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Vol. 164, Issue 2, February 2014, pp. 233-241




Source Signals Separation and Reconstruction Following Principal Component Analysis

1, 2 WANG Cheng, 1 GUAN Wei, 1 GOU Jin, 2 YAN Gui-Rong, 3 LAI Xiong-Ming

1 College of Computer Science and Technology, Hua Qiao University, Xiamen 361021, China
2 State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, China
3 College of Mechanical and Automation, Hua Qiao University, Xiamen 361021, China
1 Tel: +0086-592-6162559, 008615980843865, fax: +0086-592-6162556

E-mail: wangcheng@hqu.edu.cn


Received: 20 November 2013 /Accepted: 28 January 2014 /Published: 28 February 2014

Digital Sensors and Sensor Sysstems


Abstract: For separation and reconstruction of source signals from observed signals problem, the physical significance of blind source separation modal and independent component analysis is not very clear, and its solution is not unique. Aiming at these disadvantages, a new linear and instantaneous mixing model and a novel source signals separation reconstruction solving method from observed signals based on principal component analysis (PCA) are put forward. Assumption of this new model is statistically unrelated rather than independent of source signals, which is different from the traditional blind source separation model. A one-to-one relationship between linear and instantaneous mixing matrix of new model and linear compound matrix of PCA, and a one-to-one relationship between unrelated source signals and principal components are demonstrated using the concept of linear separation matrix and unrelated of source signals. Based on this theoretical link, source signals separation and reconstruction problem is changed into PCA of observed signals then. The theoretical derivation and numerical simulation results show that, in despite of Gauss measurement noise, wave form and amplitude information of unrelated source signal can be separated and reconstructed by PCA when linear mixing matrix is column orthogonal and normalized; only wave form information of unrelated source signal can be separated and reconstructed by PCA when linear mixing matrix is column orthogonal but not normalized, unrelated source signal cannot be separated and reconstructed by PCA when mixing matrix is not column orthogonal or linear.


Keywords: Source signals separation and reconstruction, Principal component analysis, Linear and instantaneous mixing model, Statistically unrelated, Wave form and amplitude.


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