线性正则变换域的复能量密度函数

线性正则变换是经典Fourier变换的广义形式,目前在非平稳信号的参数检测与估计方面取得了优异的应用效果,但线性正则变换理论体系还不完善.探讨了线性正则变换相关的复能量密度函数的基本概念,并详细推导研究了其基本的数学性质与特点,在上述理论的基础上,通过仿真实验来验证所得到结论的准确性.为其在实际应用中发挥更大的作用奠定了基础.     

基采用时频区域检测的雷达信号盲分选算法

为了解决欠定条件下密集雷达信号分选问题,提高雷达信号盲分选算法精度,提出了一种采用时频区域检测的雷达信号盲分选算法,首先利用短时傅立叶变换将混合信号映射至时频平面进行处理,然后通过聚类算法估计出混合矩阵,从而反解出源信号矩阵,进而估计出每一雷达源信号,能够在信号的时频平面投影相交且欠定的条件下,实现信号分选功能.仿真实验结果表明:提出的算法相比于传统的类MUSIC算法及其衍生的相关改进算法具有更高的分选精度和算法收敛性,且估计得到的源信号时域波形更优,体现了其有效性和优越性.     

一种新的信号处理方法——线调频小波变换

线调频小波变换是处理非平稳信号一种新的方法 .本文分析了线调频小波变换是短时 Fourier变换和小波变换的时频分析的统一形式 ,并能根据信号的特点生成新的时频分析方法 ,说明了线调频小波变换具有传统处理方法无法比拟的优点     

可加模型的无交叉分位回归曲线与房价问题研究

高维数据分析是当前研究的热点话题,而在对其进行分析时,非参数方法由于其灵活,无需对模型进行假定,得到了广泛的发展和认可。其中可加模型不仅能够有效地对变量进行降维,避免"维数灾难"的发生;而且能够得到各个变量的边际效应,具有很好的解释性。为了得到更加稳健的估计量,本文考虑利用分位回归方法对可加模型进行估计。分位回归方法由于其能够全面地刻画因变量在各个分位点上的变化趋势,并不受误差分布的限制,使得该方法具有更广泛的应用性。本文综合考虑以上优势,提出局部线性最小化检验函数估计方法和局部线性双核估计方法对可加模型进行估计。并且该方法能够有效地避免可加模型分位回归曲线的交叉问题.蒙特卡洛结果显示,与传统的均值估计法相比,不论误差分布的形式,我们提出的方法更具有优越性。用北京市二手房房价数据进行实证分析,进一步验证了本文提出的估计方法。     

部分线性混合效应模型中方差分量的稳健估计

部分线性混合效应模型中方差分量是我们感兴趣的参数, 文献中已经给出许多估计方法. 但是其中很多方法都可以归结为广义估计方程方法(GEE), 如: 最大似然估计(MLE), 约束最大似然估计(REMLE)等, 而GEE方法对异常点很敏感. 本文提出一组关于部分线性混合效应模型(PLMM)中均值和方差分量的稳健估计方程, 对均值和方差分量同时进行稳健估计; 并进行了随机模拟考察所提出稳健估计的有效性, 最后通过两个实例, 说明了所提方法的可行性.     

最小二乘法的多角度分析及其应用

在现代工程领域,经常遇到数据处理问题,这类问题很多时候需要利用最小二乘法进行求解.本文从多元函数微分学、线性代数、数理统计三个角度详细解释了这一方法的原理,并简要介绍了最小二乘法在高光谱图像线性解混和信号估计中的应用.     

加权平衡损失函数下回归系数的最佳线性无偏估计

这篇文章我们研究了回归系数的最佳线性无偏估计. 在加权平衡损失函数下, 我们得到了回归系数的最佳线性无偏估计. 同时提出了度量最佳线性无偏估计和最小二乘估计的相对效率. 并且我们给出了它们的上下界.     

多元线性模型中回归系数的线性可容许估计

基于Zellner的平衡损失的思想,本文提出了矩阵形式的平衡损失函数,并在该损失函数下讨论了多元回归系数线性估计的可容许性.给出了六种不同形式的可容许定义,证明了这六种容许性在齐次和非齐次线性估计类中是一致的,且得到了其共同的可容许估计的充要条件.     

部分线性模型的随机约束岭估计

研究了部分线性回归模型附加有随机约束条件时的估计问题.基于Profile最小二乘方法和混合估计方法提出了参数分量随机约束下的Profile混合估计,并研究了其性质.为了克服共线性问题,构造了参数分量的Profile混合岭估计,并给出了估计量的偏和方差.     

因变量缺失下线性变量含误差模型的估计

主要考虑线性模型在自变量测量含误差以及因变量缺失情况下的估计问题.对于模型中的回归系数,我们基于最小二乘方法提出了两类估计,其中一类估计只由完整观测数据构成,而另外一类估计利用的则是利用简单插补方法构造的完整数据.证明了这两类估计是渐近正态性的.     

