The W transform and its improved methods for time-frequency analysis of seismic data

The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.

Wigner-Ville distribution and its application in seismic attenuation estimation

The attenuation of seismic signals is often characterized in the frequency domain using statistical measures of the power spectrum. However, the conventional Fourier transform-based power spectrum estimation methods suffer from time-frequency resolution problems. Wigner-Ville distribution, which is a member of Cohen class time-frequency distributions, possesses many appealing properties, such as time-frequency marginal distribution, time-frequency localization, etc. Therefore, Wigner-Ville distribution offers a new way for estimating the attenuation of seismic signals. This paper initially gives a brief introduction to Wigner-Ville distribution and the smoothed Wigner-Ville distribution that is effective in reducing the cross-term effect, and then presents a method for seismic attenuation estimation based on the instantaneous energy spectrum of the Wigner-Ville distribution. A real data example from central Tarim Basin in western China is presented to illustrate the effectiveness of the proposed method. The results show that the Wigner-Ville distribution-based seismic attenuation estimation method can effectively detect the difference between reef, shoal and lagoon facies by their attenuation properties, indicating that the estimated seismic attenuation can be used for reef and shoal carbonate reservoir characterization.

Novel Time-frequency Analysis and Representation of EEG

A novel method of EEG time-frequency analysis and representation based on a wavelet network is presented. The wavelet network model can represent the EEG data effectively. Based on the wavelet network model, a novel time-frequency energy distribution function is obtained, which has the same time-frequency resolution as Wigner-Ville distribution and is free of cross-term interference. There is a great potential for the use of the novel time-frequency representation of nonstationary biosignal based on a wavelet network in the field of the electrophysiological signal processing and time-frequency analysis.

Nonexistence of cross-term free time-frequency distribution with concentration of Wigner-Ville distribution

Wigner-Ville distribution (WVD) is recognized as being a powerful tool and a nucleus in time-frequency representation (TFR) which gives an excellent time-frequency concentration, and more importantly, has many desirable properties. A major shortcoming of WVD is the inherent cross-term (CT) interference. Although solutions to this problem from the bulk of contributions to the literature concerning TFR are currently available, none has been able to completely eliminate the CT’s in WVD. It is therefore a common belief that if there exists an auxiliary time-frequency distribution (TFD) which has the same auto-terms (AT’s) as that in WVD, but has CT’s with the opposite sign, then, by adding the auxiliary TFD to WVD, an ideal TFD, which preserves the concentration of WVD while annihilating the CT’s, is readily obtained. However, we prove that the auxiliary TFD does not exist. Moreover, it is found that in general, CT free joint distributions with their concentrations close to that of WVD do not exist either.

基于WVD/ATDM的铝合金板孔损伤位置与区域识别

为识别铝合金板孔损伤位置及区域,以Lamb波为研究基础,提出基于魏格纳-威利分布(WVD,WignerVille distribution)和到达时间差值法(ATDM,arrival time difference method)的损伤识别技术。首先,采集实验铝合金板健康和有损模型的Lamb信号,对其差值信号进行WVD分析,准确提取损伤反射信号到达时间;其次,通过ATDM建立各传感器间的距离差值关系,确定孔损伤位置中心并预测最大损伤半径,从而实现对孔损伤关键指标的识别;最后,通过数值模拟进一步验证该方法,结果表明,基于WVD/ATDM的损伤识别技术不仅能准确识别出孔损伤位置,而且能够有效地识别损伤区域面积。

Simulation Study on Multi-Rate Time-Frequency Analysis of Non-Stationary Signals

A new time-frequency analysis method is proposed in this study using a multi-rate signal decomposition technique for the analysis of non-stationary signals. The method uses a multi-rate filter bank for an improved non-stationary signal decomposition treatment, and uses the Wigner-Ville distribution(WVD) analysis for signal reconstruction. The method presented in this study can effectively resolves the time and frequency resolution issue for non-stationary signal analysis and the cross-term issue typically encountered in time-frequency analysis.The feasibility and accuracy of the proposed method are evaluated and verified in a numerical simulation.

半导体光纤环形激光器输出状态分析与分类

研究了不同注入电流、不同输出偏振度下,半导体光纤环形激光器输出光的混沌特性.分别采用时域观察法、C-C法、Wigner-ville分布时频分析法、最大Lyapunov指数法联合分析输出光的时域、频域统计特性.从而将激光器输出按偏振度划分为三类:偏振度在0%到20%,随着电流的增大,激光器输出偏振混沌激光,其类型发生阶跃性跳变;偏振度在30～80%,激光器输出仍以偏振混沌激光为主,其类型不随电流增大而发生跳变;偏振度趋于90～100%,激光器输出以强度混沌激光为主,偏振混沌光随着偏振度趋向100%而下降为零.利用虚假邻点法计算嵌入维数和回归图法重构吸引子,得到上述三种输出类型的复杂程度依次是:椭圆吸引子(6维)、方形吸引子(7维)、点形吸引子(5维).由此得出,半导体光纤环形激光器用于偏振混沌通信的最佳区域为:偏振度处于30%至80%,注入电流处于330mA～550mA.

基于时间分段数据的弹道目标微多普勒时频分析方法

鉴于反导雷达需要同时保持对多个目标的跟踪而不能对同一目标进行较长时间的连续观测问题,提出了一种基于时间分段数据的时频分析方法.该方法不直接求取理想时间信号,而是结合双线性插值和AR估计求取理想时间信号的相关函数,并以Winger-Ville分布(WVD)方法得到时频图.仿真结果表明,该方法精度高于时域线性插值方法.

Radar Signal Intra-Pulse Feature Extraction Based on Improved Wavelet Transform Algorithm

With the new system radar put into practical use, the characteristics of complex radar signals are changing and developing. The traditional analysis method of one-dimensional transformation domain is no longer applicable to the modern radar signal processing, and it is necessary to seek new methods in the two-dimensional transformation domain. The time-frequency analysis method is the most widely used method in the two-dimensional transformation domain. In this paper, two typical time-frequency analysis methods of short-time Fourier transform and Wigner-Ville distribution are studied by analyzing the time-frequency transform of typical radar reconnaissance linear frequency modulation signal, aiming at the problem of low accuracy and sen-sitivity to the signal noise of common methods, the improved wavelet transform algorithm was proposed.