本論文於頻域上以獨立成分分析法做聲源分離，在現實環境中聲音以摺積混合抵達麥克風，透過短時間傅立葉轉換，可以有效簡化時域上獨立成分分析計算，但有兩個不確定因素影響訊號重組，分別為膨脹問題與排列問題。本論文提出一套演算法針對膨脹問題與排列問題做處理，並利用到達時間差定位聲源來向來判斷是否為雙聲源，避免單一聲源做分離時影響分離效果與增加運算時間，對於膨脹問題，使用高斯混合模型近似各個頻率柱上的分離訊號與混合訊號的分布，找出最大權重參數對應之平均數差來處理，減少高頻部分因膨脹問題所造成之雜訊；對於排列問題部分，利用同一聲源的各個頻帶在時間變化的呈現會有較大的相關性，將相關性較大的分離訊號歸類為同一聲源，本論文首先找出一組相關性較大之多個頻率柱做為基準，欲排列之分離訊號再與基準頻率柱比較，並找出最佳排列順序，簡化繁複的排列步驟與運算複雜度。與文獻[30]相比，本論文提出方法之運算時間減少17秒，訊號干擾比SIR值增加4dB，並於現場問卷調查評估音質與分離效果部分，分數亦增加1.4分。評估分離效果部分，以混合音檔與分離音檔各三組給受測者聆聽並寫下字句來判斷正確率，三組分離音檔之正確字數相較於混合音檔各提升41%、26%、45%之正確率，由結果可知，本論文提出之演算法與文獻[30]相比可以有效簡化排列問題之複雜度與減少雜音，達到提升音質與增進運算速度之目標。

In a real environment, sound sources are mixed through convolution mixture, and it is difficult to separate sources in the time domain. Therefore, we use independent component analysis (ICA) in the frequency domain. Using ICA in the frequency domain could reduce the computation, but there are two important ambiguities: scaling problem and permutation problem. These ambiguities affect reconstruction of separated source. In this thesis, a new approach is proposed for solving the scaling problem and permutation problem. Besides, Time difference of arrival (TDOA) is used to confirm that two sources exist simultaneously. To solve the scaling problem, the Gaussian mixture model is uesd to approximate the distribution of the separated signal and the mixed signal. The difference between the mean of separated signal and the mean of the mixed signal is compensated to solve the scaling problem. Considering the permutation problem, the present algorithm relies on the assumption that the correlations should be high between the temporal envelopes of neighboring frequencies from the same sound source. First, we find the five neighboring frequency bins which have a high correlation with each other as a standard. After that, separated source in other frequency bins could confirm permutation through the correlation with the standard. We compare with the result of the approach of [30]. Computation time is reduced by 17 seconds and SIR enhances by 4 dB. In the part of the questionnaire, we get a higher score than [30]. 66 subjects were recruited to conduct a listening comprehension test. The accuracy of listening comprehension of separated sources is 41%, 26%, 45% higher than unprocessed sounds. The results show that our approach reduces computation cost and enhances sound quality when compared to the existing method [30].

中文摘要 i
Abstract ii
目錄 I
圖目錄 III
表目錄 V
第一章 緒論 1
1.1研究動機 1
1.2研究方法 1
1.3研究目標 3
1.4章節介紹 4
第二章 獨立成份分析 5
2.1 背景與基本理論 6
2.2 假設 6
2.3 前置處理 7
2.4 獨立性函數 9
2.5 最佳化演算法 11
2.6 不確定性因素 13
第三章 聲源分離 16
3.1 聲源分離系統 16
3.2 頻域聲源分離流程 17
3.3 雙聲源判斷 18
第四章 膨脹問題、排列問題及環形摺積問題之解決方法 22
4.1 膨脹問題 22
4.2 排列問題 25
第五章 實驗方法及結果 31
5.1 實驗器材 31
5.2 評估方式 35
5.3 實驗結果 37
第六章 結論與未來展望 40
6.1 結論 40
6.2 未來展望 41
參考文獻 42
附錄 47
A.1 受測者名單 47
A.2 複數獨立成分分析收斂式推導 48
A.3 口試委員評論與建議 50
A.4 Google 語音辨識系統評估 51

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