在這篇論文裡，會提出一個以經驗模態分解(EMD) 為基礎的新穎技術並對噪音強健性自動語音辨識系統做測試。EMD是一種概括傅立葉分析(Fourier analysis) 且用
於處理非線性和非平穩時間的函數，在我們的情況下就是處理語音特徵序列。對數能量維度的特徵向量(log energy feature)做前置處理時，我們會使用從EMD分析中所得到的本質模態函數(IMF)，正弦函數是本質模態函數的一種特殊情況。我們將提出來的方法以Aurora 2.0跟Aurora 3.0語料庫做測試。我們在Aurora 2.0語料庫中，不匹配的條件情況下(mismatched tasks)(乾淨語料訓練)得到44.9%相對於基本結果(baseline)的進步率。在Aurora 3.0語料庫中，高度不匹配的條件情況下(high-mismatch tasks)得到49.5%相對於基本結果的進步率。這些實驗結果顯示我們提出的方法會有很大的進步。

In this thesis, a novel technique based on the empirical mode decomposition (EMD) methodology
is proposed and examined for the noise-robustness of automatic speech recognition systems. The EMD analysis is a generalization of the Fourier analysis for processing nonlinear and non-stationary time functions, in our case, the speech feature sequences. We use the intrinsic mode functions (IMF), which include the sinusoidal functions as special cases,
obtained from the EMD analysis in the post-processing of the log energy feature. We evaluate
the proposed method on Aurora 2.0 and Aurora 3.0 databases. On Aurora 2.0, we obtain a 44.9% overall relative improvement over the baseline for the mismatched (clean-training) tasks. The results show an overall improvement of 49.5% over the baseline for Aurora 3.0 on the high-mismatch tasks. It shows that our proposed method leads to significant improvement.

List of Tables iii
List of Figures iv
誌謝vi
Chapter 1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2 Related Works 3
2.1 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Common Techniques of Noise Robustness . . . . . . . . . . . . . . . . . . . 6
2.2.1 Spectral Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 MVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Spline Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Cubic Spline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.2 Number of Unknowns . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.3 Number of Knowns . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.4 The Two Extra Constraints . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter 3 Methods 10
3.1 EMD and Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
i
3.3 Spline Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4 The Properties of EMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.5 Features Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Chapter 4 Experiments 20
4.1 Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.1 Aurora 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.2 Aurora 3.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4.1 Applying the EMD-Base Post-Processing to the Log-Energy Feature
Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4.2 The EMD-Base Post-Processing . . . . . . . . . . . . . . . . . . . . 25
4.4.3 Comparison the Results of Subtracting Different Numbers of IMFs . 27
4.4.4 Subtracting a Dynamic Number of IMFs . . . . . . . . . . . . . . . . 29
Chapter 5 Conclusion and Future Works 32
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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