多维非平稳信号的时频分析方法研究

时频分析方法能够同时描述信号在时间和频率域的能量密度与分布情况,为非平稳信号处理提供了有力的工具。文中对非平稳信号的双线性时频分析方法进行了讨论,分析了几种固定核函数的Cohen类分布在典型非平稳信号时频分析中的优缺点;详细讨论并实现了多维信号的Cohen类分布,比较了几种固定核函数的Cohen类分布分析多维信号时在抑制交叉项、自项分辨率保持方面的优缺点与核函数参数选择问题。     

时频分布的分辨率比较

利用时频聚集性较好的高斯函数作为标准信号,分析了短时傅里叶变换、小波变换、谱图、尺度图、Wigner-Ville分布的分辨率以及交叉项对分辨率的影响,并对它们的分辨率进行了比较;为了进行时间-尺度分布与时频分布的比较,提出了改进小波变换;在分辨率比较中,给出了几种典型情况的模拟结果.     

基于稀疏时频分布的跳频信号参数估计

基于常规时频分析方法的跳频信号参数估计中,采用核函数抑制时频分布交叉项会导致时频聚集性的下降,不利于信号参数提取。针对此问题,该文提出一种基于稀疏时频分布(STFD)的跳频信号处理方法。该方法首先根据Cohen类分布的原理和跳频信号模糊函数的特点,以模糊域矩形窗为核函数,构建了一种Cohen类的矩形核分布(RKD)。RKD可有效抑制交叉项,但其时频分辨率较低。为提高RKD的时频性能,在压缩感知框架下,利用跳频信号时频分布的稀疏特性,对RKD附加稀疏性约束,建立稀疏时频分布(STFD)的优化求解模型。STFD不仅能有效抑制交叉项,而且具有良好的时频聚集性。仿真分析表明,与传统时频分析方法相比,该文提出的基于STFD的跳频信号参数估计方法性能更优。     

基于发动机冷试的非平稳信号分析与特征提取

联合时频是分析非平稳信号的有力工具,文章通过几种时频分析如STFT、Wigner-Ville分布、小波变换和小波能量商,对发动机冷试振动信号进行分析。结果表明:STFT、WV、及WT均能一定程度反应信号的时频分布,STFT频率分辨率有限,WV分布存在一定的交叉干扰项,小波变换能够在各个尺度对信号进行观察,小波包能量商能够清楚地观察信号的能量分布,能够作为发动机状态的特征向量。     

复小波包域复数高斯尺度混合模型图像降噪

提出一种基于四树复小波包变换(QCWPT)复数高斯尺度混合(CGSM)模型的图像去噪新方法。含噪图像经多尺度QCWPT被分解成一个低频复数逼近子图和若干高频复数方向细节子图。在大尺度下,可认为低频逼近子图为信号复系数予以保留;对各尺度复数方向子图按照对数熵代价函数确定最优复小波包基。把能很好刻画小波系数边缘分布形状和局部邻域强相关性的高斯尺度混合(GSM)模型扩展到复小波域,新的CGSM模型具有很好刻画图像幅值和相位信息的能力,并利用该模型对复系数进行贝叶斯最小均方(BLS)估计,从而实现去噪目的。实验结果表明,无论是峰值信噪比(PSNR)指标还是视觉效果,本文方法的去噪性能均好于双树复小波变换(DCWT)、QCWPT和小波域GSM模型去噪,并且在有效去噪的同时,具有很好的图像边缘和细节保护能力。     

二次时频表示中核函数的优化设计

二次时频分布是分析非平稳信号的有力工具，在具有许多优良特性的同时，存在严重的交叉干扰项。在Wigner-Ville分布及Cohen类时频分布具有固定核函数的基础上，研究了基于信号的核函数优化设计的两种方法，径向高斯核函数和最优相位核函数的设计方法。基于信号的核函数的时频表示可以有效地抑制或转移交叉分量，提高时频表示的可读估计，改善其主要性能。     

小波变换用于快速跳频信号的测频

小波变换具有局部显微特性,对瞬时信号有较强的捕获能力。该文从连续小波变换与离散小波变换的定义出发,分析了小波变换的带通滤波特性与分析尺度的关系,并通过比较不同尺度下小波变换结果,得到了一个小波变换测频方法,理论与仿真结果表明,与傅立叶交换相比,该方法可以大大改善快速跳频信号的测频精度与抗噪声性能。     

