基于过采样和时频分析的盲源分离算法
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摘要
随着通信技术的快速发展,在信号处理领域和神经网络学界兴起的一种技术,成为学者们的研究热点之一,这就是盲源分离(Blind Signal Process, BSP)技术。该技术起源于二十世纪九十年代,其过程就是在源信号和传输系统未知的情况下仅仅利用观测信号的信息来恢复和还原源信号。盲源分离技术应用广泛,涉及到众多领域。
经典的盲源分离问题通常假设信号源为平稳信号源,但是在实际应用中遇到的很多信号都是非平稳信号。尤其在通信、生物医学、雷达领域,大多的信号其统计特性都是具有周期性的循环平稳信号。因此,从循环平稳特性的角度来研究盲源分离问题是很有必要和现实意义的。
本学位论文从循环平稳理论的角度对盲源分离课题进行了研究,主要包括盲源分离的基础理论知识、主要算法、循环平稳理论、时频分析等。
本文所做的工作主要有：
(1)总结并研究了循环平稳理论在信号盲分离领域中的应用。具体介绍了盲源分离的概念、原理,分析了瞬时混合盲源分离和卷积混合盲源分离的数学模型,对盲源分离算法进行了简单的分类,主要分析了基于信息理论的盲源分离算法。
(2)系统分析了循环平稳理论,具体介绍了循环平稳的概念,一阶二阶循环统计量,过采样模型及其过采样后信号的性质等。
(3)在盲源分离方面,重点研究了基于信号循环平稳性的盲源分离问题。提出了新的盲源分离迭代算法。该算法利用了源信号过采样后的循环平稳特性,对混合信号白化并将循环频率引入到分离矩阵的更新方程中。通过联合处理,进一步提高了算法的收敛速度和收敛精度。将该算法和传统的Infomax算法相比较,本算法拥有较快的收敛速度,较好的分离效果。
(4)本文将循环平稳信号的特性引入到时频领域,更好的展现了信号的频率随时间变化的特点。具体介绍了二次时频分布理论,并详细研究了对循环平稳信号的时频分析,结合联合矩阵近似对角化算法,以时频点矩阵集合联合近似对角化算法为基础提出了基于时频分布的循环平稳信号盲源分离算法。
With the rapid development of communication technology, blind source separation (Blind Signal Process, BSP) technology has become one of the hot topics by the researchers in the field of signal processing and neural network circles. This technology originated in the 1990s, whose process is that just use the information of observation signals to restore the source signals in the case of unknown source signal and transmission system. Blind source separation technology has been used widely in many fields.
It is assumed that the signal is stationary in the problem of Classical blind source separation, but in practical many signals processed are non-stationary. Especially in communications, biomedical, radar field, most of the statistical properties of the signal is cyclostationary with a periodic. Therefore, the blind source separation is necessary and significant in the perspective of cyclostationarity.
This paper studies blind source separation based on cyclostationary theory, which greatly includes the basic theoretical knowledge of blind source separation, its main algorithm, cyclostationarity theory, time-frequency analysis, etc.
The major contribution of this paper includes:
1. It summarizes the cyclo stationary theory and analyzes its application in the field of blind signal separation. Specifically it introduces the concept and principle of blind source separation, analyses the mathematical models of the instantaneous mixed blind source separation and convolutional mixed blind source separation, simply classifies blind source separation algorithm, and especially analyzes blind source separation algorithm based on the information theory.
2. It analyzes the cyclostationary theory systematically, specifically introduces the concept of cyclostationarity, cyclic statistics, over-sampling model and the properties of signals.
3. On the aspect of blind source separation, it focuses on blind source separation problems based on Cyclostationarity, and proposed a new iterative algorithm for blind source separation. The algorithm utilizes the cyclostationarity of source signals after oversampling, simplifies the mixed signals and introduces Cyclic Frequency into the separable matrix update equation. Through the combined treatment, it further improves the algorithm's convergence speed and convergence accuracy. Compared with traditional Infomax algorithm, the results show that the algorithm has rapid convergence speed, and better separation effect.
4. It introduces the characteristics of cyclostationary signals to the time-frequency domain, better showing the characteristics that the signal frequency changes by time. Specifically it describes the theory of the second time frequency distribution and researches time-frequency analysis of cyclostationary signals in detail. It combines the joint matrix approximate diagonalization algorithm, and proposes a new blind source separation algorithm based on cyclostationary signal in Time-frequency distribution.
