基于科恩分布的地球物理信号的时频分析

在简要讨论几种科恩类广义双线性时频分布的基础上,探讨双线性时频分布的算法实现与仿真流程,进而模拟出地磁脉动信号的几种时频分布,同时还对Pc脉动的几种双线性时频分布进行了比较,给出了相应的交叉项抑制和参数选取的方法。结果表明,在核函数参数选取适当的情况下,广义双线性时频表示是分析地球物理信号的有力工具。     

Shift covariant time-frequency distributions of discrete signals

Many commonly used time-frequency distributions are members of the Cohen (1989) class. This class is defined for continuous signals, and since time-frequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the class of all quadratic time-frequency distributions that are covariant to time shifts and frequency shifts. We extend this method to three types of discrete signals to derive what we call the discrete Cohen classes. The properties of the discrete Cohen classes differ from those of the original Cohen class. To illustrate these properties, we also provide explicit relationships between the classical Wigner distribution and the discrete Cohen classes     

The discrete Zak transform application to time-frequency analysisand synthesis of nonstationary signals

Algorithms to compute coefficients of the finite double sum expansion of time-varying nonstationary signals and to synthesize them from a finite number of expansion coefficients are presented. The algorithms are based on the computation of the discrete Zak transform (DZT). Fast algorithms to compute DZT are presented. Modifications to the algorithms which increase robustness are given     

An adaptive time-frequency filtering method for nonstationary signals based on the generalized S-transform

Aiming at the serious interference of the cross term existing in the time-frequency(TF) filtering method,an adaptive TF filtering method for nonstationary signals based on the generalized S-transform is proposed.Firstly the time-frequency distribution spectrum of the signal is got by the generalized S-transform,then the clustered energy of the signal on the timefrequency plane is identified by the TF region extraction algorithm,thirdly the TF filtering factor is constructed based on the distribution charact...     

Modified Cohen-Lee time-frequency distributions and instantaneousbandwidth of multicomponent signals

Cohen (1989, 1995) has introduced and extensively studied and developed the concept of the instantaneous bandwidth of a signal. Specifically, instantaneous bandwidth is interpreted as the spread in frequency about the instantaneous frequency, which is itself interpreted as the average frequency at each time. This view stems from a joint time-frequency distribution (TFD) analysis of the signal, where instantaneous frequency and instantaneous bandwidth are taken to be the first two conditional spectral moments, respectively, of the distribution. However, the traditional definition of instantaneous frequency, namely, as the derivative of the phase of the signal, is not consistent with this interpretation, and new definitions have therefore been proposed previously. We show that similar problems arise with the Cohen-Lee (1988, 1989) instantaneous bandwidth of a signal and propose a new formulation for the instantaneous bandwidth that is consistent with its interpretation as the conditional standard deviation in frequency of a TFD. We give the kernel constraints for a distribution to yield this new result, which is a modification of the kernel proposed by Cohen and Lee. These new kernel constraints yield a modified Cohen-Lee TFD whose first two conditional moments are interpretable as the average frequency and bandwidth at each time, respectively     

The running time-frequency distributions

This paper introduces the running kernels that yield recursive structures for time-frequency distributions (TFDs). The running kernels offer important properties not possessed by the commonly used block distribution kernels. The introduced kernels allow an invariance in computations with respect to the extent of the kernel in the time or the lag variable. However, contrary to the wide class of block kernels that satisfy the desired timefrequency (t-f) properties, most recursive (running) time-frequency distributions (RTFDs) violate the marginal and the support properties. This paper considers both the direct and the indirect types of recursion and presents examples for illustration.This research was supported in part by the US Air Force, grant no. AFOSR F49620-93-C0063 and a grant from the Office of Research and Sponsored Projects at Villanova University.     