Uncertainty principles associated with the offset linear canonical transform

As a time‐shifted and frequency‐modulated version of the linear canonical transform (LCT), the offset linear canonical transform (OLCT) provides a more general framework of most existing linear integral transforms in signal processing and optics. To study simultaneous localization of a signal and its OLCT, the classical Heisenberg's uncertainty principle has been recently generalized for the OLCT. In this paper, we complement it by presenting another two uncertainty principles, ie, Donoho‐Stark's uncertainty principle and Amrein‐Berthier‐Benedicks's uncertainty principle, for the OLCT. Moreover, we generalize the short‐time LCT to the short‐time OLCT. We likewise present Lieb's uncertainty principle for the short‐time OLCT and give a lower bound for its essential support.     

Uncertainty principles associated with quaternionic linear canonical transforms

In the present paper, we generalize the linear canonical transform (LCT) to quaternion‐valued signals, known as the quaternionic LCT (QLCT). Using the properties of the LCT, we establish an uncertainty principle for the two‐sided QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion‐valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternionic signal minimizes the uncertainty. Copyright © 2016 John Wiley & Sons, Ltd.     

A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation

To model a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes is important to extract information, such as the underlying dynamics, hidden in the signal. Recently, the synchrosqueezed wavelet transform (SST) and its variants have been developed to estimate instantaneous frequencies and separate the components of non-stationary multicomponent signals. The short-time Fourier transform-based SST (FSST for short) reassigns the frequency variable to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. However, FSST works well only with multicomponent signals having slowly changing frequencies. To deal with multicomponent signals having fast-changing frequencies, the second-order FSST (FSST2 for short) was proposed. The key point for FSST2 is to construct a phase transformation of a signal which is the instantaneous frequency when the signal is a linear chirp. In this paper we consider a phase transformation for FSST2 which has a simpler expression than that used in the literature. In the study the theoretical analysis of FSST2 with this phase transformation, we observe that the proof for the error bounds for the instantaneous frequency estimation and component recovery is simpler than that with the conventional phase transformation. We also provide some experimental results which show that this FSST2 performs well in non-stationary multicomponent signal separation.     

An image adaptive, wavelet-based watermarking of digital images

In digital management, multimedia content and data can easily be used in an illegal way—being copied, modified and distributed again. Copyright protection, intellectual and material rights protection for authors, owners, buyers, distributors and the authenticity of content are crucial factors in solving an urgent and real problem. In such scenario digital watermark techniques are emerging as a valid solution. In this paper, we describe an algorithm—called WM2.0—for an invisible watermark: private, strong, wavelet-based and developed for digital images protection and authenticity. Using discrete wavelet transform (DWT) is motivated by good time-frequency features and well-matching with human visual system directives. These two combined elements are important in building an invisible and robust watermark. WM2.0 works on a dual scheme: watermark embedding and watermark detection. The watermark is embedded into high frequency DWT components of a specific sub-image and it is calculated in correlation with the image features and statistic properties. Watermark detection applies a re-synchronization between the original and watermarked image. The correlation between the watermarked DWT coefficients and the watermark signal is calculated according to the Neyman–Pearson statistic criterion. Experimentation on a large set of different images has shown to be resistant against geometric, filtering and StirMark attacks with a low rate of false alarm.     

Theory, implementation and applications of nonstationary Gabor frames

Signal analysis with classical Gabor frames leads to a fixed time-frequency resolution over the whole time-frequency plane. To overcome the limitations imposed by this rigidity, we propose an extension of Gabor theory that leads to the construction of frames with time-frequency resolution changing over time or frequency. We describe the construction of the resulting nonstationary Gabor frames and give the explicit formula for the canonical dual frame for a particular case, the painless case. We show that wavelet transforms, constant-Q transforms and more general filter banks may be modeled in the framework of nonstationary Gabor frames. Further, we present the results in the finite-dimensional case, which provides a method for implementing the above-mentioned transforms with perfect reconstruction. Finally, we elaborate on two applications of nonstationary Gabor frames in audio signal processing, namely a method for automatic adaptation to transients and an algorithm for an invertible constant-Q transform.     

基于分数阶Fourier变换的结构瞬时频率识别北大核心CSCD

为识别时变信号的瞬时频率,由分数阶Fourier变换定义推导出了一般信号的频率与单一变量旋转角度α的关系式,从理论上解释了分数阶Fourier变换本质上是一种普通Fourier变换结合伸缩平移窗的算法,进而在分数阶Fourier域建立了非平稳信号瞬时频率的一般表达式,实现了结构瞬时频率的识别.采用任意非线性调频信号仿真算例和三自由度有阻尼时变结构系统的数值算例对提出的方法进行了比较分析.结果表明,该文提出的方法与理论值吻合良好,并具有一定的抗噪性,验证了方法的可靠性和实用性,可以应用于时变结构瞬时频率的识别.     

Octonion short-time linear canonical transform

We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT.     

Fractional time-varying energy distributions of ECG signals

We introduce here fractional Cohen class of time-frequency distributions (FCCTFDs) containing fractional modulations which is kernel of fractional Fourier transform (FFT). The fractional modulation depends on angular parameter α and can be interpreted as a rotation by an angle α in time-frequency plane. This distribution promotes to track time-variant energy of a biological signals and represents it in time-frequency domain. It uses the fractional ambiguity function (FAF) of signal multiplied by a suitable kernel which is designed for the biological signals generally having multi-non-stationary components. This result improves and generalizes some of the previous time-frequency distributions derived in the literature.