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International Journal of Plant Engineering and Management 2007年第2期12卷 116-120页

作者： WANG Sheng-chun HAN Jie LI Zhi-nong LI Jian-feng School of Mechanical Engineering Shandong University Jinan 250061 P. R. China Research Institute of Vibration Engineering Zhengzhou University Zhengzhou 450002 P. R. China

The time-varying autoregressive （TVAR） modeling of a non-stationary signal is studied. In the proposed method, time-varying parametric identification of a non-stationary signal can be translated into a linear time-invariant problem by introducing a set of basic functions. Then, the parameters are estimated by using a recursive least square algorithm with a forgetting factor and an adaptive time-frequency distribution is achieved. The simulation results show that the proposed approach is superior to the short-time Fourier transform and Wigner distribution. And finally, the proposed method is applied to the fault diagnosis of a bearing , and the experiment result shows that the proposed method is effective in feature extraction.

关键词： time-varying autoregressive modeling parameter estimation time-frequency distribution fault diagnosis

frequency-Shift Keying Signal Demodulation Based on time-frequency distribution

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Frequency-Shift Keying Signal Demodulation Based on Time-Fre...

Digital modulation classification using multi-layer perceptron and time-frequency features

ICEMI'2005第七届国际电子测量与仪器学术会议

作者： Yang Yizhen Wei Xueye Wang Liqing (School of electronic and information engineering Beijing Jiaotong University Beijing 100044)

This paper presents a method for the demodulation of frequency-Shift Keying (FSK) signal based on time-frequency distribution. This method can overcome the disadvantages of FSK signal demodulation in

关键词： time-frequency distribution FSK instantaneous frequency track circuit.

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Journal of Systems Engineering and Electronics 2007年第2期18卷 249-254页

作者： Yuan Ye Mei Wenbo Dept. of Industrial Design and Information Engineering Beijing Institute of Clothing Technology Beijing 100029 P. R. China Dept. of Electronic Engineering Beijing Inst. of Technology Beijing 100081 P. R. China

Considering that real communication signals corrupted by noise are generally nonstationary, and timefrequency distributions are especially suitable for the analysis of nonstationary signals, time-frequency distributions are introduced for the modulation classification of communication signals： The extracted time-frequency features have good classification information, and they are insensitive to signal to noise ratio （SNR） variation. According to good classification by the correct rate of a neural network classifier, a multilayer perceptron （MLP） classifier with better generalization, as well as, addition of time-frequency features set for classifying six different modulation types has been proposed. Computer simulations show that the MLP classifier outperforms the decision-theoretic classifier at low SNRs, and the classification experiments for real MPSK signals verify engineering significance of the MLP classifier.

关键词： Digital modulation classification time-frequency feature time-frequency distribution Multi-layer perceptron.

Quasi-LFM radar waveform recognition based on fractional Fourier transform and time-frequency analysis

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Journal of Systems Engineering and Electronics 2021年第5期32卷 1130-1142页

作者： XIE Cunxiang ZHANG Limin ZHONG Zhaogen Department of Information Fusion Naval Aviation UniversityYantai 264001China School of Aviation Basis Naval Aviation UniversityYantai 264001China

Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.

关键词： quasi-linear frequency modulation(quasi-LFM)radar waveform time-frequency distribution fractional Fourier transform(FrFT) assembled classifier

Joint time-frequency Analysis of Seismic Signals:A Critical Review

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Structural Durability & Health Monitoring 2018年第2期12卷 65-83页

作者： Roshan Kumar Wei Zhao Vikash Singh Miami College of Henan University Henan475000China Yokohama University 24000Japan

This paper presents an evaluation of time-frequency methods for the analysis of seismic signals.Background of the present work is to describe,how the frequency content of the signal is changing in time.The theoretical basis of short time Fourier transform,Gabor transform,wavelet transform,S-transform,Wigner distribution,Wigner-Ville distribution,Pseudo Wigner-Ville distribution,Smoothed Pseudo Wigner-Ville distribution,Choi-William distribution,Born-Jordan distribution and cone shape distribution are presented.The strengths and weaknesses of each technique are verified by applying them to a particular synthetic seismic signal and recorded real time earthquake data.

关键词： time-frequency distribution Seismic signals Cross-term interference Autoterm Gabor transform Wigner-Ville distribution

Analysis of frequency shifting in seismic signals using Gabor-Wigner transform

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Earthquake Engineering and Engineering Vibration 2015年第4期14卷 715-724页

作者： Roshan Kumar P.Sumathi Ashok Kumar Deaprtment of Earthquake Engineering IIT Roorkee Deaprtment of Electrical Engineering IIT Roorkee

A hybrid time-frequency method known as Gabor-Wigner transform (GWT) is introduced in this paper for examining the time-frequency patterns of earthquake damaged buildings. GWT is developed by combining the Gabor transform (GT) and Wigner-Ville distribution (WVD). GT and WVD have been used separately on synthetic and recorded earthquake data to identify frequency shifting due to earthquake damages, but GT is prone to windowing effect and WVD involves ambiguity function. Hence to obtain better clarity and to remove the cross terms (frequency interference), GT and WVD are judiciously combined and the resultant GWT used to identify frequency shifting. Synthetic seismic response of an instrumented building and real-time earthquake data recorded on the building were investigated using GWT. It is found that GWT offers good accuracy for even slow variations in frequency, good time-frequency resolution, and localized response. Presented results confirm the efficacy of GWT when compared with GT and WVD used separately. Simulation results were quantified by the Renyi entropy measures and GWT shown to be an adequate technique in identifying localized response for structural damage detection.