Positive time-frequency distributions based on joint marginalconstraints

The authors study the formulation of members of the Cohen-Posch (1985) class of positive time-frequency energy distributions. Minimization of cross-entropy measures with respect to different priors and the case of no prior or maximum entropy were considered. They conclude that, in general, the information provided by the classical marginal constraints is very limited, and thus, the final distribution heavily depends on the prior distribution. To overcome this limitation, joint time and frequency marginals are derived based on a “direction invariance” criterion on the time-frequency plane that are directly related to the fractional Fourier transform     

Second-order time-frequency synthesis of nonstationary randomprocesses

We present time-frequency methods for the synthesis of finite-energy, nonstationary random processes. The energetic characteristics of the process to be synthesized are specified in a joint time-frequency domain via a time-frequency model function. The synthesis methods optimize the autocorrelation function of the process such that the process' Wigner-Ville spectrum is closest to the given model function. An optional signal subspace constraint allows the incorporation of additional properties such as bandlimitation and also permits the reformulation of the synthesis methods in a discrete-time setting. The synthesized process is expressed either in terms of an orthonormal basis of the constraint subspace or via its Karhunen-Loeve expansion. An example involving the prolate spheroidal functions is given, and computer simulation results are provided     

基于时频分析的雷达信号到达角估计

现有的空间时频分布(STFD)的信号表示只适用于窄带、连续信号的分析，而雷达侦察系统要求对脉冲、线性调频等信号同时进行到达角(DOA)、频率和信号时域参数的估计。本文给出了现有空间时频分布对雷达信号DOA估计的条件，并提出了基于修正STFD矩阵的DOA估计算法。通过对各阵元输出作时频分析，估计信号的频率参数，然后据此构造方向向量和修正STFD矩阵，即可构造MUSIC空间谱。该算法不受基于现有STFD算法的条件限制。     

Kernel decomposition of time-frequency distributions

Bilinear time-frequency distributions (TFDs) offer improved time-frequency resolution over linear representations, but suffer from difficult interpretation, higher implementation cost, and the lack of associated low-cost signal synthesis algorithms. In the paper, the authors introduce some new tools for the interpretation and quantitative comparison of high-resolution TFDs. These tools are used in related work to define low-cost high-resolution TFDs and to define linear, low-cost signal synthesis algorithms associated with high-resolution TFDs. First, each real-valued TFD is associated with a self-adjoint linear operator ψ. The spectral representation of ψ expresses the TFD as a weighted sum of spectrograms (SPs). It is shown that the SP decomposition and Weyl correspondence do not yield useful interpretations for high-resolution TFDs due to the fact that ψ is not positive     

Tomographic time-frequency analysis and its application towardtime-varying filtering and adaptive kernel design for multicomponentlinear-FM signals

Since line integrals through the Wigner spectrum can be calculated by dechirping, calculation of the Wigner spectrum may be viewed as a tomographic reconstruction problem. In the paper, the authors show that all time-frequency transforms of Cohen's class may be achieved by simple changes in backprojection reconstruction filtering. The resolution/cross-term tradeoff that occurs in time-frequency kernel selection is shown to be analogous to the resolution-ringing tradeoff that occurs in computed tomography (CT). “Ideal” reconstruction using a purely differentiating backprojection filter yields the Wigner distribution, whereas low-pass differentiating filters produce cross-term suppressing distributions such as the spectrogram or the Born-Jordan distribution. It is also demonstrated how this analogy can be exploited to “tune” the reconstruction filtering (or time-frequency kernel) to improve the ringing/resolution tradeoff. Some properties of the projection domain, which is also known as the Radon-Wigner transform, are characterized, including the response to signal delays or frequency shifts and projection masking or convolution. Last, time-varying filtering by shift-varying convolution in the Radon-Wigner domain is shown to yield superior results to its analogous Cohen's class adaptive transform (shift-invariant convolution) for the multicomponent, linear-FM signals that are investigated     

Principal decomposition of time-frequency distributions

The authors present a novel time-frequency analysis technique which uses principal components analysis to map any given time-frequency distribution (TFD) of a signal into a set of three 1-D principal decomposition functions. These three functions may then be considered to be `separable' components of a time-frequency function which they refer to as the principal approximation function for the original TFD. They show how principal decomposition analysis is useful for the enhancement and frequency-tracking of nonstationary harmonic signals     

基于时频原子方法的雷达辐射源信号特征提取

针对电子战面临的高密集、信号形式复杂多变的雷达辐射源环境,提出一种全新的雷达辐射源信号特征提取方法.在过完备的时频原子库基础上,采用匹配追踪(MP)方法对信号进行时频原子分解,并通过改进的量子遗传算法(IQGA)降低MP搜索过程的时间复杂性,得到表示雷达辐射源信号特征信息的最佳时频原子,为后期的辐射源信号分选和识别进行特征准备.实验结果证实了该方法的有效性和可行性,所提取的时频原子特征具有一定的抗噪性能.     

