一种新的变换域自适应LMS滤波算法

为了改善时变系统中的LMS算法收敛速度,一般可以在变换域进行自适应处理。通过研究和分析分数阶傅里叶变换与时-频平面的关系,提出在分数阶傅里叶变换域进行自适应时-频滤波。所提出的方法首先搜索最佳变换域,然后在分数阶傅里叶变换域进行LMS自适应滤波。仿真结果表明,与目前一些基于变换域的方法对比,新方法通过对时-频平面的旋转,可以显著加速算法收敛性。     

一种基于Radon变换的时频分析方法

针对CW脉冲和线性调频(LFM)信号,利用Radon变换沿直线积分的特性,将其与时频分布(TFD)结合在一起,抑制多频率分量信号各个分量之间的交叉项干扰,提高时频分布的时频二维分辨力。通过仿真数据验证算法具有良好的时频分辨能力以及抑制交叉项干扰能力。     

A four-parameter atomic decomposition of chirplets

A new four-parameter atomic decomposition of chirplets is developed for compact and precise representation of signals with chirp components. The four-parameter chirplet atom is obtained from the unit Gaussian function by successive applications of scaling, fractional Fourier transform (FRFT), and time-shift and frequency-shift operators. The application of the FRFT operator results in a rotation of the Wigner distribution of the Gaussian in the time-frequency plane by a specified angle. The decomposition is realized by using the matching pursuit algorithm. For this purpose, the four-parameter space is discretized to obtain a small but complete subset in the Hilbert space. A time-frequency distribution (TFD) is developed for clear and readable visualization of the signal components. It is observed that the chirplet decomposition and the related TFD provide more compact and precise representation of signal inner structures compared with the commonly used time-frequency representations     

The fractional Fourier transform and time-frequency representations

The functional Fourier transform (FRFT), which is a generalization of the classical Fourier transform, was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community, to which it may, however, be potentially useful. The FRFT depends on a parameter α and can be interpreted as a rotation by an angle α in the time-frequency plane. An FRFT with α=π/2 corresponds to the classical Fourier transform, and an FRFT with α=0 corresponds to the identity operator. On the other hand, the angles of successively performed FRFTs simply add up, as do the angles of successive rotations. The FRFT of a signal can also be interpreted as a decomposition of the signal in terms of chirps. The authors briefly introduce the FRFT and a number of its properties and then present some new results: the interpretation as a rotation in the time-frequency plane, and the FRFT's relationships with time-frequency representations such as the Wigner distribution, the ambiguity function, the short-time Fourier transform and the spectrogram. These relationships have a very simple and natural form and support the FRFT's interpretation as a rotation operator. Examples of FRFTs of some simple signals are given. An example of the application of the FRFT is also given     

分数Fourier变换、矩阵群和时-频分析

本文从矩阵群的观点出发讨论了分数Fourier变换的数学描述并通过数字仿真直观地说明了它进行信号时-频分析的两个特点.结果表明,在矩阵描述下,经典的Fourier变换相当于一个置换矩阵;一般的分数Fourier变换相当于一个广义置换矩阵;分数Fourier变换全体构成的变换族可以用一个矩阵群来描述,多次变换运算完全转化为相应的矩阵乘法运算.最后,数字信号分数Fourier变换的仿真计算表明,分数Fourier变换具有独特的时-频分析性质.     

分数阶Fourier变换及其应用

本文介绍了一种崭新的信号分析工具－分数阶Ｆｏｕｒｉｅｒ变换（ＦＲＦＴ）。本文在简单介绍了ＦＲＦＴ的几种不同的引入途径和其基本性质之后，在时－频平面对ＦＲＦＴ进行了研究，用经典的Ｆｏｕｒｉｅｒ变换的观点对ＦＲＦＴ进行了解释，并推导了ＦＲＦＴ与Ｒａｄｏｎ－Ｗｉｇｎｅｒ变换的关系。最后，根据ＦＦＲＴ的特点，提出了它在时频信号分析中的两种新的应用途径。     

Linear frequency-modulated signal detection using Radon-ambiguitytransform

A novel time-frequency technique for linear frequency modulated (LFM) signal detection is proposed. The design of the proposed detectors is based on the Radon transform of the modulus square or the envelope amplitude of the ambiguity function (AF) of the signal. A practical assumption is made that the chirp rate is the only parameter of interest. Since the AF of LFM signals will pass through the origin of the ambiguity plane, the line integral of the Radon transform is performed over all lines passing through the origin of the ambiguity plane. The proposed detectors yield maxima over chirp rates of the LFM signals. This reduces the two-dimensional (2-D) problem of the conventional Wigner-Ville distribution (WVD) based detection or the Radon-Wigner transform (RWT) based detector to a one-dimensional (1-D) problem and consequently reduces the computation load and keeps the feature of “built-in” filtering. Related issues such as the finite-length effect, the resolution, and the effect of noise are studied. The result is a tool for LFM detection, as well as the time-varying filtering and adaptive kernel design for multicomponent LFM signals     

