基于Gabor变换的对星载合成孔径雷达电子侦察信号的检测和特征分析研究

随着星载合成孔径雷达各种性能的不断提高,以常规参数测量作为特征的信号识别技术很难满足电子侦察的需求,基于雷达信号的脉内细微特征分析技术已经成为当前电子侦察的重要发展方向.为了提高在低信噪比条件下对雷达脉冲信号的检测概率和参数估计能力,本文使用了直接采样信号的Gabor变换进行信号检测和特征分析.Gabor变换是按照信号的先验知识选择合适的基函数,获得只有少数几个系数的Gabor展开,从而能够对信号作比较精确的表示.通过使用Gabor系数做检测统计量做噪声背景下的信号检测,可以得到雷达时域的常规参数.信号检测后得到的信号Gabor变换可以对信号的脉内细微特征进行分析.通过对脉内细微特征的分析可以获得敌方合成孔径雷达的技术参数,从而对它的用途和工作模式进行有效的推测.为了验证算法的有效性,本文进行了实测数据的分析实验.通过实验,本文使用的分析方法可以有效地用于雷达侦察信号检测和脉内细微特征分析,可以为后续处理提供有力的技术信息支撑.     

线性正则变换域的框架理论研究

框架理论是研究信号采样特别是非均匀采样问题的一个重要工具,基于框架理论的Gabor展开是在时频混合空间描述信号的非正交展开,而Weyl-Heisenberg框架理论是Gabor展开的理论基础,它描述了信号在时频平面的局部性质与特点,在信号的短时Fourier变换(STFT)、Gabor展开中起到非常重要的作用.本文探讨了W-H框架在线性正则变换下的特点,得到了在时域和线性正则变换域联合空间中信号的展开形式,为在线性正则变换域中讨论信号的展开和非均匀采样问题打下了良好的理论基础.     

用Gabo:展开进行地震数据的滤波

Gabor展开是用一组在时域及频域都局部化且具有能量集中性质的函数来展开信号,这种特征使得Gabor展开适于处理那些时间无关或非平稳的信号。利用框架理论,类似于SVD特征映像滤波方法,本文用Gabor展开滤波方法来进行地震信号的去噪处理。仿真结果显示出Gabor展开滤波方法的优越性。     

Zak变换在Gabor展开理论中的应用

利用离散Zak变换及其性质,本文首次给出了在过采样条件下,频域离散Gabor展开系数与时域离散Gabor展开系数之间的简捷关系,这对Zak变换的应用和完善Gabor展开理论是很有意义的,论文最后给出了计算实例。     

从噪声中恢复瞬态信号的Gabor级数法

该文研究了从噪声中恢复原瞬态信号问题。根据瞬态信号和噪声的Gabor系数在时-频平面上分布不同的特点,借用假设检验理论,提出了一种恢复被噪声污染的原瞬态信号的Gabor级数方法,进行了计算机仿真和对实际信号的处理。     

实值离散Gabor变换块时间递归算法的并行格型结构实现方法

Gabor变换在很多领域被认为是非常有用的方法,如语音与图像处理,雷达、声纳、振动信号的处理与理解等,然而实时应用却因其很高的计算复杂性而受到限制.为了减小计算复杂性,我们曾提出了实值离散Gabor变换法.本文首先简单回顾了作者曾提出的实值离散Gabor变换及其与复值离散Gabor变换的关系,然后为了有效地和快速地计算实值离散Gabor变换,提出了在临界抽样条件下和在过抽样条件下,一维实值离散Gabor变换系数求解的块时间递归算法以及由变换系数重建原信号的块时间递归算法,研究了两算法使用并行格型结构的实现方法,并讨论和比较了算法的计算复杂性和优越性.     

优化Gabor小波权重的EBGM算法

在EBGM算法中,计算人脸特征点的相似度时,认为每个Gabor小波系数对结果的影响是相同的,从而给予所有系数同等权重,但实验测试表明情况并非如此.充分挖掘了人脸的统计特性,通过对不同特征点在频域分布特征的提取,提出一种对Gabor小波系数进行分类并赋予其不同权重的优化方法.实验测试证明,该算法能有效地提高识别率.     

