臺灣博碩士論文加值系統

黃鍔博士在1998年提出了希爾伯特-黃轉換，其方法是將訊號經由經驗模態分解法，將訊號資料變化的內部時間尺度作為特徵而分解成多個本質模態函數分量，再對這些本質模態函數分量利用希爾伯特轉換可得到隱藏在訊號中有意義之瞬時資訊。
本文引入由經驗模態分解法改良而得之總體經驗模態分解法及其相關之後處理法以濾除訊號中的雜訊成份。針對經由總體經驗模態分解法的後處理法得到之本質模態函數，運用經驗模態分解法的特性，由獨立成份分析法中量測訊號的熵進而計算共同資訊之方式對訊號做第一次的雜訊濾除，接著利用可針對本質模態函數自適性修正的門檻值制定機制對訊號做第二次的雜訊濾除。而後再利用自適性中心權重均值濾波器濾除訊號剩餘的雜訊成份，運用三重雜訊濾除的機制，成功濾除訊號中的大部分雜訊。
本文利用4種測試訊號及2種語音訊號附加不同程度之雜訊干擾針對此方法進行模擬實驗。結果顯示本文所做之方法相較小波及其它文獻中現存的方法，在低訊號雜訊比的情況下可擁有不錯的雜訊濾除效果。本文所做之方法由於利用經驗模態分解法的特性，能盡量保留訊號本身的原始特性，對信號成份破壞較少且能同時兼顧濾除雜訊的性能，並擁有不錯的強健性與穩定性。

A signal analyzing method, Hilbert-Huang Transform (HHT), was proposed by Norden E. Huang et al. in 1998. By using Emprical Mode Decomposition (EMD), signal could be decomposed into a finite number of intrinsic mode functions (IMFs) based on the local characteristic time-scale of the signal. Devoting these IMFs with Hilbert Transform could obtain meaningful instantaneous information about the signal.
In this thesis, Ensemble Empirical Mode Decomposition (EEMD) and the post-processing of EEMD that were improved from the original EMD were involved to reduce the noise contained in the signal. By using the characteristic of EMD, the "Mutual Information" by calculating the entropy of signal from Independent Component Analysis was used to reduce the noisy component at first filtering, and a threshold-filtering selection method adapted to IMFs filtered the signal at second try. Adaptive Center-Weighted Mean Filter was then used to reduce the rest noisy component in the signal. Such attempting of triple-filtering could success removing most noisy component inside the IMFs that was generated by post-processing of Ensemble Empirical Mode Decomposition.
The proposed method was tested by 4 test signals and 2 voice signals added with various level of noise under simulation experiment. From the simulation result, compared with wavelets and other existing method, the proposed method had better performance of de-noising in low SNR circumstances. The proposed method could retain more information of the signal with less destruction in de-noising process, and take into account the noise reduction with a better robustness and stability.

目錄
誌謝 I
摘要 II
Abstract III
目錄 IV
圖目錄 VI
表目錄 XII
簡稱術語對照表 XIV
符號說明 XVI
第一章 緒論 1
1.1 研究背景與動機 1
1.2 文獻回顧 2
1.3 論文架構 4
第二章 希爾伯特-黃轉換理論 6
2.1 希爾伯特轉換 8
2.2 瞬時頻率 9
2.3 本質模態函數 12
2.4 經驗模態分解法 14
2.4.1 篩選過程 15
2.4.2 停止準則 21
2.5 希爾伯特頻譜與邊際頻譜 27
2.6 總體經驗模態分解法 30
2.7 總體經驗模態分解法的後處理 34
第三章 應用總體經驗模態分解法於雜訊濾除 37
3.1 重要性測試 38
3.2 基於門檻值的IMF雜訊濾除法 40
3.2.1 門檻值的制定 40
3.2.2 門檻值的處理方式 42
3.3 利用EMD、EEMD的特性濾除訊號雜訊 44
3.3.1 雜訊在IMF中的關係 44
3.3.2 分界層決定策略 45
3.4 結合EEMD濾波法及基於門檻值的IMF雜訊濾除法之雜訊濾除法 49
3.5 雜訊濾除理論 50
3.5.1 利用後處理EEMD得到IMF群 50
3.5.2 利用共同資訊決定分界層 51
3.5.3 自適應中心權重均值濾波器 54
3.5.4 基本週期標記 55
3.5.5 雜訊濾除流程 60
第四章 實驗結果與分析 63
4.1 評估效能指標 63
4.2 實驗說明 64
4.3 標準測試訊號之雜訊濾除與分析 66
4.4 語音訊號的雜訊濾除與分析 106
第五章 結論與未來展望 137
5.1 結論 137
5.2 未來展望 142
參考資料 143

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