关键词： time-frequency distribution seismic signals cross-term interference Gabor transform Wigner- Ville distribution Gabor-Wigner transform

Feature Extraction and Recognition for Rolling Element Bearing Fault Utilizing Short-time Fourier Transform and Non-negative Matrix Factorization

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Chinese Journal of Mechanical Engineering 2015年第1期28卷 96-105页

作者： GAO Huizhong LIANG Lin CHEN Xiaoguang XU Guanghua School of Mechanical Engineering Xi'an Jiaotong University The 705 Research Institute China Shipbuilding Industry Corporation Key Laboratory for Modern Design and Rotor-Bearing System of Education Ministry Xi'an Jiaotong University State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University

Due to the non-stationary characteristics of vibration signals acquired from rolling element bearing fault, thc time-frequency analysis is often applied to describe the local information of these unstable signals smartly. However, it is difficult to classitythe high dimensional feature matrix directly because of too large dimensions for many classifiers. This paper combines the concepts of time-frequency distribution（TFD） with non-negative matrix factorization（NMF）, and proposes a novel TFD matrix factorization method to enhance representation and identification of bearing fault. Throughout this method, the TFD of a vibration signal is firstly accomplished to describe the localized faults with short-time Fourier transform（STFT）. Then, the supervised NMF mapping is adopted to extract the fault features from TFD. Meanwhile, the fault samples can be clustered and recognized automatically by using the clustering property of NMF. The proposed method takes advantages of the NMF in the parts-based representation and the adaptive clustering. The localized fault features of interest can be extracted as well. To evaluate the performance of the proposed method, the 9 kinds of the bearing fault on a test bench is performed. The proposed method can effectively identify the fault severity and different fault types. Moreover, in comparison with the artificial neural network（ANN）, NMF yields 99.3% mean accuracy which is much superior to ANN. This research presents a simple and practical resolution for the fault diagnosis problem of rolling element bearing in high dimensional feature space.

关键词： time-frequency distribution non-negative matrix factorization rolling element bearing feature extraction

Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis

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Applied Mathematics(A Journal of Chinese Universities) 2013年第4期28卷 505-530页

作者： QIAN Tao ZHANG Li-ming Department of Mathematics University of Macao Macao Department of Computer and Information Science University of Macao Macao

We present recent work of harmonic and signal analysis based on the complex Hardy space approach.

关键词： Mobius transform Blaschke form mono-component Hardy space adaptive Fourier decomposi-tion rational approximation rational orthogonal system time-frequency distribution digital signal processing,uncertainty principle higher dimensional signal analysis in several complex variables and the Clifford algebrasetting.

Detection of Doppler Blood Flow Velocity Based on Wavelet Transform time-frequency distributions

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Detection of Doppler Blood Flow Velocity Based on Wavelet Tr...

A Random Nonstationary Pulse Train Model

The Sixth International Conference on Measurement and Control of Granular Materials

作者： Zhang Yufeng Zhou Yi Chen Jianhua Department of Electronic Engineering,Information School,Yunnan University Kunming 650091,P.R.China.

The blood flow velocity is normally computed by extracting the time-varying maximum frequency and mean frequency envelop from time-frequency of Doppler blood flow signal. An alternative method,Wavelet transform,is introduced to improve the traditional short-time Fourier transform’s performance in estimating time-frequency distribution of Doppler blood flow signals and to get more accurate time-varying maximum frequency and mean frequency envelops.

关键词： Keywords: Blood flow velocity Doppler signal wavelet time-frequency distribution

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Journal of Beijing Institute of Technology 2021年第3期30卷 228-237页

作者： Leon Cohen Department of Physics Hunter College of the City University of New York695 Park Ave.New YorkNY 10065USA

A simple and mathematically tractable model of a nonstationary process is developed.The process is the sum of waves where the parameters of the waves are random.Explicit expres-sions for the mean and autocorrelation function at each position as a function of time are obtained.In the case of infinite time,the model evolves into a stationary process.The time-frequency distri-bution at each position is also obtained.An explicit example is given where the initial waves are Gaussian.The case where there is dispersion in the propagation is also discussed.

关键词： nonstationary process mean and autocorrelation function time-frequency distribution Gaussian waves