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Journal articles on the topic 'Wigner-Ville distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Bai, Rui-Feng, Bing-Zhao Li, and Qi-Yuan Cheng. "Wigner-Ville Distribution Associated with the Linear Canonical Transform." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/740161.

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The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates the Wigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of Wigner-Ville distribution associated with the linear canonical transform is given. Then, the main properties of the newly defined Wigner-Ville transform are investigated in detail. Finally, the applications of the ne

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2

Wang, Yanghua, Ying Rao, and Duo Xu. "Multichannel maximum-entropy method for the Wigner-Ville distribution." GEOPHYSICS 85, no. 1 (2020): V25—V31. http://dx.doi.org/10.1190/geo2019-0347.1.

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The Wigner-Ville distribution is a powerful technique for the time-frequency spectral analysis of nonstationary seismic data. However, the Wigner-Ville distribution suffers from cross-term interference between different wave components in seismic data. To mitigate cross-term interference, we have developed a multichannel maximum-entropy method (MEM) to modify the Wigner-Ville kernel. The method is related to the conventional maximum-entropy spectral analysis (MESA) algorithm because both algorithms use Burg’s reflection coefficients for the calculation of the prediction-error filter (PEF). The

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3

Guanghua, Chen, Ma Shiwei, Liu Ming, Zhu Jingming, and Zeng Weimin. "Wigner-Ville distribution and cross Wigner-Ville distribution of noisy signals." Journal of Systems Engineering and Electronics 19, no. 5 (2008): 1053–57. http://dx.doi.org/10.1016/s1004-4132(08)60196-6.

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4

Bahri, Mawardi. "On Two-Dimensional Quaternion Wigner-Ville Distribution." Journal of Applied Mathematics 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/139471.

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We present the two-dimensional quaternion Wigner-Ville distribution (QWVD). The transform is constructed by substituting the Fourier transform kernel with the quaternion Fourier transform (QFT) kernel in the classical Wigner-Ville distribution definition. Based on the properties of quaternions and the QFT kernel we obtain three types of the QWVD. We discuss some useful properties of various definitions for the QWVD, which are extensions of the classical Wigner-Ville distribution properties.

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Zhang, Hui Xing, Jie Li, Qi Lin, Jian Zhi Qu, and Qi Zheng Yang. "Contrast of Time-Frequency Analysis Methods and Fusion of Wigner-Ville Distribution and Wavelet Transform." Advanced Materials Research 805-806 (September 2013): 1962–65. http://dx.doi.org/10.4028/www.scientific.net/amr.805-806.1962.

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Time-frequency analysis is a powerful tool for analyzing non-stationary signals, which can describe the signals frequency varying with time and provide us the joint information of time domain and frequency domain of the signal. We use a synthetic signal to realize the time-frequency analysis methods of wavelet transform, S transform and Wigner-Ville distribution. Through comparing and analyzing those time-frequency distributions, we propose a new method of integrating wavelet transform and Wigner-Ville distribution. This new method gives a better result than that of wavelet transform and Wigne

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6

Chen, Guang-Hua, and Jia-Lin Cao. "Statistical performance of the wigner-ville distribution and the cross Wigner-Ville distribution." Journal of Shanghai University (English Edition) 7, no. 4 (2003): 379–83. http://dx.doi.org/10.1007/s11741-003-0014-y.

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7

Latfaoui, Mahieddine, and Fethi Bereksi Reguig. "Time frequency analysis of ultrasound doppler signal by s-transform and wigner-ville distribution." Indonesian Journal of Electrical Engineering and Computer Science 14, no. 3 (2019): 1220. http://dx.doi.org/10.11591/ijeecs.v14.i3.pp1220-1227.

