臺灣博碩士論文加值系統

本論文提出一個以快速獨立成分分析法（Fast Independent Component Analysis,FastICA）為基礎的時域聲音訊號分離演算法．藉由模擬觀察到的FastICA特性，發展出一種新的演算法，讓原本無法分離含時間延遲差距（Time-delay difference）訊號的FastICA方法，可以在本論文所提出的演算法架構之下，分離出個別之聲音訊號。本論文所提的演算法，其待處理的兩個混合訊號主要由兩個聲源經由不同的混合系統(mixing system)混合而成．本篇論文將會詳細介紹FastICA原理和及新提出的演算法並提供實現的方法，同時以模擬及實驗驗證此演算法的可行性．

This thesis proposed a time-domain algorithm for audio-signal separation based on FastICA (Fast Independent Component Analysis [b]）. Existing FastICA can not separate signals with time-delay difference directly. In this thesis, two microphones are used to measure the sound sources with time-delay. By pre-processing of the measured signal, the algorithm proposed is able to separate the same signals. FastICA algorithm and the new algorithm will be introduced in detail. The computational procedures to implement the new algorithm are also explained. Simulations and experiments are conducted to prove the effectiveness of this algorithm.

摘　　 要 i
ABSTRACT ii
誌　　 謝 iii
Contents v
List of Tables viii
List of Figures ix
CHAPTER 1 Introduction 1
1.1 Motivation 1
1.2 Goal 2
1.3 Summary 2
CHAPTER 2 Basic ICA 3
2.1 Basic Concepts of ICA 4
2.1.1 Problem Description 4
2.1.2 Definition 5
2.1.3 Formulation 6
2.1.4 Conditions of ICA 7
2.1.5 Main Structure of ICA Methods 11
2.1.6 Applications 12
2.2 Pre-processing Methods 16
2.2.1 Reasons for Pre-processing 16
2.2.2 Useful Pre-processing Methods 17
2.2.3 Centering 18
2.2.4 Whitening 19
2.3 Basic ICA 22
2.3.1 Object Function 22
2.3.2 Optimal Method 27
2.3.3 FastICA 29
2.4 Problems of Basic ICA In Audio Signal Processing 39
2.4.1 Neglect of Time Structure 39
2.4.2 Permutation Problem 40
2.4.3 Indeterminate Performance 40
CHAPTER 3 A New Time-Domain Algorithm Based on FastICA 42
3.1 Basic Concepts of Target Signals 43
3.1.1 Properties of Array Signal 43
3.1.2 Properties of Audio Signal 46
3.2 Special Property of FastICA 47
3.3 Proposed Algorithm 53
3.3.1 Destination 53
3.3.2 Conditions 53
3.3.3 Computing Flow 54
3.3.4 New Steps In Pre-processing 55
3.3.5 New Step In Post-processing 59
3.3.6 Architecture of Proposed Algorithm 59
3.4 Comparison with Other BSS Methods 60
3.4.1 Array Signal Processing 60
3.4.2 Frequency-domain ICA 61
CHAPTER 4 Implementation, Simulation and Experiments of the New Algorithm 62
4.1 Implementation 63
4.1.1 Time-delay Difference Estimation Using Time-lagged Correlation Matrix 63
4.1.2 Signal Shift in Time Domain with Unit Samples 64
4.1.3 Better Initial Guess of De-mixing Matrix Estimation with Cross-correlation 65
4.1.4 Implementation of FastICA 68
4.1.5 Comparison between Outputs with Kurtosis 68
4.2 Simulation 68
4.2.2 Mixing Program 71
4.2.3 Results of Simulation 71
4.3 Experiment 75
CHAPTER 5 Conclusion and Future Works 79
5.1 Conclusion 79
5.2 Future Works 80
References 81
Appendix A: Matlab Code of FastICA 82
Appendix B: Mixing Program 83

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