An Investigation of Stationary Signal Blind Separation Using Adaptive Algorithms
Blind source separation attempts to recover unknown independent sources from a given set of observed mixtures. The two adaptive algorithms -EASI and RLS are introduced in this chapter, the separation simulation of a set of stationary signals is constructe
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An Investigation of Stationary Signal Blind Separation Using Adaptive Algorithms Xu Peng-fei and Jia Yin-jie
Abstract Blind source separation attempts to recover unknown independent sources from a given set of observed mixtures. The two adaptive algorithms -EASI and RLS are introduced in this chapter, the separation simulation of a set of stationary signals is constructed. Through the comparative analysis, the result shows that the RLS algorithm has better convergence speed and the steady state performance than the EASI algorithm for blind signal separation of stationary signal. In the RLS algorithm, we need select appropriate forgetting factor to meet the demand of convergence speed and steady state performance. Keywords Blind signal separation Forgetting factor
Stationary signal Adaptive algorithm
101.1 Introduction The seminal work on blind source separation (BSS) was first introduced by Jutten and Herault [1] in 1985, the problem is to extract the underlying source signals from a set of mixtures, where the mixing matrix is unknown. In other words, BSS seeks to recover original source signals from their mixtures without any prior X. Peng-fei (&) Faculty of Computer and Communication Engineering, Huaian College of Information Technology, 223003 Huai’an, Jiangsu, China e-mail: [email protected] J. Yin-jie Faculty of Computer Engineering, HuaiYin Institute of Technology, 223003 Huai’an, Jiangsu, China e-mail: [email protected]
W. Lu et al. (eds.), Proceedings of the 2012 International Conference on Information Technology and Software Engineering, Lecture Notes in Electrical Engineering 210, DOI: 10.1007/978-3-642-34528-9_101, Ó Springer-Verlag Berlin Heidelberg 2013
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information on the sources or the parameters of the mixtures. This situation is common in acoustics, radio, medical signal, image processing, hyper spectral imaging and other areas. The problem of basic linear BSS can be expressed algebraically as follows (assumes that the signal is continuous signal): The vector of the source signals is: SðtÞ ¼ ½s1 ðtÞ; s2 ðtÞ. . .sn ðtÞT
ð101:1Þ
where the source signals are assumed to be statistically independent. The vector of the observed or mixed signals is: XðtÞ ¼ ASðtÞ ¼ ½x1 ðtÞ; x2 ðtÞ. . .xm ðtÞT
ð101:2Þ
where A is a non-singular (m 9 n) mixing matrix. The problem can be formulated as the computation of an unmixing or separating matrix W, whose output y is given below. YðtÞ ¼ WXðtÞ
ð101:3Þ
YðtÞ is a scaled and permuted version of the original source signals. In short, the basic goal of BSS is to find the separating matrix W, without knowing the mixing matrix A. To evaluate the performance of the BSS algorithms, we use the cross-talking error as the performance index [2]: ! ! n n n n cij cij X X X X 1 E¼ ð101:4Þ 1 þ maxk jcik j i¼1 j¼1 j¼1 i¼1 maxk ckj where C ðC ¼ WAÞ is the matrix with elements of cij . The lowest bound of E is 0, in general, the smaller the value of E is, the better the separation effect is. Simply put, ECT is the d
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