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<p>Ultrasound Doppler signal processing is a necessity in several disciplines of medicine. The interpretation of these signals allows a good diagnosis of patients in order to detect certain diseases. In this work, we will use different non-parametric time-frequency techniques such as the Wigner-Ville distribution (WVD), the Pseudo-Wigner-Ville distribution (PWVD), the smoothed pseudo Wigner-Ville distribution (SPWVD), and the S-transform in order to analyze the Ultrasonic Doppler signal of the femoral arteries.</p>

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8

Sun, Kewen, Baoguo Yu, Mireille Elhajj, Washington Yotto Ochieng, Tengteng Zhang, and Jianlei Yang. "A Novel GNSS Interference Detection Method Based on Smoothed Pseudo-Wigner–Hough Transform." Sensors 21, no. 13 (2021): 4306. http://dx.doi.org/10.3390/s21134306.

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This paper develops novel Global Navigation Satellite System (GNSS) interference detection methods based on the Hough transform. These methods are realized by incorporating the Hough transform into three Time-Frequency distributions: Wigner–Ville distribution, pseudo -Wigner–Ville distribution and smoothed pseudo-Wigner–Ville distribution. This process results in the corresponding Wigner–Hough transform, pseudo-Wigner–Hough transform and smoothed pseudo-Wigner–Hough transform, which are used in GNSS interference detection to search for local Hough-transformed energy peak in a small limited are

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9

Zou, J., J. Chen, J. C. Niu, and Z. M. Geng. "Application of the Wigner-Ville distribution to identification of a cracked rotor." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 217, no. 5 (2003): 551–56. http://dx.doi.org/10.1243/095440603765226849.

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The dynamic equation of transient response in a cracked rotor is modelled, and is based on the simple hinge crack model. The numerical simulation solutions of the uncracked rotor and the cracked rotor are obtained from the model. Using the Wigner-Ville distribution, the time-frequency features of the cracked rotor and the uncracked rotor are compared, and a new algorithm using the Wigner-Ville distribution to identify the cracked rotor is proposed. By simulation research, the sensitivity of the Wigner-Ville distribution to the stiffness variation is investigated, and the influence of the unbal

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10

Bhat, Mohammad Younus, Aamir Hamid Dar, Irfan Nurhidayat, and Sandra Pinelas. "An Interplay of Wigner–Ville Distribution and 2D Hyper-Complex Quadratic-Phase Fourier Transform." Fractal and Fractional 7, no. 2 (2023): 159. http://dx.doi.org/10.3390/fractalfract7020159.

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Two-dimensional hyper-complex (Quaternion) quadratic-phase Fourier transforms (Q-QPFT) have gained much popularity in recent years because of their applications in many areas, including color image and signal processing. At the same time, the applications of Wigner–Ville distribution (WVD) in signal analysis and image processing cannot be ruled out. In this paper, we study the two-dimensional hyper-complex (Quaternion) Wigner–Ville distribution associated with the quadratic-phase Fourier transform (WVD-QQPFT) by employing the advantages of quaternion quadratic-phase Fourier transforms (Q-QPFT)

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11

Wang, Hai Bin, Jun Bo Long, and Dai Feng Zha. "Pseudo Cohen Time-Frequency Distributions in Infinite Variance Noise Environment." Applied Mechanics and Materials 475-476 (December 2013): 253–58. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.253.

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stable distribution has been suggested as a more appropriate model in impulsive noise environment.The performance of conventional time-frequency distributions (TFDs) degenerate in stable distribution noise environment. Hence, three improved methods are proposed based on Fractional Low Order statistics, Fractional Low Order Wigner-Ville Distribution (FLO-WVD), Fractional Low Order Statistic pseudo Wigner-Ville Distribution (FLO-PWVD), Fractional Low Order Statistic Cohen class distribution (FLO-Cohen). In order for real-time, on-line operation and fairly long signals processing, a new smoothed

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12

DEBBAL, S. M. "Heart Cardiac Sounds analysis using the Wigner distribution (WD) Method." Clinical Cardiology and Cardiovascular Interventions 04, no. 15 (2021): 01–04. http://dx.doi.org/10.31579/2641-0419/216.

