Frequency estimation error in Pisarenko harmonic decomposition method

1988 ◽  
Vol 76 (1) ◽  
pp. 82-84
Author(s):  
Y.H. Hu ◽  
B.C. Phan
Keyword(s):  
Decomposition Method ◽  
Frequency Estimation ◽  
Estimation Error ◽  
Harmonic Decomposition

Statistical Analysis of Frequency Estimation Methods of Vibration Signal

2009 ◽  
Vol 413-414 ◽  
pp. 195-200 ◽  
Author(s):  
Jian Ping Xuan ◽  
Tie Lin Shi ◽  
Guang Lan Liao ◽  
Shi Yuan Liu
Keyword(s):  
Frequency Estimation ◽  
Estimation Error ◽  
Vibration Signal ◽  
Error Variance ◽  
Estimation Methods ◽  
Signal Subspace ◽  
Subspace Decomposition ◽  
Estimate Frequency ◽  
Harmonic Decomposition ◽  
Cramer Rao Bound

In the fault diagnosis of a machine, frequencies of its vibration are important indicators to show conditions of the machine. There are two main categories of methods to estimate frequency. One is based on the fast Fourier transform, and the other is on the signal subspace decomposition. Using FFT directly to estimate frequency may introduce larger estimation error, several approaches are proposed to correct or decrease the error, which comprise phase difference, energy centrobaric, interpolation and search method. The signal subspace decomposition method (SSDM) consists of Pisarenko harmonic decomposition, multiple signal classification. In order to assess the performance of these methods, the Cramer-Rao bound is used to compare with the error variance of difference frequency estimation methods, and simulations are based on Monte Carlo experiments for various record sizes and signal-to-noise ratios (SNR’s). The results show that there is a turning point about 25 dB for FFT based methods, above which FFT based methods are less sensitive to the noise, and SSDM achieves higher precision estimation at higher SNR and for the short time series, but produces poor accuracy at lower SNR’s.

scholarly journals Symmetry Classes and Matrix Representations of the 2D Flexoelectric Law

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 674
Author(s):  
Houssam Abdoul-Anziz ◽  
Nicolas Auffray ◽  
Boris Desmorat
Keyword(s):  
Decomposition Method ◽  
Symmetry Class ◽  
Matrix Representations ◽  
Symmetry Classes ◽  
The Matrix ◽  
Harmonic Decomposition

We determine the different symmetry classes of bi-dimensional flexoelectric tensors. Using the harmonic decomposition method, we show that there are six symmetry classes. We also provide the matrix representations of the flexoelectric tensor and of the complete flexoelectric law, for each symmetry class.

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