The Relationship Between Non-Zero Singular Values and Frequencies and Its Application to Signal Decomposition

ZHAO Xue-zhi; YE Bang-yan

doi:10.3969/j.issn.0372-2112.2017.08.029

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The Relationship Between Non-Zero Singular Values and Frequencies and Its Application to Signal Decomposition

更新时间：2025-07-16

- The Relationship Between Non-Zero Singular Values and Frequencies and Its Application to Signal Decomposition
- Acta Electronica Sinica Vol. 45, Issue 8, Pages: 2008-2018(2017)
- 作者机构：
  
  华南理工大学机械与汽车工程学院,广东,广州,510640
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2017.08.029
  CLC： TN911.72O151.21
- Published：2017
- 稿件说明：
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ZHAO Xue-zhi, YE Bang-yan. The Relationship Between Non-Zero Singular Values and Frequencies and Its Application to Signal Decomposition[J]. Acta Electronica Sinica, 2017, 45(8): 2008-2018.
DOI：

ZHAO Xue-zhi, YE Bang-yan. The Relationship Between Non-Zero Singular Values and Frequencies and Its Application to Signal Decomposition[J]. Acta Electronica Sinica, 2017, 45(8): 2008-2018. DOI： 10.3969/j.issn.0372-2112.2017.08.029.

摘要

研究了Hankel矩阵方式下确定性信号的非零奇异值和信号所含频率数量之间的关系，发现只要矩阵维数大于信号中频率数量的二倍，此后不管维数再怎样增大，非零奇异值的数目始终维持为信号中频率数量的两倍不变.研究了非零奇异值和单个频率之间存在的对应关系，提出利用奇异值分解来分离单个的频率成分，发现了奇异值分解分离单个频率成分的条件，在这种条件下奇异值分解可以准确地分离出任何的单个频率成分.利用奇异值分解的这一特性对轴承振动信号进行特征提取，分离出了轴承各个振动频率清晰的时域波形，由此准确地揭示了轴承的实际振动状态.

Abstract

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 how much 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.

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