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This paper is concerned a “The Wigner distribution (WD)” analysis of the Heart cardiac (or phonocardiogram signals: PCG). The Wigner distribution (WD) and the corresponding WVD (Wigner Ville Distribution) have shown good performances in the analysis of non-stationary and quantitative measurements of the time-frequency PCG signal characteristics. It is shown that these transforms provides enough features of the PCG signals that will help clinics to obtain diagnosis.

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13

Kumar, Amit, Akhilesh Prasad, and Pankaj Jain. "The Weyl correspondence in the linear canonical transform domain." Filomat 37, no. 22 (2023): 7431–44. http://dx.doi.org/10.2298/fil2322431k.

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The main objective of the paper is to generalize and enrich the Weyl transform by introducing the Weyl correspondence in the linear canonical transform (LCT) domain. In this paper, we propose the linear canonical-Wigner transform in harmonic analysis of phase space along with the admissible Wigner-Ville distribution (WVD) and Weyl transform in the LCT domain and discuss some useful results. Further we establish the relationship between the Wigner-Ville distribution and the Weyl transform in the LCT domain.

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Kumar, Roshan, Vikash Singh, and Mohamed Ismail. "Post-Earthquake Damage Identification of Buildings with LMSST." Buildings 13, no. 7 (2023): 1614. http://dx.doi.org/10.3390/buildings13071614.

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The structure is said to be damaged if there is a permanent shift in the post-event natural frequency of a structure as compared with the pre-event frequency. To assess the damage to the structure, a time-frequency approach that can capture the pre-event and post-event frequency of the structure is required. In this study, to determine these frequencies, a local maximum synchrosqueezing transform (LMSST) method is employed. Through the simulation results, we have shown that the traditional methods such as the Wigner distribution, Wigner–Ville distributions, pseudo-Wigner–Ville distributions, s

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15

Cao, Jia-Lin, and Guang-Hua Chen. "Fast computation of wigner-ville distribution." Journal of Shanghai University (English Edition) 7, no. 3 (2003): 265–69. http://dx.doi.org/10.1007/s11741-003-0036-5.

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16

Wang, Peng, Ji Hua Cao, and Xiao Chang Ni. "Blind Separation of Non-Stationary Convoluted Mixtures Based on Time-Frequency Analysis." Advanced Materials Research 538-541 (June 2012): 2571–75. http://dx.doi.org/10.4028/www.scientific.net/amr.538-541.2571.

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The signals of convoluted mixtures have a stated of non-stationary identity, and the change of their spectrum with time-varying usually could not be observed from the frequency domain, but they can be observed by the time-frequency method. Therefore, the blind separation of non-stationary convoluted mixtures based on time-frequency analysis is proposed in this paper. For the non-stationary identity, the space-albinism of the mixed matrices and the joint diagonalization of the time-frequency matrices are simulated to separate the convoluted mixtures. Two kinds of time-frequency analysis methods

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17

Wang, Y., and Y. C. Jiang. "New time–frequency distribution based on the polynomial Wigner–Ville distribution and L class of Wigner–Ville distribution." IET Signal Processing 4, no. 2 (2010): 130. http://dx.doi.org/10.1049/iet-spr.2009.0026.

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18

Feng, Wuwei, Xin Chen, Cuizhu Wang, and Yuzhou Shi. "Application research on the time–frequency analysis method in the quality detection of ultrasonic wire bonding." International Journal of Distributed Sensor Networks 17, no. 5 (2021): 155014772110183. http://dx.doi.org/10.1177/15501477211018346.

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Imperfection in a bonding point can affect the quality of an entire integrated circuit. Therefore, a time–frequency analysis method was proposed to detect and identify fault bonds. First, the bonding voltage and current signals were acquired from the ultrasonic generator. Second, with Wigner–Ville distribution and empirical mode decomposition methods, the features of bonding electrical signals were extracted. Then, the principal component analysis method was further used for feature selection. Finally, an artificial neural network was built to recognize and detect the quality of ultrasonic wir

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19

Mousa, Allam, and Rashid Saleem. "Using Reduced Interference Distribution to Analyze Abnormal Cardiac Signal." Journal of Electrical Engineering 62, no. 3 (2011): 168–72. http://dx.doi.org/10.2478/v10187-011-0028-9.