基于时频点聚类的LFM信号波达方向估计

基于空间时频分布(spatial time-frequency distribution, STFD)的多重信号分类(multiple signal classification, MUSIC)算法常用于非平稳信号波达方向(direction of arrival, DOA)估计, 其关键是选取合适的信号时频点.文中针对传统时频MUSIC算法不能提取各信号时频点且在小角度间隔时估计性能不佳的问题, 以线性调频(line frequency modulation, LFM)信号为研究对象, 提出了基于时频点聚类的DOA估计算法.该算法首先对阵列接收信号进行白化, 利用白化后的接收信号构造STFD矩阵, 达到抑制STFD矩阵的交叉项、突出信号自项的目的, 然后利用K均值聚类提取各信号时频点, 最后运用MUSIC算法估计DOA.对不同角度间隔和不同信噪比时三种算法的估计均方根误差进行了仿真对比, 结果表明:相比经典时频MUSIC算法, 文中算法在小角度间隔和低信噪比时有更好的估计性能.     

基于时频分析的多跳频信号盲检测

为了减小低信噪比下干扰和噪声对跳频信号检测的影响,提出一种基于时频分析的多跳频信号盲检测算法.针对跳频信号、定频信号、高斯白噪声具有的不同时频分布特点,该算法利用短时傅里叶变换得到的时频图构造时频对消比;理论分析得到各信号的时频对消比是不同的,因此将其作为检测统计量,实现高斯白噪声背景下跳频、定频信号的盲检测.仿真结果...     

基于排序时频特性的雷达脉内调制信号识别

提出了一种基于排序时频特性的雷达脉内调制信号识别算法.该算法可分为三步:首先,通过检验信号时频曲线的互易回归特性,识别出线性调频信号;然后,通过检验信号时频RANKIT图的正态性,识别出常规信号;最后,检验信号平方后时频RANKIT图的正态性,用以区分二相编码与四相编码信号.仿真结果表明,该算法无需接收信号的任何先验知识,在较低信噪比条件下可实现对常用雷达脉内调制方式的有效识别.     

Volterra series representation of time-frequency distributions

This paper addresses a Volterra series representation of bilinear (or quadratic) time-frequency distributions that belong to Cohen's class, whereby the analogy of the bilinear class with a second-order double Volterra series is utilized. In addition, a different viewpoint for the bilinear kernel and a complementary interpretation concerning the quadratic time-frequency distributions are provided.     

Robust time-frequency distributions based on the robust short time fourier transform

Design of time-frequency distributions (Tfds) that are robust to the impulse noise influence is considered. The robustTfds based on the robust short-time Fourier transform (Stft) are proposed. An efficient procedure to evaluate the robustStft is given. RobustTfds based on the robustStft have better energy concentration around the signal instantaneous frequency (If) than the robustStft itself. Also, theseTfds are more resistant to higher impulse noise than the robustTfds obtained using the local autocorrelation function (Laf) based minimization problem.     

Nonlinear adaptive prediction of nonstationary signals

We describe a computationally efficient scheme for the nonlinear adaptive prediction of nonstationary signals whose generation is governed by a nonlinear dynamical mechanism. The complete predictor consists of two subsections. One performs a nonlinear mapping from the input space to an intermediate space with the aim of linearizing the input signal, and the other performs a linear mapping from the new space to the output space. The nonlinear subsection consists of a pipelined recurrent neural network (PRNN), and the linear section consists of a conventional tapped-delay-line (TDL) filter. The nonlinear adaptive predictor described is of general application. The dynamic behavior of the predictor is demonstrated for the case of a speech signal; for this application, it is shown that the nonlinear adaptive predictor outperforms the traditional linear adaptive scheme in a significant way     

Results on AR-modelling of nonstationary signals

Modelling of nonstationary signals can be performed using time-varying AR-models. The time-dependent AR-coefficients are assumed to be well represented by a linear combination of a small number of known time functions. This paper intends to compare two methods for the identification of such models. The first one is a blockwise method in which the parameters are estimated using the Morf-Dickinson-Kailath-Vieira algorithm for the resolution of covariance equations. In the second method, the identification is performed by a recursive least-squares algorithm. Finally, an extension of the second method for the detection of abrupt changes in AR-processes is presented.