基于小波包变换的分数阶光学加密技术研究

提出一种基于小波包变换(WPT)的分数阶光学图 像加密方法。利用WPT能够对图像多层次分解的特性,结合分数傅里叶变换(FRFT)的灵活性 ,将双随机相位、小波函数的类型及尺度因子和分数阶次作为密钥, 实现了图像的多重密钥加解密。同时,实现了图像小波域上的选择性加密,使加密样式变得 更灵 活多样,还增强了加密图像的抵抗恶意的攻击能力。数值模拟了加密和解密过程,分析了加 密效果和解密图像质量,验证了本文方法的可行性。     

基于小波域隐马尔科夫树模型的图像分割

改进了传统的基于小波域隐马尔科夫树模型的图像分割方法.由于传统方法均为直接选择小波子带系数作为训练特征,不能直接得到像素级分割结果;同时传统方法在后融合方面对所有尺度均采用同一种上下文背景,而忽略不同尺度上初分割类标志图的特点.因此,本文在粗分割阶段首先处理了训练时参数设置的问题,并选取了更能表征纹理的特征,能直接得到像素级分割结果;在多尺度融合阶段,充分利用不同尺度上类标志图的特性,不仅考虑粗尺度信息对融合结果的影响也考虑了细尺度信息对结果的影响.实验表明本文算法的视觉效果好干与本文进行比较的Choi提出的HMTseg以及孙强提出的WD-HMTseg遥感图像分割算法.     

基于小波模极大值能量的船舶轴频电场检测

为了有效地从海洋环境电场背景中检测微弱的船舶轴频电场信号,对轴频信号小波模极大值的尺度分布特性进行了分析,在得出轴频观测信号中噪声模极大值的幅度和分布稠度均随尺度增大而减小的结论的基础上,通过提取最大分解尺度的模极大值能量作为特征值,利用滑动检测方法对目标进行检测,并且避免了小波模极大值的重构过程,因而计算量小,检测速度较快.最后,分别使用实测数据和仿真数据对该算法进行了验证,结果表明此算法在低信噪比情况下具有较好的检测效果,当SNR为-10.8dB时仍然具有79%的检测率.     

On generalized-marginal time-frequency distributions

We introduce a family of time-frequency (TF) distributions with generalized marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitude squared of the fractional Fourier transforms of the signal. We present a necessary and sufficient condition for a TF distribution in Cohen's class to satisfy generalized marginals. We then modify the existing well-known TF distributions in Cohen's class, such as Choi-Williams (1989) and Page distributions, so that the modified ones have generalized marginals. Numerical examples are presented to show that the proposed TF distributions have the advantages of both Wigner-Ville and other quadratic TF distributions, which only have the conventional marginals. Moreover, they also indicate that the generalized-marginal TF distributions with proper marginals are more robust than the Wigner-Ville and the Choi-Williams distributions when signals contain additive noise     

Time-frequency kernel design by the two-dimensional frequencytransformation method

A subclass of Cohen's class of time-frequency (TF) distributions is introduced in which the TF distribution kernels are provided via the frequency transformation method (FTM), used in two dimensional (2-D) filter design. The FTM kernels have finite extent in time and frequency and allow the TF distribution to be efficiently implemented in all four domains     

非线性调频信号的自适应时频滤波算法

针对传统的时域或频域滤波算法对非线性调频信号滤波去噪效果不好的问题,本文提出了一种时频域内非线性调频信号的自适应滤波去噪算法。首先对原信号进行广义S变换获得其时频分布,接下来利用有效信号时频分布特性选取时频通域,构造区域滤波算子并去除掉时频通域外的噪声分量的时频分布;然后利用有效信号分量的时频聚集性构造自适应时频滤波算子,对含有随机噪声的有效信号分量进行滤波处理,得到滤波去噪后的信号的时频分布;最后利用广义S逆变换将处理后的时频分布变换到时间域,得到滤波去噪后的信号。通过仿真实验的结果可知,本文提出的算法在非线性调频信号的滤波去噪和有效特性保持方面取得了较好的效果。      

分形随机噪声信号处理的小波谱相关方法

提出了广义小波谱相关的概念,简要分析了其基本性质及其与谱相关的关系,通过对白噪声的谱相关和小波谱相关特性的研究,推导出分形噪声的小波谱相关函数,通过与白噪声的对比研究,分析了分形随机噪声在小波谱相关域的特性.考虑实际海杂波的特性,提出了一种分形噪声调幅调频的海杂波模型,分析了海杂波在小波谱相关域的表现,体现了小波谱相关对海杂波处理的优势.利用小波谱相关对分形噪声背景下的伪码脉冲串信号进行了识别仿真,结果表明该方法能有效抑制分形噪声,准确提取信号参数.     

