多阶次分数阶傅里叶域特征融合的主动声呐目标稀疏表示分类方法

海洋环境噪声和混响干扰严重、目标可分性差是主动声呐目标分类识别中的瓶颈问题.针对这一问题,该文基于主动声呐目标回波信号模型和分数阶傅里叶变换(FRFT)原理,推导了多阶次FRFT域特征表征形式,建立了FRFT域稀疏表示模型,提出了一种多阶次FRFT域特征融合的主动声呐目标稀疏表示分类方法.该方法通过FRFT的能量聚集性...     

多阶次分数阶傅里叶域特征融合的主动声呐目标稀疏表示分类方法

海洋环境噪声和混响干扰严重、目标可分性差是主动声呐目标分类识别中的瓶颈问题.针对这一问题,该文基于主动声呐目标回波信号模型和分数阶傅里叶变换(FRFT)原理,推导了多阶次FRFT域特征表征形式,建立了FRFT域稀疏表示模型,提出了一种多阶次FRFT域特征融合的主动声呐目标稀疏表示分类方法.该方法通过FRFT的能量聚集性和稀疏分解的残差去除过程,达到了抑制噪声和混响干扰的目的;通过多阶次FRFT域特征的融合,增加目标之间的可分性,进而实现海洋环境中低信混比条件下的主动声呐目标分类.实验结果表明,所提方法在信混比达到0 dB的条件下,分类准确率能够达到90％以上.     

Sampling of Bandlimited Signals in Fractional Fourier Transform Domain

Fractional Fourier transformed bandlimited signals are shown to form a reproducing kernel Hilbert space. Basic properties of the kernel function are applied to the study of a sampling problem in the fractional Fourier transform (FRFT) domain. An orthogonal sampling basis for the class of bandlimited signals in the FRFT domain is then given. A nonuniform sampling theorem for bandlimited signals in the FRFT domain is also presented. Numerical experiments are given to demonstrate the effectiveness of the proposed nonuniform sampling theorem.     

Sampling and Reconstruction of Sparse Signals in Fractional Fourier Domain

Sampling theory for continuous time signals which have a bandlimited representation in fractional Fourier transform (FrFT) domain-a transformation which generalizes the conventional Fourier transform-has blossomed in the recent past. The mechanistic principles behind Shannon's sampling theorem for fractional bandlimited (or fractional Fourier bandlimited) signals are the same as for the Fourier domain case i.e. sampling (and reconstruction) in FrFT domain can be seen as an orthogonal projection of a signal onto a subspace of fractional bandlimited signals. As neat as this extension of Shannon's framework is, it inherits the same fundamental limitation that is prevalent in the Fourier regime-what happens if the signals have singularities in the time domain (or the signal has a nonbandlimited spectrum)? In this paper, we propose a uniform sampling and reconstruction scheme for a class of signals which are nonbandlimited in FrFT sense. Specifically, we assume that samples of a smoothed version of a periodic stream of Diracs (which is sparse in time-domain) are accessible. In its parametric form, this signal has a finite number of degrees of freedom per unit time. Based on the representation of this signal in FrFT domain, we derive conditions under which exact recovery of parameters of the signal is possible. Knowledge of these parameters leads to exact reconstruction of the original signal.     

分数阶Fourier域非均匀采样LFM信号的检测概率

为了减少分数阶Fourier域线性调频(LFM)信号处理的计算量,满足实时性要求,提出了一种新的非均匀采样方法.与传统的非均匀采样方法相比,该方法既解决了整个采样时段内由于过采样造成的数据冗余性,也消除了信号时变特征造成的局部冗余性.最后,应用该方法得到了非均匀采样LFM信号在分数阶Fourier变换域的频谱表达式,并对不同信噪比(SNR)条件下信号的检测概率进行了研究.结果表明,该方法具有较好的抗噪声能力.     

