5.3 Experimental investigation: conference room 26
Chapter 6 CONCLUSIONS 52
REFERENCES 53

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