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Using Reduced Interference Distribution to Analyze Abnormal Cardiac SignalDue to the non-stationary, multicomponent nature of biomedical signals, the use of time-frequency analysis can be inevitable for these signals. The choice and selection of the proper Time-Frequency Distribution (TFD) that can reveal the exact multicomponent structure of biological signals is vital in many applications, including the diagnosis of medical abnormalities. In this paper, the instantaneous frequency techniques using two distribution functions are applied for analysis of biological signals. These distributions

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20

Cai, Jian-Hua, and Wei-Wen Hu. "Feature Extraction of Gear Fault Signal Based on Sobel Operator and WHT." Shock and Vibration 20, no. 3 (2013): 551–59. http://dx.doi.org/10.1155/2013/367045.

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Taking Wigner-Ville distribution of gear fault signal as a picture,Sobeloperator was applied for edge detection of picture and then Hough transform was used to extract signal feature. Some simulated and measured signals have been processed to demonstrate the effectiveness of new method, which was compared with traditional Wigner-Hough transform and SPWD-Hough transform. The results show that the proposed method can suppress cross term which is produced from using Wigner-Ville distribution to analyze multi-component signal, especially under the condition of low signal to noise ratio. The improv

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21

Shin, Young S., and Jae-Jin Jeon. "Pseudo Wigner–Ville Time-Frequency Distribution and Its Application to Machinery Condition Monitoring." Shock and Vibration 1, no. 1 (1993): 65–76. http://dx.doi.org/10.1155/1993/372086.

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Machinery operating in a nonstationary mode generates a signature that at each instant of time has a distinct frequency. A Time-frequency domain representation is needed to characterize such a signature. Pseudo Wigner–Ville distribution is ideally suited for portraying a nonstationary signal in the time-frequency domain and is carried out by adapting the fast Fourier transform algorithm. The important parameters affecting the pseudo Wigner–Ville distribution are discussed and sensitivity analyses are also performed. Practical examples of an actual transient signal are used to illustrate its dy

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22

Andrieux, J., M. Feix, G. Mourgues, P. Bertrand, B. Izrar, and V. Nguyen. "Optimum smoothing of the Wigner--Ville distribution." IEEE Transactions on Acoustics, Speech, and Signal Processing 35, no. 6 (1987): 764–69. http://dx.doi.org/10.1109/tassp.1987.1165204.

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23

Bala Narayanan, S., and K. M. M. Prabhu. "New method of computing Wigner-Ville distribution." Electronics Letters 25, no. 5 (1989): 336. http://dx.doi.org/10.1049/el:19890234.

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24

Chan, S. C., and K. L. Ho. "On computing the discrete Wigner–Ville distribution." Electronics Letters 26, no. 10 (1990): 636–38. http://dx.doi.org/10.1049/el:19900417.

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25

Bergmann, N. "New formulation of discrete Wigner-Ville distribution." Electronics Letters 27, no. 2 (1991): 111. http://dx.doi.org/10.1049/el:19910074.

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26

Amirmazlaghani, Maryam, and Hamidreza Amindavar. "Statistical modeling and denoising Wigner–Ville distribution." Digital Signal Processing 23, no. 2 (2013): 506–13. http://dx.doi.org/10.1016/j.dsp.2012.08.016.

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27

LEE, JOON-HYUN, J. KIM, and HAN-JUN KIM. "DEVELOPMENT OF ENHANCED WIGNER–VILLE DISTRIBUTION FUNCTION." Mechanical Systems and Signal Processing 15, no. 2 (2001): 367–98. http://dx.doi.org/10.1006/mssp.2000.1365.

