基于分数阶傅里叶变换的宽带LFM相干信号的DOA估计

提出一种基于分数阶傅里叶变换(FRFT)的宽带线性调频信号(LFM)相干信号的波达方向(DOA)估计方法。针对分数阶傅里叶变换的谱峰聚集特点,该算法构造了分数阶傅里叶域(FRF域)的宽带LFM信号的阵列数据模型,在FRF域内利用Toeplitz矩阵重构特性,实现对相干信号的解相干,最后通过谱峰搜索完成入射信号的DOA估计。算法在不减小阵列有效孔径的情况下,增加了可估计相干信号源数目,并在低信噪比条件下能够得到较好的性能。实验仿真证明了该算法的有效性。     

基于分数阶傅里叶变换的多项式相位信号参数估计

研究了一种基于分数阶傅里叶变换(FRFT)的多项式相位信号快速估计方法,对于线性调频信号(LFM),即用信号延时相关解调的方法得到调频斜率的粗略估计,从而得到分数阶旋转角度的范围,简化为小范围的一维搜索问题。多项式相位信号的检测通过延时相关解调可转化为LFM信号的检测,再运用FRFT便可进行参数估计。理论分析与仿真结果表明该方法简单,估计性能好。     

LFM宽带雷达信号的多通道盲压缩感知模型研究

在传统压缩感知(Compressed sensing, CS)基础上,提出了一种基于盲压缩感知(Blind compressed sensing, BCS)理论的线性调频(Linear frequency modulated, LFM)雷达信号欠采样与重构的多通道模型.这一机制在稀疏基未知的条件下,利用LFM信号在分数阶傅里叶变换(Fractional Fourier transform, FRFT)域上良好的能量聚集特性,将多个LFM信号看作是在多个未知阶次下FRFT域的稀疏表达,通过时延相关解线调和逐次消去相结合的的欠采样方法逐一估计出每个通道的LFM信号满足聚集性条件的特定分数阶傅里叶域,以此构造出该通道LFM信号对应的DFRFT正交稀疏基字典,以各DFRFT 正交基为对角块构建混合信号正交稀疏基字典,最后利用块重构算法从测量值中估计出稀疏信号,同时验证了LF M信号多通道BCS问题解的唯一性,从而实现了稀疏基未知情况下针对多路LFM宽带雷达信号的多通道盲压缩感知.     

基于分数阶傅里叶变换的宽带LFM相干信号二维DOA估计

在分数阶傅里叶(FRF)域从离散角度推导了二维DOA估计数学模型,并在此模型基础上提出基于分数阶Fourier变换的二维相干信号DOA估计新算法.该方法利用分数阶傅里叶变换良好的能量聚集性,在分数阶傅里叶(FRF)域构造前后向空间平滑DOA矩阵.通过对DOA矩阵进行特征值分解,估计信号子空间和噪声子空间,由信号子空间的特征值和特征向量得到宽带LFM相干信号的二维到达角,避免了二维谱峰搜索和交叉项,也无需参数配对.理论推导与实验仿真验证了算法的有效性.     

基于混沌调制DFRFT旋转因子的语音加密

将分数阶傅里叶变换(FRFT)和混沌密码学相结合,提出一种新的变换域加密算法——混沌密钥调制FRFT旋转因子,用于实现语音信号的实时加解密。采用特征分解型离散FRFT算法,使语音实时加密系统在语音信号解密过程中具备良好的还原特性。理论分析和测试结果表明,该算法安全性较高,优于单纯混沌加密或单纯分数阶傅里叶变换的加密方法。     

一种新的宽带LFM信号到达角估计

利用分数阶傅里叶变换(FrFT)良好的信号选择性和抗干扰能力,提出了基于FrFT-自聚焦的宽带LFM(线性调频)信号到达角估计(DOA)方法,实现宽带LFM信号DOA高分辨率估计,仿真实验验证了新方法的有效性。     

一种简化的分数阶傅里叶变换及其应用

首先在分数阶傅里叶计算分解的基础上,引入了一种简化分数阶傅里叶算法(Reduced fractional Fourier transform,RFRFT),然后推导了时限LFM信号的RFRFT模平方,给出了其归一化前后信号参数的变换关系,同时借助角度变换提高了RFRFT估计参数的分辨率和读数精度;最后结合一次相位差分法将其推广至多分量高阶PSS的参数估计,并通过仿真验证了算法的有效性.     

基于FRFT自相似参数估计的异常流量检测方法

针对传统异常流量检测方法检测精度较低, Hurst指数估计受估计序列尺度的影响, 提出了基于分数阶傅里叶变换（FRFT）估计Hurst指数的方法。在此基础上, 实现了基于Hurst指数变化的异常检测, 有效解决了方法实现过程中FRFT最佳估计的分数阶阶数选择及Hurst参数求解的关键问题。实验表明, 基于FRFT的估计不受序列非平稳性影响, 对Hurst指数估计具有较高的估计精度, 并且可以准确地检测网络异常。     

基于FrFt的最小频移键控通信系统线性调频干扰抑制技术

分析线性调频（Linear Frequency Modulation,LFM）干扰对最小频移键控（Minimum Shift Keying,MSK）通信系统性能的影响,当LFM干扰超出MSK自身抗干扰容限时接收信号的误码率严重恶化,因此必须在信号接收端对LFM干扰进行抑制.通过对LFM干扰信号在分数阶傅立叶变换（Fractional Fourier Transform,FRFT）的特性分析,提出在分数域进行LFM干扰抑制的方法并通过仿真分析验证了该方法能够有效消除LFM干扰,误码率曲线明显改善.     