数字信号处理中的滑窗表示

离散时间信号的短时付里叶变换解释为滑窗谱,它是信号加窗后的付氏变换。这种滑窗谱是两个变量的函数:一是离散时间指数,它表示窗口的位置;二是连续频率变量.文章证明了信号可以由取样了的滑窗谱重建,也就是由滑窗谱在特定的时间频率域中点阵上各点的值来重建。取样点阵是矩形的,矩形元素在时间频率域上的面积为2π。本文证明,一种直接根据滑窗谱的取样值来表示信号的精微方法是Gabor 信号表示法。为此引入了互易窗的概念,并且阐明了窗和互易窗是怎样联系在一起的,Gabor 信号表示法将信号表示成由互易窗经适当移位和调制以后的展开式,展开系数就是取样了的滑窗谱的值。     

基于Gabor-Curvelet联合变换的雷达Chirp信号检测与估计

针对微弱雷达回波Chirp信号检测与估计问题,提出基于Gabor-Curvelet联合变换的方法。首先计算回波的Gabor时频变换,得到2D时频分布图,噪声时频分布一般随机地分布在整个时频面上,能量分散,而Chirp信号时频分布是直线或曲线。对时频2D图像进行曲波（curvelet）变换,曲波能对曲线进行稀疏表示,可检测强噪声中的雷达回波Chirp信号并估计信号参数。仿真结果证明了此方法的有效性,有待研究的问题是曲波系数的门限设定问题。     

基于Gabor变换的超声回波信号时频估计

在无损检测中,超声回波往往是一个重叠较严重,含有噪声的多回波信号。根据Gabor变换时频分析的特点,该文提出一种基于Gabor变换的超声回波信号时频估计方法。该文建立回波信号与Gabor变换分析窗函数相似度(即距离)模型,通过模型相似度最小化问题转化为求解回波信号Gabor变换系数模的最大值来估计回波信号的传播时间(TOF)和中心频率(CF),最后推导它们的克拉美-罗界(CRLB)以评价算法的性能。Monte Carlo仿真和实验结果表明该文提出的算法,无论对低信噪比的单回波信号或重叠的多回波信号都能达到较高的精度,而且估计的均方误差在高信噪比时,达到CRLB,即使在低信噪比,也接近CRLB。     

基于重排Gabor谱方法的跳频信号参数估计

对接收到的跳频信号进行时频分析是跳频信号参数估计的重要步骤。利用重排方法对信号的时频谱图进行重排,有效地抑制了交叉干扰项,提高了信号的时频聚集性并且改善了信号时频谱图的可读性。对跳频信号的Gabor谱进行重排,能够在低信噪比条件下估计出跳频信号的跳频周期、跳变时刻和跳频频率等参数。仿真结果表明,与Gabor谱方法比较,采用重。排Gabor谱方法对跳频信号进行分析,提高了跳频信号的跳频周期和跳变时刻估计的准确性。     

Shear madness: new orthonormal bases and frames using chirpfunctions

The proportional-bandwidth and constant-bandwidth time-frequency signal decompositions of the wavelet, Gabor, and Wilson orthonormal bases have attracted substantial interest for representing nonstationary signals. However, these representations are limited in that they are based on rectangular tessellations of the time-frequency plane. While much effort has gone into methods for designing nice wavelet and window functions for these frameworks, little consideration has been given to methods for constructing orthonormal bases employing nonrectangular time-frequency tilings. The authors take a first step in this direction by deriving two new families of orthonormal bases and frames employing elements that shear, or chirp, in the time-frequency plane, in addition to translate and scale. The new scale-shear fan bases and shift-shear chevron bases are obtained by operating on an existing: wavelet, Gabor (1946), or Wilson basis set with two special unitary warping transformations. In addition to the theoretical benefit of broadening the class of valid time-frequency plane tilings, these new bases could possibly also be useful for representing certain types of signals, such as chirping and dispersed signals     

稀疏重构下的非线性调频信号参数估计算法

非线性调频信号广泛应用于雷达声纳领域，其具有多阶多项式相位、未知参数多的特点，给参数估计带来困难。针对此问题，本文提出一种稀疏重构下的非线性调频信号参数估计算法。该方法利用Gabor原子良好时频特性，以 范数稀疏正则最小二乘模型为目标函数，并推导了问题的二阶锥规划（SOCP）形式，最终通过求解的Gabor原子进行参数估计。算法分析信号的时频特征，完成信号的分解重构，适应于各类调频信号。仿真实验证明，本文算法对调频信号二阶与一阶相位参数估计精度都贴近CRB，而对二阶参数的估计较二次相位差分算法更适应较低信噪比。      