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28

Widjaja, Joewono, and Porntip Chuamchaitrakool. "Holographic particle tracking using Wigner–Ville distribution." Optics and Lasers in Engineering 51, no. 3 (2013): 311–16. http://dx.doi.org/10.1016/j.optlaseng.2012.09.009.

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Chuamchaitrakool, Porntip, Joewono Widjaja, and Hiroyuki Yoshimura. "Holographic particle sizing using Wigner–Ville distribution." Optics and Lasers in Engineering 67 (April 2015): 186–90. http://dx.doi.org/10.1016/j.optlaseng.2014.11.016.

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30

Pinho, Alexandre De Jesus, and Milton José Porsani. "APPLICATION OF TIME-FREQUENCY DECOMPOSITION METHOD FOR GAS RESERVOIR IDENTIFICATION IN THE SERGIPE - ALAGOAS BASIN." Revista Brasileira de Geofísica 36, no. 2 (2018): 189. http://dx.doi.org/10.22564/rbgf.v36i2.943.

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ABSTRACT. The sedimentary basin of Sergipe-Alagoas, located on the Brazilian east bank, presents one of the most complete stratigraphic sections of the Brazilian continental margin. Hydrocarbon exploration activities began more than 50 years ago. The recent discoveries of hydrocarbons (gas and oil of high API grade) in turbiditic reservoirs of deep waters have further awakened the exploratory interest of the basin. Problems related to the processing and interpretation of seismic data have always received great attention from the scientific community. Currently, the use of time-frequency decomp

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31

Xie, Ping, Yu Xin Yang, Guo Qian Jiang, Yi Hao Du, and Xiao Li Li. "A NewFault Detection and Diagnosis Method Based on Wigner-Ville Spectrum Entropy for the Rolling Bearing." Applied Mechanics and Materials 197 (September 2012): 346–50. http://dx.doi.org/10.4028/www.scientific.net/amm.197.346.

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The rolling bearings are one of the most critical components in rotary machinery. To prevent unexpected bearing failure, it is crucial to develop the effective fault detection and diagnosis techniques to realize equipment’s near-zero downtime and maximum productivity. In this paper, a new fault detection and diagnosis method based on Wigner-Ville spectrum entropy (WVSE) is proposed. First, the local mean decomposition (LMD) and the Wigner-Ville distribution (WVD) are combined to develop a new feature extraction approach to extract the fault features in time-frequency domain of the bearing vibr

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Wu, Guang Zhi, Gang Fu, and Yan Jun Wu. "Detection and Parameter Estimation of Chirp Signal Based on Time-Frequency Analysis." Advanced Materials Research 989-994 (July 2014): 3989–92. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.3989.

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Based on the relationship between the Radon-Wigner transform and fractional Fourier transform and the time frequency distribution, using the property that Radon-Wigner transform has better performance in time and frequency domain, detection and parameter estimation of Chirp signal have been done by Radon-Wigner transform or fractiona1 Fourier transform. The theoretica1 analysis and simulation prove that two techniques are better than generic time-frequency transform, such as Wigner-Ville transform.

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33

Fedosenkov, D. B., A. A. Simikova, S. M. Kulakov, and B. A. Fedosenkov. "COHEN’S CLASS TIME-FREQUENCY DISTRIBUTIONS FOR MEASUREMENT SIGNALS AS A MEANS OF MONITORING TECHNOLOGICAL PROCESSES." Izvestiya. Ferrous Metallurgy 62, no. 4 (2019): 324–29. http://dx.doi.org/10.17073/0368-0797-2019-4-324-329.

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The article presents and describes Cohen’s class time-frequency distributions which are expedient to use as a mathematical tool that allows to create a convenient – in terms of information content and semantic clarity – visual-graphical representation of the opera ting modes of various technological processes including processes of ferrous metallurgy. It was noted that a controlling process is usually implemented without simultaneous visual monitoring of each scalar (one-dimensional) coordinate that is under control, but the presence of such monitoring is an important condition for the compute

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Pan, M. C., H. Van Brussel, P. Sas, and B. Verbeure. "Fault Diagnosis of Joint Backlash." Journal of Vibration and Acoustics 120, no. 1 (1998): 13–24. http://dx.doi.org/10.1115/1.2893797.