On alias-free formulations of discrete-time Cohen's class ofdistributions

The transition of the Cohen's (1989) class of distributions from the continuous-time case to the discrete-time case is not straightforward because of aliasing problems. We classify the aliasing problems, which occur for joint time-frequency representations (TFRs), into two categories: type-I and type-II aliasings. Type-I aliasing can be avoided by properly defined discrete-time versions of some members of Cohen's class (in particular, properly defined kernels), whereas type-II aliasing can be reduced and/or eliminated by increasing the sampling rate. A type-I alias-free formulation of the discrete-time Cohen's class (AF-DTCC), which is equivalent to the AF-GDTFT of Joeng and Williams (see ibid., vol.40, no.2, p.1084, 1992) is then introduced based on the fact that the Cohen's class can be expressed as the 2-D Fourier transform of the generalized ambiguity function (AF). Based on this definition, two discretization schemes for kernel functions are presented in both the AF domain and the time-lag domain, and are shown to be equivalent under certain conditions. We also do the following: (1) we show that a discrete-time Wigner-Ville distribution (DWVD) and discrete-time spectrogram (DSPG) are type-I alias-free and members of AF-DTCC; (2) we use all the available correlation information from a given data sequence by using the Woodward AF instead of the Sussman AF; (3) we give kernel constraints in the AF domain for various distribution properties; and (4) we provide a type-I and type-II alias-free formulation for those distributions whose kernel functions satisfy the finite frequency-support constraint     

Time-Width Versus Frequency Band Mapping of Energy Distributions

Most of the signal processing operations involve some kind of a transformation or approximation of the signal. The transform coefficients or the approximation parameters reveal many hidden characteristics of a signal that can be appropriately processed to extract useful information. In recent years, adaptive time-frequency (TF) transformations have significantly contributed to this area. The TF transformation can be classified into two main categories based on 1) signal decomposition approaches and 2) bilinear TF distributions (also known as Cohen's class). TF distributions are nonparametric in nature and mainly used for visualization purposes. On the other hand, decomposition approaches are parametric in nature and highly suitable for objective feature extraction. This paper focuses on a particular TF decomposition approach (adaptive TF transformation) based on matching pursuit-type algorithm. Using this decomposition approach, a novel time-width versus frequency band (TWFB) energy mapping is proposed that possesses both parameterization benefits and meaningful visual patterns with favorable properties for pattern recognition. This organized mapping of the TF decomposition parameters allows the application of pruning algorithms such as local discriminant bases (LDB) to identify application specific TF subspaces. The identification of these subspaces enables efficient processing of information and reduces the computational effort considerably. The visual patterns of the TWFB mappings exhibit high potential of becoming a powerful pattern analysis tool. The paper covers in detail the formulation of the TWFB mapping and some of its properties. Experiments performed with speech and synthetic signals produced desirable results demonstrating the benefits of TWFB for pattern recognition related applications     

Alias-free generalized discrete-time time-frequency distributions

A definition of generalized discrete-time time-frequency distribution that utilizes all of the outer product terms from a data sequence, so that one can avoid aliasing, is introduced. The new approach provides (1) proper implementation of the discrete-time spectrogram, (2) correct evaluation of the instantaneous frequency of the underlying continuous-time signal, and (3) correct frequency marginal. The formulation provides a unified framework for implementing members of Cohen's class, which was formulated in the continuous-time domain. Some requirements for the discrete-time kernel in the new approach are discussed in association with desirable distribution properties. Some experimental results are provided to illustrate the features of the proposed method     

小波包域值法去除合成孔径雷达图像斑点噪声

合成孔径雷达(SAR)图像的斑点噪声使图像的解译能力明显降低,影响了SAR图像的应用,去除图像斑点噪声是SAR图像处理及应用的前提。去除的方法在图像域有很多,在频率域,也有基于FFT变换和小波变换的许多方法。文中根据沙漠地区的SAR图像的特点,对基于图像域和频率域的几种滤波方法进行了比较,提出了一种基于小波包变换的SAR图像斑点噪声去除方法,结果表明该方法既去除了斑点噪声,又保持了边缘特征信息。     

一种基于小波相位滤波及视觉非线性的医学图像自适应增强新方法

针对经典方法对ＳＮＲ低的医学图像存在噪声过度放大及伪像产生问题,本文在精细尺度上,根据信号与噪声的ＷＴ相位在相继尺度上关联性的不同进行去噪,在大尺度上则采用Ｓｅｍｉｓｏｆｔ阈法对ＤＷＴ系数进行快速缩减去噪,根据人眼的视觉特性对ＷＴ系数的增益进行非线性的自适应控制,较之经典方法,本文方法具有增强图像视觉效果佳,无伪像产生的优点,且在噪声抑制、保边沿及增强各种细节上效果良好。     

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。