基于Gabor空间的未知调频率LFM信号压缩采样与重构

针对现有压缩采样系统在宽带线性调频信号压缩采样过程中存的采样系统不适用、调制信息依赖等问题,提出了一种基于Gabor空间的线性调频信号压缩采样与重构方法,在未知调频率的条件下,实现了线性调频信号的压缩采样与有效重构。首先,结合压缩感知以及平移不变空间理论,设计了基于Gabor空间的压缩采样系统,分析了压缩采样系统组成部分以及工作原理。然后,利用信号在Gabor空间的稀疏性,建立了Gabor系数的压缩重构模型,并在充分考虑噪声、失配的条件下,分析了原始信号重构误差上界。最后,通过数值仿真实验,验证了所提方法的有效性,实验结果表明,基于Gabor空间的压缩采样系统具有采样频率低,采样点数少,以及工作稳定性高等优点。      

Noise reduction for NMR FID signals via Gabor expansion

The parameters in a nuclear magnetic resonance (NMR) free induction decay (FID) signal contain information that is useful in biological and biomedical applications and research. A real time-sampled FID signal is well modeled as a finite mixture of modulated exponential sequences plus noise. The authors propose to use the generalized Gabor expansion for noise reduction, where the generalized Gabor expansion represents a signal in terms of a collection of time-shifted and frequency-modulated versions of a single sequence (prototype sequence). For FID signal-fitting, the authors choose the exponential sequence as the prototype function. Using the generalized Gabor expansion and exponential prototype sequences for FID model-fitting, an NMR FID signal can be-well represented by the Gabor coefficients distributed in the joint time-frequency domain (JTFD). The Gabor coefficients reflect the weights of modulated exponential sequences in a signal. One of the important features is that the nonzero Gabor coefficients of a modulated exponential sequence will span a very small area in the JTFD, whereas the Gabor coefficients of the noise will not. If the exponent constant of the prototype sequence in the generalized Gabor expansion matches that of a modulated exponential sequence in the signal, then only one of the Gabor coefficients is nonzero in the JTFD. This is a very important property since it can be exploited to separate a signal from noise and to estimate modulated exponential sequence parameters     

Joint time-frequency analysis

It has been well understood that a given signal can be represented in an infinite number of different ways. Different signal representations can be used for different applications. For example, signals obtained from most engineering applications are usually functions of time. But when studying or designing the system, we often like to study signals and systems in the frequency domain. Although the frequency content of the majority of signals in the real world evolves over time, the classical power spectrum does not reveal such important information. In order to overcome this problem, many alternatives, such as the Gabor (1946) expansion, wavelets, and time-dependent spectra, have been developed and widely studied. In contrast to the classical time and frequency analysis, we name these new techniques joint time-frequency analysis. We introduce the basic concepts and well-tested algorithms for joint time-frequency analysis. Analogous to the classical Fourier analysis, we roughly partition this article into two parts: the linear (e.g., short-time Fourier transform, Gabor expansion) and the quadratic transforms (e.g., Wigner-Ville (1932, 1948) distribution). Finally, we introduce the so-called model-based (or parametric) time-frequency analysis method     

临界抽样Gabor展开的非局部性分析

Ｇａｂｏｒ展开是一在时－频混合空间描述信号的非正交展开。由于展开的非正交性，使得展开系数的计算较为困难。现有的关于Ｇａｂｏｒ展开的文献大都集中在讨论Ｇａｂｏｒ展开的计算，而对临界抽样Ｇａｂｏｒ展开的非局部性问题没有给予足够的重视。本文将证明当临界抽样Ｇａｂｏｒ展开的窗函数为连续或对称函数时，Ｇａｂｏｒ展开不仅存在非局部性问题，而且收敛性也得不到保证。同时我们还将给出临界抽样Ｇａｂｏｒ展开非局部性的     

Gabor expansion for adaptive echo cancellation

A good echo cancellation algorithm should have a fast convergence rate, small steady-state residual echo, and less implementation cost. The normalized least mean square (NLMS) adaptive filtering algorithm may not achieve this goal. We show that using the Gabor expansion is a way to achieve this goal. For direct digital signal processing compatibility the Gabor expansion introduced in this paper is for discrete-time signals, although the Gabor expansion also can be used for continuous-time signals. The Gabor expansion can be defined as a discrete-time signal representation in the joint time-frequency domain of a weighted sum of the collection of functions (known as the synthesis functions). There are several design issues in the echo canceller based on the Gabor expansion: the design of the analysis functions for the far-end speech, the design of the analysis functions for the near-end signal containing the echo plus the near-end speech, the design of the adaptive filters in the subsignal path, and the design of the synthesis functions. All the adaptive filters are designed using identical NLMS adaptive filtering algorithms