Polyspectral analysis of mixed processes and coupled harmonics

Polyspectral analysis of processes with mixed spectra is considered, and scaled polyperiodograms are introduced to clarify issues related to stationarity, ergodicity, and suppression of additive stationary noise in harmonic retrieval problems. Spectral and polyspectral approaches are capable of retrieving (un)coupled harmonics, not only when the harmonics have constant amplitudes, but also when they are observed in nonzero mean multiplicative noise. Fourier series polyspectra and asymptotic properties of scaled polyperiodograms provide general tools for higher order analysis of time series with mixed spectra. A single record phase coupling detector is derived to obviate the assumption of independent multiple records required by existing methods. The novelties are illustrated by simulation examples     

乘法噪声中非线性耦合谐波分析

针对信号的非平稳性质,引入傅里叶级数多谱和比例多周期图的概念,分别提出了零均值乘法噪声二次耦合及非零均值乘法噪声三次耦合谐波频率估计方法,仅使用单个数据记录即可得到耦合频率估计,并且可以抑制加性平稳噪声而无须假定其颜色和分布.最后给出了仿真实验结果.     

Retrieval of self-coupled harmonics

Presence of coupled harmonics in the data is a symptom attributed to nonlinear mechanisms generating the available time series. Self-coupling amounts to presence of frequency pairs (ω₀, kω₀) and perhaps phase pairs (φ₀, kφ₀) as well, with k an integer. It appears in periodic signals, or, when harmonics undergo nonlinear transformations. Self-coupled harmonics observed in additive noise are retrieved from the peaks of diagonal (scaled) polyperiodogram slices, which contrary to existing higher order approaches, do not increase dimensionality and thus computations when dealing with nonlinearities of increasing orders. Performance evaluation of the resulting frequency estimator reveals decreasing variance with slices of polyperiodograms of increasing order, and ability to suppress stationary mixing noise irrespective of its color and distribution. Detection and estimation of self-phase coupling via polyperiodogram slices obviates limitations of existing methods that require availability of multiple independent records. Theory and algorithms are illustrated with simulated and voiced speech data     

NONPARAMETRIC POLYSPECTRAL ESTIMATORS FOR k-TH-ORDER (ALMOST) CYCLOSTATIONARY COMPLEX PROCESSES

Higher-order almost cyclostationary complex processes are complex random signals with almost periodically time-varying statistics, which is important to the research of non-Gaussian signals in information system. In tins paper, smoothed polyperiodograms are proposed for related to cyclic polyspectral estimation and are shown to be consistent and asymptotically complex normal. Asymptotic covariance expressions are derived along with their computable forms.     

Nonparametric polyspectral estimators for kth-order (almost)cyclostationary processes

Second- and higher-order almost cyclostationary processes are random signals with almost periodically time-varying statistics. The class includes stationary and cyclostationary processes as well as many real-life signals of interest. Cyclic and time-varying cumulants and polyspectra are defined for discrete-time real kth-order cyclostationary processes, and their interrelationships are explored. Smoothed polyperiodograms are proposed for cyclic polyspectral estimation and are shown to be consistent and asymptotically normal. Asymptotic covariance expressions are derived along with their computable forms. Higher than second-order cyclic cumulants and polyspectra convey time-varying phase information and are theoretically insensitive to any stationary (for nonzero cycles) as well as additive cyclostationary Gaussian noise (for all cycles)     

基于二维循环统计量的二维谐波信号参数估计

本文利用二维循环统计量方法对二维平稳乘性噪声与二维平稳加性噪声共存情况下的二维谐波信号参数估计问题进行了讨论.利用二维循环统计量能够有效地抑制二维平稳乘性噪声和二维平稳加性噪声的特点,有效地从噪声中提取出信号参数.仿真实验对算法作了说明.     

Nonparametric polyspectral estimators for k-th-order (almost) cyclostationary complex processes

Higher-order almost cyclostationary complex processes are complex random signals with almost periodically time-varying statistics, which is important to the research of non-Gaussian signals in information system. In this paper, smoothed polyperiodograms are proposed for related to cyclic polyspectral estimation and are shown to be consistent and asymptotically complex normal. Asymptotic covariance expressions are derived along with their computable forms.     