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The aim of this paper is to develop appropriate techniques to detect and classify the joint backlash of a robot by monitoring its vibration response during normal operating conditions. In this investigation, Wigner-Ville distributions combined with two-dimensional correlation techniques have been employed to diagnose the joint faults of multi-link robots. In the study reported here, signal detection based on the Wigner-Ville distribution is proposed as a tool for pattern differentiation. To evaluate the performance of different detection procedures, the detection of a simulated impact transien

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35

Bhat, Mohammad Younus, Ibrahim M. Almanjahie, Aamir H. Dar, and Javid G. Dar. "Wigner-Ville distribution and ambiguity function associated with the quaternion offset linear canonical transform." Demonstratio Mathematica 55, no. 1 (2022): 786–97. http://dx.doi.org/10.1515/dema-2022-0175.

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Abstract Wigner-Ville transform or Wigner-Ville distribution (WVD) associated with quaternion offset linear canonical transform (QOLCT) was proposed by Bhat and Dar. This work is devoted to the development of the theory proposed by them, which is an emerging tool in the scenario of signal processing. The main contribution of this work is to introduce WVD and ambiguity function (AF) associated with the QOLCT (WVD-QOLCT/AF-QOLCT). First, the definition of the WVD-QOLCT is proposed, and then several important properties such as dilation, nonlinearity, and boundedness are derived. Second, we deriv

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Shanmuga Sundaram, R., and K. M. M. Prabhu. "Numerically stable algorithm for computing Wigner–Ville distribution." IEE Proceedings - Vision, Image, and Signal Processing 144, no. 1 (1997): 46. http://dx.doi.org/10.1049/ip-vis:19970817.

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37

Abeysekera, S. S. "Computation of Wigner-Ville distribution for complex data." Electronics Letters 26, no. 16 (1990): 1315. http://dx.doi.org/10.1049/el:19900845.

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Pan, W. "Fast calculation method for multicomponent Wigner-Ville distribution." Electronics Letters 28, no. 4 (1992): 398. http://dx.doi.org/10.1049/el:19920249.

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Bahri, Mawardi, and Muh Saleh Arif Fatimah. "Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform." Journal of Applied Mathematics 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/3247364.

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The quaternion Wigner-Ville distribution associated with linear canonical transform (QWVD-LCT) is a nontrivial generalization of the quaternion Wigner-Ville distribution to the linear canonical transform (LCT) domain. In the present paper, we establish a fundamental relationship between the QWVD-LCT and the quaternion Fourier transform (QFT). Based on this fact, we provide alternative proof of the well-known properties of the QWVD-LCT such as inversion formula and Moyal formula. We also discuss in detail the relationship among the QWVD-LCT and other generalized transforms. Finally, based on th

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40

Er-Raoudi, Mina, M. Diany, H. Aissaoui, and M. Mabrouki. "Application of the Reassigned Smoothed Pseudo Wigner-Ville Distribution in Gear Defect Diagnosis." Mapta Journal of Mechanical and Industrial Engineering (MJMIE) 4, no. 2 (2021): 21–29. http://dx.doi.org/10.33544/mjmie.v4i2.148.

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Gear is one of the most omnipresent components in the mechanical and industrial fields. Some defects can occur causing a change in the vibration signature. In the dynamic of gears system, several sources of excitation are considered. The principal objective of the present work is to study the use of the Reassigned Smoothed Pseudo Wigner Ville Distribution (RSPWVD) in the gear vibration monitoring. The used signals are obtained by the simulation of an eight degrees of freedom gearbox system for the healthy and cracked case. The considered model takes into account the presence of friction force

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41

Mohammad, Younus Bhat, and Dar Aamir Hamid. "Wigner-Ville distribution and ambiguity function of QPFT signals." Annals of the University of Craiova Mathematics and Computer Science Series 50, no. 2 (2023): 259–76. http://dx.doi.org/10.52846/ami.v50i2.1640.

