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

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.

LOCALIZED RADON-WIGNER TRANSFORM AND GENERALIZED-MARGINAL TIME-FREQUENCY DISTRIBUTIONS

This paper introduces the localized Radon transform (LRT) into time-frequency distributions and presents the localized Radon-Wigner transform (LRWT). The definition of LRWT and a fast algorithm is derived, the properties of LRWT and its relationship with Radon-Wigner transform, Wigner distribution (WD), ambiguity function (AF), and generalized-marginal time-frequency distributions are analyzed.

Asymptotic Analysis of Quantum Dynamics in Crystals: the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.

Feature Extraction of Symmetrical Triangular LFMCW Signal Using Wigner-Hough Transform

Feature extraction of symmetrical triangular linear frequency modulation continuous wave （LFM- CW） signal is studied. Combined with its peculiar charaeteristics, a novel algorithm based on Wigner-Hough transform （WHT） is presented for the deteetion and parameter estimation of this type of waveform. The initial frequency and chirp rate of each segment of this wave are estimated, and the peak-value searching steps in the parameter spaee is given. Compared with Wigner-Ville distribution （WVD）, Pseudo-Wigner-Ville distri- bution （PWD） and Smoothed-Peseudo-Wigner-Ville distribution （SPWD）, WHT has proven itself to be the best method for feature extraetion of symmetrical triangular LFMCW signal. In the end, Monte-Carlo simulations under different SNRs are earried out, with validating results on this method.

Wigner-Hough transform based on slice's entropy and its application to multi-LFM signal detection

To enhance the capacity of the radar-reconnaissance interception receiver recognizing linear frequency modulated (LFM) at a low signal-noise ratio, this paper presents WignerHough transform (WHT) of the LFM signal and its corresponding characteristics, derives the probability density functions of the LFM signal and Gaussian white noise within WHT based on entropy (WHTE), dimension under different assumptions and puts forward a WHT algorithm based on entropy of slice to improve the capacity of detecting the LFM signal. Entropy of the WHT domain slice is adopted to assess the information size of polar radius or angle slice, which is converted into the weight factor to weight every slice. Double-deck weight is used to weaken the influences of noise and disturbance terms and WHTE treatment and signal detection procedure are also summarized. The rationality of the algorithm is demonstrated through theoretical analysis and formula derivation, the efficiency of the algorithm is verified by simulation comparison between WHT, fractional Fourier transform and periodic WHT, and it is highlighted that the WHTE algorithm has better detection accuracy and range of application against strong noise background.

New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering

Using the Weyl ordering of operators expansion formula （Hong-Yi Fan, J. Phys.A 25 （1992） 3443） this paper finds a kind of two-fold integration transformation about the Wigner operator △（ q＇,p） q-number transform） in phase space quantum mechanics,∫∫∞-∞dp＇dq＇/π △（q＇,p＇）e-2i（ p-p＇）（ q-q＇）=δ（ p-P）δ（ q-Q）,∫∫∞-∞dqdpδ（p-P）δ（q-Q）e2i（p-p＇）（q-q＇）=△（q＇,p＇）,whereQ,P are the coordinate and momentum operators, respectively. We apply it to study mutual converting formulae among Q-P ordering, P-Q ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched. The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.

Recognition Method Based on Wigner-Hough Transform for Poly-Phase Code Radar Signal

In order to solve the recognition of polyphase code radar signal, this paper gives two methods based on Frank code, i.e. the high-order spectrum recognition method and the fractional Fourier transform (FRFT) method, by analyzing the micro characteristics of polyphase code signals in time and frequency domain respectively. And a recognition algorithm based on Wigner-Hough transform (WHT) is developed in this paper. We verify the validity of each method by computer simulation and give relative merits and demerits. A set of results demonstrate that the algorithm based on Wigner-Hough transform has better recognition performance in low signal-to-noise (SNR) than others.

Relation between Fresnel transform of input light field and the two-parameter Radon transform of Wigner function of the field

This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.

基于改进Radon-wigner变换的微弱目标加速度估计算法

针对已有Radon-Wigner变换(RWT)对线性调频连续波(linear frequency modulated continuous wave,LFMCW)雷达目标加速度估计计算复杂高、精度低的问题,提出了一种改进的RWT算法。该算法通过熵值法得到加速度的粗估计,对RWT结果求二阶原点矩减小搜索计算量,并且提出了RWT插值方法,将其应用到迭代RWT中用于提高加速度估计精度。实验结果表明,该算法在低信噪比的情况下可以准确检测出匀加速微弱目标,计算量较小且精度较高。

Radon transforms of the Wigner operator on hyperplanes

The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution-a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.

Relations between chirp transform and Fresnel diffraction,Wigner distribution function and a fast algorithm for chirp transform

Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional- order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.