分数阶Fourier域上非均匀采样信号的频谱重构研究

 本文研究了分数阶Fourier变换域上非均匀采样信号的重构问题.首先得到周期非均匀采样信号经非均匀分数阶Fourier变换后的频谱表达式,研究了该分数阶频谱和信号连续分数阶频谱之间的关系,并基于该关系式提出了一种分数阶Fourier域周期非均匀采样信号的频谱重构算法;其次,讨论了分数阶Fourier变换域上更加一般情况下非均匀采样信号重构问题;最后,给出了周期非均匀采样信号频谱重构的仿真结果.     

飞机回波FRFT域的多重分形特征与目标分类

低分辨雷达体制的限制和探测过程中背景杂波的影响,使得低分辨雷达飞机目标的分类识别较为困难。本文提出一种分数域多重分形方法,通过引入分数阶Fourier变换（FRFT）寻找飞机目标回波的最优FRFT域,并在最优分数阶FRFT域提取目标回波数据的多重分形特征,结合支持向量机进行飞机目标的分类识别。实验表明,FRFT可以增强飞机目标回波的多重分形特性;从最优FRFT域提取的多重分形特征具有较好的分类识别效果,FRFT域多重分形方法的飞机目标分类识别率要高于时域多重分形方法的飞机目标分类识别率;即使在低信噪比条件下,FRFT域多重分形方法仍可实现低分辨雷达飞机目标的粗分类。     

分数阶Fourier域中多分量chirp信号的遮蔽分析

本文从分数阶Fourier变换与时频分布的关系入手,在离散分数阶Fourier变换算法基础上导出了单分量chirp信号分数阶Fourier谱强度的近似表达,并依据分数阶Fourier变换的线性性质,得到了调频率不同的两分量chirp信号间分数阶Fourier谱相互遮蔽的量化结果,给出了图例分析,并进行了仿真验证.通过本文的分析可以知道分数阶Fourier域中调频率不同的多分量chirp信号间的相互遮蔽主要取决于各自的幅度、调频率和采样时间.当多分量chirp信号幅度、调频率确定后,可以通过延长采样时间来降低各分量间的相互遮蔽.     

Fourier-Based Feature Extraction for Classification of EEG Signals Using EEG Rhythms

In this paper, we propose a method for the analysis and classification of electroencephalogram (EEG) signals using EEG rhythms. The EEG rhythms capture the nonlinear complex dynamic behavior of the brain system and the nonstationary nature of the EEG signals. This method analyzes common frequency components in multichannel EEG recordings, using the filter bank signal processing. The mean frequency (MF) and RMS bandwidth of the signal are estimated by applying Fourier-transform-based filter bank processing on the EEG rhythms, which we refer intrinsic band functions, inherently present in the EEG signals. The MF and RMS bandwidth estimates, for the different classes (e.g., ictal and seizure-free, open eyes and closed eyes, inter-ictal and ictal, healthy volunteers and epileptic patients, inter-ictal epileptogenic and opposite to epileptogenic zone) of EEG recordings, are statistically different and hence used to distinguish and classify the two classes of signals using a least-squares support vector machine classifier. Experimental results, with 100 % classification accuracy, on a real-world EEG signals database analysis illustrate the effectiveness of the proposed method for EEG signal classification.     

Estimation of the Second Derivative of Kinematic Impact Signals Using Fractional Fourier Domain Filtering

A new filtering algorithm is proposed for the accurate estimation of the second derivatives of kinematic signals with impacts. The algorithm operates in predetermined consecutive fractional Fourier transform domains and amounts to an overall linear low-pass filter with time-varying cutoff threshold, which can successfully accommodate the impact-induced changes in the frequency content of the signals. The proposed method was applied to experimentally acquired displacement data and the results have demonstrated its promising performance that was found superior to both conventional techniques and recently introduced advanced schemes.      