LFM信号检测和参数估计方法研究

针对分解型分数阶傅里叶变换(Fr FT)快速算法与实际工程应用脱节和降低LFM信号参数估计计算复杂度和精度的问题,在分析和研究分解型算法和LFM信号参数估计的基础上,提出了一种基于RAT变换和分数阶域二分法谱校正的LFM信号参数估计的方法,并在Fr FT运算中采用量纲归一化。仿真结果表明,本方法可以提高LFM信号参数估计的精度和有效降低计算复杂度,估计精度可以达到CRLB,从而证明了本方法的有效性。     

Fractional Fourier domain analysis of decimation and interpolation

The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal. Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security. Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital fre- quency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sam- pling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations.     

基于FRFT的线性调频信号映射方法的快速算法

针对基于分数傅立叶变换(Fractional Fourier transform，FRFT)的线性调频信号(LFM)的参数估计方法，提出了基于Radon变换的判决准则，并建立了相应的快速算法。该映射方法将具有同样调频斜率、同样多普勒中心频率、不同初始相位的信号映射到同一个点。该快速算法的计算量等同于FRFT的计算量，计算结果的精确度取决于连续两次的FRFT运算。     

The multiple-parameter fractional Fourier transform

The fractional Fourier transform （FRFT） has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform （WFRFT） is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ Z^M . Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform （MPFRFT）. It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.     

基于FMFCC和HMM的说话人识别

美尔频率倒谱系数(MFCC)是说话人识别中常用的特征参数,而语音信号是非平稳信号,MFCC并不能很好的反映语音的时频特性。针对这一缺陷,为了提高说话人的识别率,结合新的时频分析工具分数傅立叶变换(FRFT)。将MFCC推广到分数形式,得到分数美尔频率倒谱系数(FMFCC),用以表征语音信号的特征;并利用可分性测度验证了特征参数的有效性;通过建立20个不同说话人的FMFCC特征库,采用隐马尔可夫模型(HMM)对说话人进行仿真识别。仿真结果表明,在合适的变换阶次下,说话人的平均识别率可达93%以上。     

基于FRFT的Wigner-Ville分布交叉项抑制方法

针对多分量线性调频信号的魏格纳-维尔分布(Wigner-Ville Distribution,WVD)交叉项干扰问题,提出一种抑制交叉项的方法。该方法利用分数阶傅里叶变换(Fractional Fourier Transform,FRFT)在最佳FRFT域中对给定的线性调频信号具有最好的能量聚集性,将多分量线性调频信号在FRFT域上分解为若干个单分量信号,线性叠加单分量信号的WVD,从而达到抑制交叉项的效果。此外,当多分量线性调频信号为周期信号时周期间存在干扰,进一步提出了在基于FRFT的WVD交叉项抑制方法中增加周期遮蔽处理。仿真结果表明,在保持较高的时频分辨率时,该方法能够有效抑制交叉项,并且有一定的抗噪声能力。     

Research on resolution between multi-component LFM signals in the fractional Fourier domain

When the initial frequencies and chirp rates of multi-component linear frequency modulation (LFM or chirp) signals are close,the signals may not be distinguished in the fractional Fourier domain (FRFD).Consequently,some signals cannot be detected.In this paper,first,the spectral distribution characteristics of a continuous LFM signal in the FRFD are analyzed,and then the spectral distribution characteristics of a LFM signal in the discrete FRFD are analyzed.Second,the critical resolution distance between the peaks of two LFM signals in the FRFD is deduced,and the relationship between the dimensional normalization parameter and the distance between two LFM signals in the FRFD is also deduced.It is discovered that selecting a proper dimensional normalization parameter can increase the distance.Finally,a method to select the parameter is proposed,which can improve the resolution ability of the fractional Fourier transform (FRFT).Its effectiveness is verified by simulation results.     

Sampling expansion for irregularly sampled signals in fractional Fourier transform domain

Real-world signals are often not band-limited, and in many cases of practical interest sampling points are not always measured regularly. The purpose of this paper is to propose an irregular sampling theorem for the fractional Fourier transform (FRFT), which places no restrictions on the input signal. First, we construct frames for function spaces associated with the FRFT. Then, we introduce a unified framework for sampling and reconstruction in the function spaces. Based upon the proposed framework, an FRFT-based irregular sampling theorem without band-limiting constraints is established. The theoretical derivations are validated via numerical results.     

A novel fractional wavelet transform and its applications

The wavelet transform (WT) and the fractional Fourier transform (FRFT) are powerful tools for many applications in the field of signal processing.However,the signal analysis capability of the former is limited in the time-frequency plane.Although the latter has overcome such limitation and can provide signal representations in the fractional domain,it fails in obtaining local structures of the signal.In this paper,a novel fractional wavelet transform (FRWT) is proposed in order to rectify the limitations of the WT and the FRFT.The proposed transform not only inherits the advantages of multiresolution analysis of the WT,but also has the capability of signal representations in the fractional domain which is similar to the FRFT.Compared with the existing FRWT,the novel FRWT can offer signal representations in the time-fractional-frequency plane.Besides,it has explicit physical interpretation,low computational complexity and usefulness for practical applications.The validity of the theoretical derivations is demonstrated via simulations.     

基于SWT和FRFT的脉冲星TOA估计算法

提出了一种基于平稳小波和分数阶傅立叶变换的脉冲星超分辨率TOA估计算法。首先,对一个周期内的脉冲星信号进行多层平稳小波分解。然后,估计出与各层低频系数分数阶傅立叶变换相对应的TOA。最后,对脉冲星信号到达时间进行复合估计。实验结果表明,在低采样率,强噪声背景的情况下,该算法能获得稳定、准确的脉冲信号到达时间。