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《Acta Electronica Sinica》 2017-08
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The Relationship Between Non-Zero Singular Values and Frequencies and Its Application to Signal Decomposition

ZHAO Xue-zhi;YE Bang-yan;School of Mechanical and Automotive Engineering,South China University of Technology;  
The relationship between the number of non-zero singular values of the deterministic signal under the Hankel matrix and the number of frequencies in this signal is studied. It is found that if the dimension of matrix is larger than two times the number of frequencies,then no matter howmuch the dimension of matrix is increased,the number of non-zero singular values is always twice as much as the number of frequencies. The corresponding relationship between the non-zero singular values and single frequency component is studied,and singular value decomposition( SVD) is proposed to separate the single frequency component. The condition under which SVD separates the single frequency component is found,and SVD can accurately separate any single frequency component under this condition. This property of SVD is applied to the feature extraction of the bearing vibration signal,the time domain waveform of each vibration frequency is accurately extracted and the bearing vibration status is accurately revealed.
【Key Words】: singular value decomposition non-zero singular value signal decomposition matrix dimension
【Fund】: 国家自然科学基金(No.51375178);; 广东省自然科学基金(No.S2012010008789)
【CateGory Index】: TN911.7
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