New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

As a natural and important extension of Fan＇s paper （Fan Hong-Yi 2010 Chin. Phys. B 19 040305） by employing the formula of operators＇ Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator A （#, ~） （in its entangled form） in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to （a1-a2） and （a1＋a2） can be solved and the contents of phase space quantum mechanics can be enriched, where ai,ai are bosonic creation and annihilation operators, respectively.

采用STFT-Wigner变换抑制Wigner-Ville分布交叉项

对于多分量非平稳信号分析,维格纳时频分布Wigner-Ville(WVD)存在严重的交叉项干扰。而GWT避免了Wigner-Ville分布的交叉项干扰而且具有良好的时频聚集性。但由于Gabor变换的时频聚集性不佳,当多分量信号进行Gabor变换时如果信号中各分量频率混叠,Gabor Wigner transform(GWT)就不能得到理想的结果。提出一种改进的STFT-Wigner算法,可以有效的抑制交叉项,并保持较高的时频聚集性。通过分析仿真信号和实测振动信号表明该方法能够取得良好的效果。

基于Wigner-Hough变换的径向加速度估计

雷达-目标径向加速度是表征雷达和目标相对运动关系重要特征,可用于机动目标跟踪、目标识别等,因此研究直接从雷达回波估计径向加速度很有必要.本文给出了基于Wigner-Hough变换的径向加速度估计算法和算法实现流程,并分析了接收回波信号时长对加速度最小可分辨单元的影响,最后进行了仿真试验,仿真结果证实了该算法的有效性.

基于Radon-Wigner变换的多分量LFM信号的检测

Radon- Wigner变换是一种直线积分的投影变换 ,它对多分量 L FM信号提供了较好的时频局域性 ,从而有利于多分量 L FM信号的解释和分析 .通过时域解线调和频域解线调处理可以完整地在时频平面计算出 Radon变换 .对于多分量 L FM信号的分析好于 Wigner- Ville变换等常用的时频变换 .

基于Wigner-Hough变换的LFM信号检测性能分析

根据Wigner-Hough变换思想和广义似然比检验理论,分析了双门限情况下线性调频信号的检测性能,给出了虚警概率和检测概率的数学表达式,该表达式是Hough变换的积累单元数和检测门限的函数,然后对概率密度函数进行了合理近似,并给出了Hough变换的积累单元数计算公式,最后的计算机仿真比较了傅立叶变换和Wigner-Hough变换的LFM(Linear Frequency Modulated)信号检测性能和基于Wigner-Hough变换的不同目标起伏类型的LFM信号检测性能.

基于改进Wigner-Hough变换的多分量LFM信号特征提取

为了解决Wigner-Hough变换对多分量线性调频(LFM)信号特征提取受噪声困扰的问题,提出采用数字图像处理中改进的Sobel算子对含噪声信号的WVD时频图进行边缘特征检测,利用Hough变换对信号特征进行提取.通过对WHT,SPWD-Hough变换以及改进WHT 3种方法进行计算机仿真比较结果表明,改进的WHT对多分量LFM信号的特征提取效果最好.

基于Wigner-Hough变换的多分量LFM信号检测及离散计算方法

igner Hough变换对LFM信号有压缩和聚焦的作用 ,这种作用的又具有阈值特性 ,本文简述Wigner Hough变换的方法及对该方法的评价 .重点讨论Wigner Hough变换的离散计算 。

用Wigner-Hough变换检测精密可控震源信号

本文提出基于Wigner-Hough变换实现精密可控震源信号的检测与变换的方法。精密控制震源发射并由地震台站观测设备记录下来的信号是连续线性调频振动信号(LFM),线性调频信号的Wigner-Ville变换是在时频平面内包含一条直线的图像,而Hough变换则是通过计算沿直线的积分可以有效检测图像中的直线,图像中的直线在Hough变换输出的图像中表现为一个峰值,用于精密控制震源信号的检测可以反映接收数据中存在的震源信号。本文针对精密控制震源信号检测中Wigner-Ville变换和Hough变换存在的问题开展研究,并提出了解决方案。通过对2009年在广东新丰江水库库区精密可控震源试验观测数据的实际处理,显示该方法是可行的,为精密控制震源信号的检测与变换找到了又一新的方法和技术途径。

基于小波变换及Wigner-Ville变换方法的超声导波信号分析

对结构中缺陷的检测和识别是无损检测中的一项重要研究课题,超声导波由于可在短时间内检测很远距离,故它的一个重要应用便是管材的检测。因而对导波检测信号的处理成为一重要研究内容,本文利用时-频分析方法中的小波变换和Wigner-Ville变换对管道和抽油杆缺陷的导波检测信号进行了分析处理。实验结果表明,进行小波变换后,缺陷回波信号的信噪比大大提高,直径仅1mm的小孔缺陷可容易地被识别出来,准确检测出其位置;通过对信号进行Wigner-Ville的相关变换,可同时在时频两域内对缺陷的回波信号进行分析,使缺陷辨别起来简单易行。两种信号处理方法的超声导波应用研究为以后导波信号的处理提供了新的实现依据。