A Sampling Theorem for Time-Frequency Localized Signals

2004 ◽  
Vol 3 (1) ◽  
pp. 45-81 ◽  
Author(s):  
Edwin Hammerich
Keyword(s):  
Sampling Theorem ◽  
Time Frequency

scholarly journals A Micro-Doppler Frequency Ambiguity Resolution Method Based on Complex-Valued U-Net

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ming Long ◽  
Jun Yang ◽  
Saiqiang Xia ◽  
Mingjiu Lv ◽  
Xu Wei ◽  
...  
Keyword(s):  
Ambiguity Resolution ◽  
Pulse Repetition Frequency ◽  
Doppler Frequency ◽  
Sampling Theorem ◽  
Repetition Frequency ◽  
Pulse Repetition ◽  
Resolution Method ◽  
Time Frequency ◽  
Short Time ◽  
Complex Valued

In order to resolute the micro-Doppler frequency ambiguity caused by radar pulse repetition frequency not high enough (i.e., pulse dimension does not satisfy the requirement of Nyquist sampling theorem), this paper presents a micro-Doppler frequency ambiguity resolution method based on complex-valued U-net. The echo sequence is interpolated by zeros in the pulse dimension to increase the equivalent pulse repetition frequency, so that the echo sequence after zero interpolation contains the real micro-Doppler frequency; at the same time, some new frequency components are generated. The variation law of the echo sequence frequency after zero interpolation is analyzed. Then, the echo sequence in time domain after zero interpolation is transformed to the time-frequency domain by short-time Fourier transform (STFT). Finally, the time-frequency results can be segmented by the model, which is trained by complex-valued U-net to eliminate the redundant frequencies generated by zero interpolation; thus, the reconstruction of real micro-Doppler frequency is realized. Theoretical analysis and simulation results show that the proposed method can solve the problem of micro-Doppler frequency ambiguity. Compared with fully convolution network (FCN) and fully convolution residual network (FCRN), the proposed method has better performance and robustness.

scholarly journals An MCM-Enhanced Compressive Sensing for Weak Fault Feature Extraction of Rolling Element Bearings under Variable Speeds

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Ya He ◽  
Kun Feng ◽  
Minghui Hu ◽  
Jinmiao Cui
Keyword(s):  
Compressive Sensing ◽  
Circulant Matrix ◽  
Sampling Theorem ◽  
Rolling Element Bearings ◽  
Measurement Matrix ◽  
Rolling Bearings ◽  
Time Frequency ◽  
Rolling Element ◽  
Shannon Sampling Theorem ◽  
Weak Fault

The compressive sensing (CS) theory provides a new slight to the big-data problem led by the Shannon sampling theorem in rolling element bearings condition monitoring, where the measurement matrix of CS tends to be designed by the random matrix (RM) to preserve the integrity of signal roughly. However, when the signal to be analyzed is infected with strong noise, not only does the signal become insufficiently sparse, but the randomness of the measurement matrix will bring down the sensing efficiency, resulting in the loss of fault feature. Thus, a sensing-enhanced CS scheme based on a series of modes after VMD decomposition is proposed under this paper. The core of this scheme is as follows: (1) the principal mode of VMD with better sparsity replaces the raw signal for compressive sensing; (2) all these modes contain the time-frequency characteristics of the raw signal; (3) a new measurement matrix called mode-circulant matrix (MCM) is defined by circulating the mode matrix, and when the amount of samples is shrunk, the sensing efficiency can be enhanced greatly. Besides, considering the fault signal of rolling bearings under variable speed, there is a need to use order tracking to overcome the nonstationarity of the signal before applying CS theory. The analysis results of simulation and experiment prove that the VMD- and MCM-based CS can successfully extract the weak fault feature of rolling bearings with operating speed changing.

A Fault Detection Approach Based on Sound Signal Analysis for Equipment Monitoring

2020 ◽  
pp. 129-139
Author(s):  
Weihai Sun ◽  
Lemei Han
Keyword(s):  
Fault Detection ◽  
Signal Analysis ◽  
Energy Analysis ◽  
Detection Method ◽  
Sound Signal ◽  
Practical Significance ◽  
Time Frequency ◽  
Detection Approach ◽  
Machine Fault ◽  
Learning Data

Machine fault detection has great practical significance. Compared with the detection method that requires external sensors, the detection of machine fault by sound signal does not need to destroy its structure. The current popular audio-based fault detection often needs a lot of learning data and complex learning process, and needs the support of known fault database. The fault detection method based on audio proposed in this paper only needs to ensure that the machine works normally in the first second. Through the correlation coefficient calculation, energy analysis, EMD and other methods to carry out time-frequency analysis of the subsequent collected sound signals, we can detect whether the machine has fault.

Time-Frequency Analysis of Partial Discharge Phenomena in SF6 gas using Wavelet Transform

1997 ◽  
Vol 117 (3) ◽  
pp. 338-345 ◽  
Author(s):  
Masatake Kawada ◽  
Masakazu Wada ◽  
Zen-Ichiro Kawasaki ◽  
Kenji Matsu-ura ◽  
Makoto Kawasaki
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Partial Discharge ◽  
Time Frequency Analysis ◽  
Time Frequency

Assessment of Time Frequency Color Index for Electrical Machines Diagnosis and Fault Severity

2016 ◽  
Vol 9 (1) ◽  
pp. 1
Author(s):  
Lahbib Sadiki ◽  
Soumia El Hani ◽  
Said Guedira ◽  
Ilias Ouachtouk
Keyword(s):  
Color Index ◽  
Electrical Machines ◽  
Time Frequency ◽  
Fault Severity

Time-Frequency Channel Parameterization with Application to Multi-Mode Receivers

2009 ◽  
Vol E92-B (12) ◽  
pp. 3717-3725
Author(s):  
Thomas HUNZIKER ◽  
Ziyang JU ◽  
Dirk DAHLHAUS
Keyword(s):  
Frequency Channel ◽  
Time Frequency ◽  
Multi Mode
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