Relations between fractional operations and time-frequencydistributions, and their applications

The fractional Fourier transform (FRFT) is a useful tool for signal processing. It is the generalization of the Fourier transform. Many fractional operations, such as fractional convolution, fractional correlation, and the fractional Hilbert transform, are defined from it. In fact, the FRFT can be further generalized into the linear canonical transform (LCT), and we can also use the LCT to define several canonical operations. In this paper, we discuss the relations between the operations described above and some important time-frequency distributions (TFDs), such as the Wigner distribution function (WDF), the ambiguity function (AF), the signal correlation function, and the spectrum correlation function. First, we systematically review the previous works in brief. Then, some new relations are derived and listed in tables. Then, we use these relations to analyze the applications of the FRPT/LCT to fractional/canonical filter design, fractional/canonical Hilbert transform, beam shaping, and then we analyze the phase-amplitude problems of the FRFT/LCT. For phase-amplitude problems, we find, as with the original Fourier transform, that in most cases, the phase is more important than the amplitude for the FRFT/LCT. We also use the WDF to explain why fractional/canonical convolution can be used for space-variant pattern recognition     

基于时频表示的LFM信号参数估计方法

宽带非平稳干扰LFM信号对DSSS系统通信性能威胁较大,为抑制其干扰,必须估算LFM信号参数。在此介绍了几种时频表示方法及其特点,然后采用Radon变换或Hough变换相结合的方法进行LFM信号参数估计,讨论了LFM参数估算过程对时频表示方法的要求。分析表明,选择适当的函数是时频分布估计LFM信号参数的重点,分数傅里叶变换有相对好的LFM信号参数估计性能。     

Multiplicative filtering in the fractional Fourier domain

In this article, we investigate the multiplicative filtering in the fractional Fourier transform (FRFT) domain based on the generalized convolution theorem which states that the convolution of two signals in time domain results in simple multiplication of their FRFTs in the FRFT domain. In order to efficiently implement multiplicative filtering, we express the generalized convolution structure by the conventional convolution operation. Utilizing the generalized convolution structure, we convert the multiplicative filtering in the FRFT domain easily to the time domain. Based on the model of multiplicative filtering in the FRFT domain, a practical method is proposed to achieve the multiplicative filtering through convolution in the time domain. This method can be realized by classical Fast Fourier transform (FFT) and has the same capability compared with the method achieved in the FRFT domain. As convolution can be performed by FFT, this method is more useful from practical engineering perspective.     

脉冲噪声下跳频信号时频图修正

为了在α稳定分布噪声的环境下获得清晰的跳频信号时频图,提出一种基于分数低阶SPWVD(Smoothed Pseudo Wigner-Vile Distribution)与形态学滤波相结合的跳频信号时频图修正算法。首先,根据接收到的多跳频信号建立跳频信号的模型和α稳定分布噪声模型;然后,采用低阶SPWVD变换抑制时频图中脉冲噪声;最后,根据形态学滤波处理方法对残留噪声进一步抑制进而得到清晰时频图。理论分析和仿真结果表明,所提算法在广义信噪比为-5 dB时仍可以得到清晰可靠的跳频信号时频图,并且基于时频图的参数估计性能优良。     

分数阶傅里叶变换时滞模型及其应用

实际采集到的信号中常常含有与信号频谱相同的延时噪声分量,难以用常规的滤波方法剔除。针对延时噪声干扰的特点,依据分数阶傅里叶变换（FRFT）的时移特性和乘积变换延时特性,提出了一个信号与同频噪声分离的时滞模型,通过对含噪信号进行相应的分数阶傅里叶变换,在变换域上可不断加大信号与同频噪声的距离,距离的增加与迭代次数成正比,从而能较好地分离同频干扰。实验中,对分数阶傅里叶变换的分离效果进行了仿真演示。     

Tomographic time-frequency analysis and its application towardtime-varying filtering and adaptive kernel design for multicomponentlinear-FM signals

Since line integrals through the Wigner spectrum can be calculated by dechirping, calculation of the Wigner spectrum may be viewed as a tomographic reconstruction problem. In the paper, the authors show that all time-frequency transforms of Cohen's class may be achieved by simple changes in backprojection reconstruction filtering. The resolution/cross-term tradeoff that occurs in time-frequency kernel selection is shown to be analogous to the resolution-ringing tradeoff that occurs in computed tomography (CT). “Ideal” reconstruction using a purely differentiating backprojection filter yields the Wigner distribution, whereas low-pass differentiating filters produce cross-term suppressing distributions such as the spectrogram or the Born-Jordan distribution. It is also demonstrated how this analogy can be exploited to “tune” the reconstruction filtering (or time-frequency kernel) to improve the ringing/resolution tradeoff. Some properties of the projection domain, which is also known as the Radon-Wigner transform, are characterized, including the response to signal delays or frequency shifts and projection masking or convolution. Last, time-varying filtering by shift-varying convolution in the Radon-Wigner domain is shown to yield superior results to its analogous Cohen's class adaptive transform (shift-invariant convolution) for the multicomponent, linear-FM signals that are investigated     