经典的盲源分离问题通常假设信号源为平稳信号源,但是在实际应用中遇到的很多信号都是非平稳信号。尤其在通信、生物医学、雷达领域,大多的信号其统计特性都是具有周期性的循环平稳信号。因此,从循环平稳特性的角度来研究盲源分离问题是很有必要和现实意义的。
本学位论文从循环平稳理论的角度对盲源分离课题进行了研究,主要包括盲源分离的基础理论知识、主要算法、循环平稳理论、时频分析等。
本文所做的工作主要有：
(1)总结并研究了循环平稳理论在信号盲分离领域中的应用。具体介绍了盲源分离的概念、原理,分析了瞬时混合盲源分离和卷积混合盲源分离的数学模型,对盲源分离算法进行了简单的分类,主要分析了基于信息理论的盲源分离算法。
(2)系统分析了循环平稳理论,具体介绍了循环平稳的概念,一阶二阶循环统计量,过采样模型及其过采样后信号的性质等。
(3)在盲源分离方面,重点研究了基于信号循环平稳性的盲源分离问题。提出了新的盲源分离迭代算法。该算法利用了源信号过采样后的循环平稳特性,对混合信号白化并将循环频率引入到分离矩阵的更新方程中。通过联合处理,进一步提高了算法的收敛速度和收敛精度。将该算法和传统的Infomax算法相比较,本算法拥有较快的收敛速度,较好的分离效果。
(4)本文将循环平稳信号的特性引入到时频领域,更好的展现了信号的频率随时间变化的特点。具体介绍了二次时频分布理论,并详细研究了对循环平稳信号的时频分析,结合联合矩阵近似对角化算法,以时频点矩阵集合联合近似对角化算法为基础提出了基于时频分布的循环平稳信号盲源分离算法。
With the rapid development of communication technology, blind source separation (Blind Signal Process, BSP) technology has become one of the hot topics by the researchers in the field of signal processing and neural network circles. This technology originated in the 1990s, whose process is that just use the information of observation signals to restore the source signals in the case of unknown source signal and transmission system. Blind source separation technology has been used widely in many fields.
It is assumed that the signal is stationary in the problem of Classical blind source separation, but in practical many signals processed are non-stationary. Especially in communications, biomedical, radar field, most of the statistical properties of the signal is cyclostationary with a periodic. Therefore, the blind source separation is necessary and significant in the perspective of cyclostationarity.
This paper studies blind source separation based on cyclostationary theory, which greatly includes the basic theoretical knowledge of blind source separation, its main algorithm, cyclostationarity theory, time-frequency analysis, etc.
The major contribution of this paper includes:
1. It summarizes the cyclo stationary theory and analyzes its application in the field of blind signal separation. Specifically it introduces the concept and principle of blind source separation, analyses the mathematical models of the instantaneous mixed blind source separation and convolutional mixed blind source separation, simply classifies blind source separation algorithm, and especially analyzes blind source separation algorithm based on the information theory.
2. It analyzes the cyclostationary theory systematically, specifically introduces the concept of cyclostationarity, cyclic statistics, over-sampling model and the properties of signals.
3. On the aspect of blind source separation, it focuses on blind source separation problems based on Cyclostationarity, and proposed a new iterative algorithm for blind source separation. The algorithm utilizes the cyclostationarity of source signals after oversampling, simplifies the mixed signals and introduces Cyclic Frequency into the separable matrix update equation. Through the combined treatment, it further improves the algorithm's convergence speed and convergence accuracy. Compared with traditional Infomax algorithm, the results show that the algorithm has rapid convergence speed, and better separation effect.
4. It introduces the characteristics of cyclostationary signals to the time-frequency domain, better showing the characteristics that the signal frequency changes by time. Specifically it describes the theory of the second time frequency distribution and researches time-frequency analysis of cyclostationary signals in detail. It combines the joint matrix approximate diagonalization algorithm, and proposes a new blind source separation algorithm based on cyclostationary signal in Time-frequency distribution.
引文
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[3]linsker R.An application of the principle of maximum information preservation to linear systems [J] Adv. Neural Inform. Processing Systems,1989.
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[14]A.Hyvarinen,Oja E.Independent component analysis by general nonlinear Hebbian like learing rules[J].Signal Processing,1998,64(3):301-313.
[15]A.Hyvarinen. A family of fixed point algorithms for independent component analysis[C].In Proceedings of ICASSP'97,1997:3917-3920.
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