摘 要

盲源信号分离是数字信号处理领域内一项重要的技术问题，其概念是在没有先验知识的情况下从若干接收到的混合信号中提取和恢复出无法直接观测到的各个源信号。本文借助盲源信号分离中的典型算法PCA（主成分分析）算法和ICA（独立成分分析）算法对多路时域线性混合叠加的盲源语音信号进行了处理并对计算机软件仿真后的实验结果进行了验证和分析，到现在盲源分离问题的研究进展已经有了很大的突破，如何高效率、短时间地对多路混叠的观察信号进行分离，得到恢复信号是本文的重点内容。本文将这两种算法展开了对比，从用户直观的评判和计算机仿真对分离结果计算了评价指标，从而比较了不同的算法得出了相应的结论。全文主要包括以下内容：

首先是绪论部分，简单介绍了盲源分离问题的研究背景和国内外研究现状。从该问题的起源开始，简单介绍了相关学者的研究内容和成果，并从一个崭新的角度提出了盲源分离问题遇到的困难和有待解决的问题。

第二是正文部分，介绍了盲源分离问题的系统概念和数学模型，使读者对这个问题有了一个清晰的认识，接着提出了拟采用的PCA和ICA算法原理，从理论上推导和证明了盲源信号分离的前提，PCA处理一般作为预处理技术对混合信号进行零均值化和白化处理，这相当于一个解相关的过程，降低了信号之间的二阶相关性。在ICA算法中按照信息熵极大化的寻优准则对信号迭代分离，依次分离出各路源信号，最后分别保存不同算法处理后的语音信号，按照既定的评价指标，对计算分离信号和源信号之间的相似系数矩阵，判断出信号的对应关系和分离效果。比较不同的结果并作出结论：PCA、直接ICA和PCA-ICA都能实现盲源信号的分离，但PCA-ICA有着更好的分离效果。

第三部分是总结部分，对全文的研究过程进行综述，根据实验结果和预期目标对比，评判盲源分离算法的优劣势，提出了不同算法的适用场合。

本文主要研究分析了盲源分离中的PCA算法、直接ICA算法和PCA-ICA算法。研究结果表明：三种算法都能将盲源信号有效分离，采用PCA-ICA 算法迭代次数减少，有更快的收敛速度。

关键词：盲源分离；PCA；ICA；信息熵；相似系数

Abstract

Blind source signal separation is an important technical problem in the field of digital signal processing. The concept is to extract and recover individual source signals that cannot be directly observed from a number of received mixed signals without prior knowledge. In this thesis, the typical algorithm principal component analysis (PCA) algorithm and independent component analysis (ICA) algorithm in blind source separation are used to process the blind source speech signal with multi-channel time-domain linear hybrid superposition and the experiment using computer are verified and analyzed. The research on blind source separation has made a great breakthrough. How to efficiently and quickly separate the multi-channel aliasing observation signals and obtain the recovery signal is the key point of the thesis. In this thesis, these two algorithms are compared. The evaluation indicators are calculated from the user's intuitive evaluation and computer simulation. The comparison of different algorithms leads to the corresponding conclusions. The full text mainly includes the following contents:

The first is the introduction part, which introduces the research background of blind source separation and the research status until now. Starting from the origin of the problem, the research contents and achievements of relevant scholars are briefly introduced, and the difficulties encountered in the separation of blind sources and the problems to be solved are proposed in a new perspective.

The second part is the body part. We introduce the system concept and mathematical model of blind source separation problem, which gives readers a clear understanding of this problem. Then we propose the principle of PCA and ICA algorithm to be adopted, which are deduced and proved theoretically. The premise of blind source signal separation, PCA is generally used as a pretreatment to zero-average and whiten the mixed signal, which is equivalent to a decorrelation process, which reduces the second-order correlation between signals. The ICA algorithm is used to separate the signals according to the optimization criterion with the smallest mutual information, and the source signals are separated in turn. Finally, the speech signals processed by different algorithms are saved separately, and the calculation is separated according to the established evaluation index. A matrix of similarity coefficients between the signal and the source signal determines the correspondence between the signals and the separation effect. Compare the different results and draw conclusions, and finally come to the conclusion: Both PCA, Direct ICA and PCA-ICA can accomplish separation of blind source signals, while PCA- ICA has better separation effect.

The third part is the summary part, which reviews the research process of the full text and the advantages and disadvantages of the blind source separation algorithm are evaluated according to the comparison between the experimental results and the expected goals. At the same time the applicable occasions of different algorithms are proposed.

This thesis mainly studies the PCA algorithm, the Direct ICA algorithm and the PCA-ICA algorithm in blind source separation. The results show that the PCA-ICA algorithm is used to make the blind source signal more effectively separated.

Key Words：Blind source separation；PCA；ICA；Information entropy; Similarity coefficient

目 录

摘 要 I

Abstract II

第1章 绪论 1

1.1 课题研究背景及意义 1

1.2 国内外研究现状和发展趋势 1

1.3 本文结构及主要内容 3

第2章 盲源分离理论 4

2.1 盲源分离概念及模型 4

2.2 盲源分离性研究 5

2.2.1 盲源分离前提 5

2.2.2 分离信号的不确定性 6

2.3 分离效果检验 7

第3章 盲源分离算法 8

3.1 PCA理论技术 8

3.2 ICA理论技术 9

3.2.1 ICA的数学模型 10

3.2.2 ICA寻优准则 10

第4章 算法实现与验证 13

4.1 算法实现过程 13

4.2 仿真结果 14

4.2.1 嘈杂环境模拟 14

4.2.2 舞会环境模拟 19

4.2.3 算法用时分析 24

4.3 仿真结果分析 25

第5章 总结与展望 27

5.1 本文内容总结 27

5.2 展望 27

参考文献 29

致 谢 31

第1章 绪论

盲源语音信号分离问题在现实生活中起着重要的作用，随着数字信号处理技术的发展，盲源分离的问题的研究取得了重大的突破[1]，也得到了越来越多研究人员的密切关注，如何高效、快速地分离出多路混叠的语音信号是本文重点研究和解决的问题。

1.1 课题研究背景及意义