Sampling and Sampling Rate Conversion of Band Limited Signals in the Fractional Fourier Transform Domain

The fractional Fourier transform (FRFT) has become a very active area in signal processing community in recent years, with many applications in radar, communication, information security, etc., This study carefully investigates the sampling of a continuous-time band limited signal to obtain its discrete-time version, as well as sampling rate conversion, for the FRFT. Firstly, based on product theorem for the FRFT, the sampling theorems and reconstruction formulas are derived, which explain how to sample a continuous-time signal to obtain its discrete-time version for band limited signals in the fractional Fourier domain. Secondly, the formulas and significance of decimation and interpolation are studied in the fractional Fourier domain. Using the results, the sampling rate conversion theory for the FRFT with a rational fraction as conversion factor is deduced, which illustrates how to sample the discrete-time version without aliasing. The theorems proposed in this study are the generalizations of the conventional versions for the Fourier transform. Finally, the theory introduced in this paper is validated by simulations.     

分数阶Fourier域强弱LFM信号检测与参数估计

分数阶Fourier变换（FRFT）由于其特有的性质,非常适合处理线性调频（LFM）信号,尤其是,作为一种线性变换,可以克服多分量LFM信号之间的交叉项干扰。但是采用逐次消去法检测多分量LFM信号时,每检测一个LFM信号,都要对信号分别求旋转角 的FRFT,再进行二维搜索,计算量较大。为了提高FRFT对多分量LFM信号的检测效率,本文给出一种在分数阶Fourier域检测强、弱LFM信号的新方法。首先,分析了逐次消去法和聚类分析法检测多分量LFM信号的原理,以及它们的优缺点。提出一种聚类分析和逐次消去相结合的信号检测方法,利用平面截取信号在平面(u,α)上的尖峰,并引入基于广度优先搜索邻居（BFSN）的聚类算法,对截取的信号尖峰进行聚类分析,获得每个LFM信号对应的信号尖峰,实现多个较强信号的检测与参数估计,再利用逐次消去法实现弱信号的检测。该方法可以同时检测多个能量相近的LFM信号,提高了检测效率,以及次强信号的参数估计精度,并有效地抑制了强信号对弱信号的遮蔽影响。通过对信号进行平面切割处理,减少了BFSN聚类算法中输入集样本数量,大大降低了算法的计算量。最后,仿真验证了该方法的有效性。      

基于分数阶Fourier变换的反辐射导弹检测技术

针对反辐射导弹的检测问题,主要是消除载机信号的干扰.本文研究了单频信号和线性调频信号的分数阶Fourier变换模函数的时移特性.研究表明,单频信号和线性调频信号的FRFT模函数具有不同的时移特性.分数阶Fourier变换是线性变换,不存在交叉项,采用分数阶Fourier变换搜索匹配动目标信号,使其能量汇聚.根据以上特点本文提出了一种基于观测信号以及其时延信号的分数阶Fourier变换模之差的反辐射导弹检测方法.此方法可以有效的消除载机信号的干扰,并且对背景噪声幅度有一定的抑制作用.仿真结果表明,在低信噪比下能有效的检测出反辐射导弹.     

分数阶Fourier变换域的反辐射导弹检测技术

通过推导单频信号和线性调频（LFM）信号旋转角正负对称的分数阶Fourier变换（FRFT）模函数,得到一个有用的结论：单频信号正负对称旋转角的FRFT模值相等,模函数关于中心点对称,而对于LFM信号,其模幅度差别很大。根据此结论提出了一种基于观测信号正负对称旋转角的FRFT模之差的反辐射导弹（ARM）检测方法。此方法可以有效地消除载机信号的干扰。仿真结果表明,此方法在低信噪比下能有效地检测出ARM。     

分数阶傅里叶变换域上带通信号的采样定理

傅里叶变换和采样定理是信号处理领域的两大基本问题,采样定理研究了傅里叶变换域上带限信号的采样和重构理论.分数阶傅里叶变换(FRFT)是傅里叶变换的一种推广,与之相应的采样理论目前还不十分完备,所以有必要从FRFT域上重新研究采样定理.本文首先得到了均匀冲激串采样信号的FRFT,然后在此基础上导出了FRFT域上带通信号和低通信号的采样定理和重构公式.这些结果是经典理论的推广,将丰富分数阶傅里叶变换的理论体系.     