复高阶周期平稳信号的非参数多谱估计

本文研究利用平滑周期图作为离散时间k阶复周期平稳过程k阶循环谱估计的相容性和渐近复正态性,并导出了其渐近协方差表达式.     

宽带雷达三维干涉测量弹道目标微动参数估计

宽带雷达微动目标3维干涉测量可为目标运动几何参数估计提供重要信息。该文针对宽带雷达斜视3维干涉测量微动目标参数估计,提出一种斜视校正干涉测量微动几何参数估计方法。方法对L型天线阵列中各天线接收回波进行干涉测距测角,通过建立2元2次非线性方程和坐标变换实现斜视扭曲校正,得到目标散射中心3维运动轨迹,继而采用滤波和优化求解实现目标微动几何参数估计,有效提高了微动目标运动几何参数估计准确性和平滑稳健性。     

一种距离扩展目标的Hough变换检测器

针对宽带雷达信号得到的距离扩展目标在有较大运动速度时积累检测困难的问题,该文提出一种基于Hough变换的检测器(HTD)。利用距离扩展目标高分辨距离像信号的相邻回波之间信号具有较大相关系数这一特点,在互相关序号与相关时间2维平面使用Hough变换进行积累来检测目标。理论推导表明Hough变换检测器不需要目标散射中心分布的先验知识和目标的运动信息,具有恒虚警(CFAR)性能。计算机仿真实验表明Hough变换检测器具有比不依赖散射中心分布信息的广义似然比(NSDD-GLRT)检测器更好的检测能力。     

基于遗传算法的复杂背景噪声中二维谐波的二次耦合分析

本文利用二维循环统计量方法对乘性噪声之间相关,乘性噪声和加性噪声之间也相关这种复杂噪声背景中二维谐波的二次非线性耦合问题做了分析。利用当且仅当二维谐波中存在二次非线性耦合谐波时,所定义的二维三阶时间平均矩谱仅在参与二次耦合谐波频率处取得极值的性质,提出了采用遗传算法来分析二维谐波的：二次非线性耦合问题的算法。仿真实验证明了算法的有效性。     

基于组合CPF变换的混合低阶相位调制信号参数估计

由线性调频信号（LFM）、三阶多项式相位调制信号（QFM）混合而成的信号在三阶相位函数随机变换（RCT算法）下可实现相位参数估计,但是当信号参数相近时算法存在峰值干扰现象。针对此情况,提出一种组合CPF变换,首先通过ICPF算法估计LFM信号相位参数,然后利用估计得到的参数重构LFM信号,以消去混合信号中的LFM信号,再通过RCT算法估计剩余QFM信号的相位参数。仿真实验表明,相较于传统RCT算法,组合CPF变换方法能够抑制信号间干扰,对混合信号具有更好的估计精度。      

一种基于四阶累量的二维空间谱估计的新方法

本文针对有色高斯噪声背景中空域信号参数估计问题，提出了一种基于四阶累量的二维空间谱估计的新方法。在这种方法中，利用两个具有位移特性的二维传感器子阵列的四阶累量信息构成一种新的矩阵—四阶累量混合波达方向矩阵。对四阶累量混合波达方向矩阵进行特征分解，可实现有色高斯噪声背景中空域信号二维空间谱估计。     

A Method for Extracting the Fundamental-Frequency Positive-Sequence Voltage Vector Based on Simple Mathematical Transformations

In this paper, a novel scheme for obtaining the fundamental-frequency positive-sequence grid voltage is proposed. The method is based on four simple mathematical transformations; two of them are in the stationary reference frame, which are able to eliminate odd harmonics from the original signals. The other two transformations are implemented in a synchronously rotating reference frame in order to eliminate even harmonics. The output of the last transformation block is the input to a synchronous reference-frame phase-locked loop for detecting the frequency and position of the positive-sequence voltage vector. The proposed algorithm was verified through simulations and experiments by applying distorted and unbalanced signals, containing positive and negative-sequence components. The results are in agreement with those theoretically predicted and indicate that the proposed scheme has a great potential for use in grid-connected converter synchronization algorithms.     