Discrete fractional Fourier transform based on orthogonalprojections

The continuous fractional Fourier transform (FRFT) performs a spectrum rotation of signal in the time-frequency plane, and it becomes an important tool for time-varying signal analysis. A discrete fractional Fourier transform has been developed by Santhanam and McClellan (see ibid., vol.42, p.994-98, 1996) but its results do not match those of the corresponding continuous fractional Fourier transforms. We propose a new discrete fractional Fourier transform (DFRFT). The new DFRFT has DFT Hermite eigenvectors and retains the eigenvalue-eigenfunction relation as a continous FRFT. To obtain DFT Hermite eigenvectors, two orthogonal projection methods are introduced. Thus, the new DFRFT will provide similar transform and rotational properties as those of continuous fractional Fourier transforms. Moreover, the relationship between FRFT and the proposed DFRFT has been established in the same way as the conventional DFT-to-continuous-Fourier transform     

基于FRFT的复合chirp信号分析

作为Fourier变换的一种广义形式,分数阶傅里叶变换（FR订）同时融合了信号在时域和频域的信息,是一种新的时频分析方法。而复合线性调频（chirp）信号相对单斜率线性调频信号具有更好的速度分辨力和距离速度联合分辨力。为了分析该信号的特征,提出了一种基于分数阶Fourier变换的分析方法。由于复合chirp信号在FR丌域呈现的冲激特性,以此实现复合chirp信号的检测。实验结果表明．该方法对复合chim信号的检测是有效的。     

基于Radon变换的线性调频信号参数提取

在电子侦察(ELINT)中对于线性调频信号的参数提取目前主要有Radon-Wigner变换,而这种算法要求运算量比较大,运算时间也比较长.文中从图像处理的角度,利用Radon变换的直线提取功能对信号的Wigner-Vill分布的时频图像进行参数提取,并且对原来的算法进行一定的改进.仿真结果证明这个算法具有实时性和精度高等特点.     

基于能量峰区域时频滤波的信号估计

本文提出了一种基于能量峰时频区域滤波的信号估计方法。首先,设计了一种基于能量阈值的时频区域提取方法,识别出信号在时频面上的能量峰,并提取出能量峰所占据的时频区域;利用线性时频滤波器获取信号中的分量,将这些分量的时频分布叠加得到改善的时频分布。仿真结果表明,对于由时频不相交分量组成的信号,本方法可以分离出其中的信号分量,并能得到较优的时频分布。     

基于分数阶傅里叶变换的运动舰船聚焦算法

为解决合成孔径雷达(SAR)图像中运动舰船目标产生的散焦现象,结合对比度最大算法和分数阶傅里叶变换(FRFT)算法,提出了一种改进的对比度分数阶傅里叶变换(CFRFT)自聚焦算法.该算法利用分数阶傅里叶变换对已成像SAR图像进行时频域分析,根据旋转角分别利用参数模型和非参数模型对二阶相位误差和高阶相位误差进行补偿,和传统的相位梯度(PGA)法相比,图像分辨率和旁瓣比提升显著,可以更有效地补偿SAR中舰船运动产生的相位误差.对不同舰船和尾迹SAR图像实验表明,算法对二阶以上的相位误差具有较好的补偿效果,误差估计准确性高,适用范围广,解决了SAR运动舰船的散焦问题,提高了海洋舰船监测的准确性.     

A resolution comparison of several time-frequency representations

Two signal components are considered resolved in a time-frequency representation when two distinct peaks can be observed. The time-frequency resolution limit of two Gaussian components, alike except for their time and frequency centers, is determined for the Wigner distribution, the pseudo-Wigner distribution, the smoother Wigner distribution, the squared magnitude of the short-time Fourier transform, and the Choi-Williams distribution. The relative performance of the various distributions depends on the signal. The pseudo-Wigner distribution is best for signals of this class with only one frequency component at any one time, the Choi-Williams distribution is most attractive for signals in which all components have constant frequency content, and the matched filter short-time Fourier transform is best for signal components with significant frequency modulation. A relationship between the short-time Fourier transform and the cross-Wigner distribution is used to argue that, with a properly chosen window, the short-time Fourier transform of the cross-Wigner distribution must provide better signal component separation that the Wigner distribution