基于分数阶傅里叶变换的窄带雷达飞机目标回波特征提取方法

该文研究了常规窄带雷达体制下,利用分数阶傅里叶变换扩展特征域,从而解决直升机、螺旋桨飞机和喷气式飞机3类飞机目标回波分类中的特征提取问题。在现代战场中,直升机、螺旋桨飞机和喷气式飞机具有不同的机动性能,并各自承担着重要的任务。因此,实现这3类飞机的分类具有重大的意义。该文针对3类飞机目标分类的传统特征数目少,包含信息量有限,导致分类性能不够好的问题,基于现有的特征提取方法引入分数阶傅里叶变换(Fractional Fourier Transform, FrFT),在经过FrFT后的分数域提取3类飞机目标回波的分数阶特征,弥补传统特征的不足。并利用线性相关向量机(Relevance Vector Machine, RVM)的特征选择功能对提取的分数阶特征进行特征选择并分类。基于仿真和实测数据的实验结果证明该文提出的分数阶特征的分类性能较传统时域、多普勒域特征有较大提升。     

基于调制域的雷达信号脉内特征提取新方法

针对传统调制域检测法在提取雷达信号脉内特征中的不足,提出了一种通过检测极值点来提取信号脉内特征的方法。首先通过检测出信号极值点,再对极值点进行运算处理,进而提取出极值点中包含的脉内特征信息。该方法借助于极值点具有最大信息量的优势,并运用二次提取频率来估计码元宽度,使得算法的信噪比性能得到有效改善。仿真结果表明,与传统调制域检测法相比,该方法在低信噪比下对于多种类型信号的脉内特征参数的估计精度平均提高30%。     

Maximum Amplitude Method for Estimating Compact Fractional Fourier Domain

A maximum-amplitude-based coarse-to-fine algorithm is proposed with two novel ideas highlighted: adopting the maximum value of the fractional Fourier amplitude spectrum to measure the compactness of a signal, and using a coarse-to-fine strategy to speed up the searching process. The simulation results on synthetic and real signals show the validity of the proposed method.      

基于EEMD与多重分形的心电信号特征提取与分类

心电信号的快速分类在心脏病医学诊断领域具有至关重要的作用,为了降低人工识别的成本,提高心电信号分类的准确率。文章以正常搏动、房性早搏、室性早搏、左束支传导阻滞及右束支传导阻滞信号为研究对象,用集合经验模态分解分解心电信号,并结合相关系数来选取本征模态函数进行重构心电信号。从心电信号的非线性动力学角度出发,用多重分形理论进行分析,研究其质量指数曲线、广义分形维数和多重分形谱,提取合适的多重分形特征,用于支持向量机的训练。实验结果表明,用该方法训练测试30次得到的分类准确率平均值为96.09%,单次实验对正常搏动、左束支传导阻滞信号的分类精确率可达97%以上,证明该方法在心电信号分类中的有效性。     

Closed-Form Analytical Expression of Fractional Order Differentiation in Fractional Fourier Transform Domain

In this paper, a closed-form analytical expression for fractional order differentiation in the fractional Fourier transform (FrFT) domain is derived by utilizing the basic principles of fractional order calculus. The reported work is a generalization of the differentiation property to fractional (noninteger or real) orders in the FrFT domain. The proposed closed-form analytical expression is derived in terms of the well-known confluent hypergeometric function. An efficient computation method has also been derived for the proposed algorithm in the discrete-time domain, utilizing the principles of the discrete fractional Fourier transform algorithm. An application example of a low-pass finite impulse response (FIR) fractional order differentiator in the FrFT domain has also been investigated to show the practicality of the proposed method in signal processing applications.