迭代二次规划遮挡点恢复

为了有效地的恢复遮挡点,本文提出一种迭代二次规划遮挡点恢复方法,该方法首先分别利用图像矩阵的行向量和列向量在图像矩阵生成的正交补空间上的投影为0的特性,构造行和列余差函数,同时,对遮挡点分别按行为主序和列为主序进行排列,利用排列后这两者之间存在一个变换关系,将行和列余差函数统一表示为一个二次优化目标函数.该方法同时考虑了遮挡点在行和列两个方向的约束,而且将遮挡点求解转化为迭代求解一个二次规划问题.实验结果表明,本文方法具有收敛速度快,恢复精度高等优点.     

Dielectric profiles reconstruction via the quadratic approach in 2-D geometry from multifrequency and multifrequency/multiview data

Deals with the reconstruction of the contrast function of a dielectric cylinder with rectangular cross section starting from the knowledge of the electric scattered far field produced under the incidence of plane waves. We analyze the set of the reconstructable Fourier harmonics of the unknown permittivity contrast function with linear and quadratic approaches. This set depends on the ranges of the wavenumbers /spl beta/, of the angles of incidence /spl theta//sub i/ of the impinging plane waves, and of the observation angles /spl theta//sub o/. We discuss a simple way to describe such a dependence, which allows us to find out that the set of the retrievable harmonics for the quadratic approach contains that for the linear one. Moreover, our investigation points out how increasing the amount of independent data through a multifrequency/multiview measurement scheme allows us to enlarge the set of the retrievable unknown harmonics with respect to a multifrequency/single-view one. Our analysis is confirmed by numerical results. Memory storage requirements and processing time consumption for the quadratic approach are greatly reduced thanks to the massive use of the fast Fourier transform algorithm.     

Nonlinear analysis of the hippocampal subfields of CA1 and thedentate gyrus

The authors discuss the use of nonlinear bispectral analysis in examining the hippocampal EEG collected at subfields of CA1 and the dentate gyrus during the vigilance state of rapid-eye-movement (REM) sleep. The cross-bispectrum and its unique capabilities of detecting and quantifying quadratic nonlinear interactions occurring between these two hippocampal subfields are explained and demonstrated with simulation examples and EEG data. It was found that quadratic nonlinear interactions exist between CA1 and the dentate gyrus in the 6-8 frequency band which dominates the theta (&thetas;) rhythm observed in the hippocampal EEG during REM sleep. As a result, energy components around the frequency band of the second-order harmonics of &thetas; rhythm are not totally spontaneous, but generated largely due to quadratic nonlinear interactions     

基于ESPRIT算法的L型阵列MIMO雷达降维DOA估计

该文针对L型阵列MIMO雷达的2维角度估计问题,基于ESPRIT算法提出两种降维DOA估计方法。首先通过降维矩阵的设计及回波数据的降维变换,将高维回波数据转换至低维信号空间;然后分别基于特征分解和传播算子获得信号子空间的估计,最后利用ESPRIT算法实现2维空间角参量的联合估计及参数的自动配对。算法不牺牲阵列孔径,最大程度地降低了回波数据的维数,具有更低的运算复杂度。仿真结果验证了该文理论分析的正确性和算法的有效性。     

Frequencies Estimation of Two Dimensional Harmonics in Additive Noise with Quaternion

1 Introduction In many applications ,such as radar ,sonar and com-munication, parameters esti mation of two di mensionalharmonics was veryi mportant .In order to get highres-olutions esti mation, many subspace methods of one di-mensional harmonics , such as MUSIC, MEMP,ES-PRIT, have been developed to esti mate parameters oftwo di mensional harmonics[1 ~3]. When additive noise was colored Gaussian noiseH.M.ibrahi m[4]and R. R. Gharieb[5]analyzed thisproblem with high-order cumulants sin…     

基于人脸模板保护的不可逆变换方法

生物特征加密技术由于生物特征认证技术和密码学方法组成。它在为生物认证系统提供精确性和便捷性的同时,也保证了生物模板的隐私性和安全性。本文针对有序人脸特征,设计了四种形态的不可逆变换函数,并将其运用到三种不可逆变换方案中。我们设计的不可逆变换方案包括:位置变换方案,特征值变换方案以及二维变换方案。在实验阶段,我们对比了三种变换方案产生模板的认证性能和安全性能,并以任意一幅人脸的变换模板为例进行重构,重构后的人脸图像与原始人脸有很大差异。实验结果表明,位置变换方案通过增加多对一区域方式来增加认证系统安全性能,且认证性能与原始生物特征几乎相同。