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The quadratic phase Fourier transform(QPFT) has received my attention in recent years because of its applications in signal processing. At the same time the applications of Wigner-Ville distribution (WVD) and ambiguity function (AF) in signal analysis and image processing can not be excluded. In this paper we investigated the Wigner-Ville Distribution (WVD) and ambiguity function (AF) associated with quadratic phase Fourier transform (WVD-QPFT/AF-QPFT). Firstly, we propose the definition of the WVD-QPFT, and then several important properties of newly defined WVD-QPFT, such as nonlinearity, bou

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Meng, Lijun, Xin Tan, and Quanquan Yu. "Study on Time-frequency Imaging of Ultrasonic Detection with Phase Shifted Fiber Bragg Grating Sensing." Measurement Science Review 23, no. 3 (2023): 106–15. http://dx.doi.org/10.2478/msr-2023-0014.

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Abstract The influence of the wavelength difference between the laser source and the phase-shifted fiber Bragg grating (PS-FBG) on the intensity of the power demodulation system based on an adjustable laser source was studied experimentally, and the optimum of the output laser wavelength was determined. Then, the research on time-frequency imaging damage identification based on smooth pseudo-Wigner-Ville distribution was carried out. The Time of Flight of the acoustic wave signal was calculated and time compensation was made according to the Wigner-Ville distribution and the Lamb wave dispersi

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Liu Cong, 刘聪, 李言俊 Li Yanjun, and 张科 Zhang Ke. "An Image Fusion Algorithm Using Pseudo Wigner Ville Distribution." Acta Optica Sinica 29, no. 10 (2009): 2716–20. http://dx.doi.org/10.3788/aos20092910.2716.

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Salem, Sameh, Fathy Ahmed, Mamdouh Ibrahim, and Abdel Rahman Elbardawiny. "A New Approach for LFMCWRadar using Wigner-Ville Distribution." International Conference on Electrical Engineering 8, no. 8 (2012): 1–9. http://dx.doi.org/10.21608/iceeng.2012.32808.

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Zaman, Shahriar, and Sheikh Md. Rabiul Islam. "Classification of FNIRS Using Wigner-ville Distribution and CNN." International Journal of Image, Graphics and Signal Processing 13, no. 5 (2021): 1–13. http://dx.doi.org/10.5815/ijigsp.2021.05.01.

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Imai, R., Y. Hashimoto, K. Kikuchi, and S. Fujii. "High-resolution beamforming by the Wigner-Ville distribution method." IEEE Journal of Oceanic Engineering 25, no. 1 (2000): 105–10. http://dx.doi.org/10.1109/48.820742.

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Prabhu, K. M. M., and R. Shanmuga Sundaram. "Fixed-point error analysis of discrete Wigner-Ville distribution." IEEE Transactions on Signal Processing 45, no. 10 (1997): 2579–82. http://dx.doi.org/10.1109/78.640723.

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Yamaoka, Tomoya, and Tadashi Oshima. "Discrete Wigner-Ville Distribution with Wide Frequency Observation Range." IEICE Communications Express 14, no. 2 (2025): 67–70. https://doi.org/10.23919/comex.2024xbl0168.

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Wang, Zaiyi, Bo Yin, and He Yan. "Weak Signal Detection Based on Pseudo Wigner Ville Distribution." Journal of Physics: Conference Series 1176 (March 2019): 062040. http://dx.doi.org/10.1088/1742-6596/1176/6/062040.

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Cher Ming Tan and Shin Yeh Lim. "Application of Wigner-Ville distribution in electromigration noise analysis." IEEE Transactions on Device and Materials Reliability 2, no. 2 (2002): 30–35. http://dx.doi.org/10.1109/tdmr.2002.802114.

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