Linear and quadratic time-frequency signal representations

A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems encountered in time-varying signal processing are provided     

Integral transforms covariant to unitary operators and theirimplications for joint signal representations

Fundamental to the theory of joint signal representations is the idea of associating a variable, such as time or frequency, with an operator, a concept borrowed from quantum mechanics. Each variable can be associated with a Hermitian operator, or equivalently and consistently, as we show, with a parameterized unitary operator. It is well known that the eigenfunctions of the unitary operator define a signal representation which is invariant to the effect of the unitary operator on the signal, and is hence useful when such changes in the signal are to be ignored. However, for detection or estimation of such changes, a signal representation covariant to them is needed. Using well-known results in functional analysis, we show that there always exists a translationally covariant representation; that is, an application of the operator produces a corresponding translation in the representation. This is a generalization of a recent result in which a transform covariant to dilations is presented. Using Stone's theorem, the “covariant” transform naturally leads to the definition of another, unique, dual parameterized unitary operator. This notion of duality, which we make precise, has important implications for joint distributions of arbitrary variables and their interpretation. In particular, joint distributions of dual variables are structurally equivalent to Cohen's class of time-frequency representations, and our development shows that, for two variables, the Hermitian and unitary operator correspondences can be used consistently and interchangeably if and only if the variables are dual     

OTDM add-drop multiplexer based on time-frequency signal processing

A time-division add-drop multiplexer capable of high-extinction-ratio operation is presented both theoretically and experimentally. The approach used is based on time-to-frequency domain conversion of optical signals and relies upon the switching of linearly chirped optical pulses. By converting a 40-Gb/s optical time-division multiplexing (OTDM) signal to 4 /spl times/ 10-Gb/s wavelength-division multiplexing (WDM) channels and using fiber Bragg gratings for frequency-domain add-drop multiplexing, a timeslot suppression ratio in excess of 30 dB and error-free operation for the dropped, through, and added channels were achieved. A further stage of WDM-to-TDM signal conversion was used to map the resulting signal back into the time domain. Moreover, it is shown that it is straightforward to simultaneously operate on multiple channels by simply cascading gratings to make more complex filtering functions without the requirement for any further synchronization of the tributary channels.     

基于二次型时频分析方法处理非平稳信号

使用时频分析方法处理非平稳信号,提取非平稳信号的时频分布。分别采用线性时频分析和二次型时频分析处理模拟仿真信号,仿真结果显示用二次型时频分析处理所得的时频分布的时频分辨率较高。仿真结果证明,二次型时频分析方法是处理非平稳信号的有效方法。     

基于时频特征的跳频信号调制识别

跳频信号在抗干扰方面具有良好的性能。准确识别跳频信号的调制方式,能够为判断敌我目标属性、干扰敌方信号等军事信息战提供有力支撑,但国内外对于跳频信号的调制识别仍存在很大空缺。本文提出一种基于时频特征的跳频信号调制识别方法,通过平滑伪魏格纳-维利分布(SPWVD)时频变换获取不同调制类型的跳频信号时频图像,将时频图像送入卷积神经网络(CNN)中进行特征提取及分类识别。仿真实验证明,本文CNN在低信噪比下取得了较好的识别效果。     

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     

信号的时频分析在SystemView中的设计与实现

时频分析是信号处理中的重要内容,用于观察信号在时域和频率的变化,常用的方法是短时傅里叶变换.基于SystemView仿真软件,在VC6.0环境下设计时频分析模块,并搭建仿真模型验证.结果表明,该模块能有效地观察信号的时频图.     

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     

A simple scheme for adapting time-frequency representations

We propose a simple, efficient technique for continuously adapting time-frequency and time-scale representations over time. The procedure computes a short-time quality measure of the representation for a range of values of a free parameter and estimates the optimal parameter value maximizing the quality measure via interpolation     

A new approach for classification of human gait based on time-frequency feature representations

We introduce a new and simple technique for human gait classification based on the time-frequency analysis of radar data. The focus is on the classification of arm movements to discern free vs. confined arm swinging motion. The latter may arise in hostage situation or may be indicative to carrying objects with one or both hands. The motion signatures corresponding to the arm and leg movements are both extracted from the time-frequency representation of the micro-Doppler. The time-frequency analysis is performed using the multiwindow S-method. With the Hermite functions acting as multiwindows, it is shown that the Hermite S-method provides an efficient representation of the complex Doppler associated with human walking. The proposed human gait classification technique utilizes the arm positive and negative Doppler frequencies and their relative time of occurrence. It is tested on various real radar signals and shown to provide an accurate classification.     

Robust time-frequency distributions based on the robust short time fourier transform

Design of time-frequency distributions (Tfds) that are robust to the impulse noise influence is considered. The robustTfds based on the robust short-time Fourier transform (Stft) are proposed. An efficient procedure to evaluate the robustStft is given. RobustTfds based on the robustStft have better energy concentration around the signal instantaneous frequency (If) than the robustStft itself. Also, theseTfds are more resistant to higher impulse noise than the robustTfds obtained using the local autocorrelation function (Laf) based minimization problem.     

基于分数阶傅立叶变换的WLFM信号DOA估计

本文提出了一种新的基于分数阶傅立叶变换的DOA估计算法,该算法首先将天线阵的观测信号变换到分数阶Fourier域,并将时域时变的方向向量转化为分数阶Fourier域时不变的方向向量,同时将线性调频信号解调为窄带平稳信号,然后在相应的分数阶Fourier域,利用root-MUSIC算法进行波达方向估计.理论分析与仿真结果表明,该方法算法简单,估计性能好.     

基于时频分析的自混合干涉信号处理方法研究

为了解决条纹计数法和相位分析法处理自混合干涉信号的不足,提出了一种基于时频分析的自混合干涉信号处理方法.采用时频分析技术获得自混合信号频率随时间的变化,利用激光与外部物体相互作用后的多普勒频移与信号频率相等的关系,非常方便地获得了外部运动物体的速度历史信息.结果表明,该方法处理自混合信号简单有效,且有较高的处理精度.     

基于时频矩阵局部对比度的跳频信号参数估计

为了提高低信噪比下跳频信号参数估计性能,提出了一种基于时频矩阵局部对比度的跳频信号参数估计算法。根据跳频信号和噪声的时频分布不同特点,利用时频矩阵在不同尺度滑窗下的局部能量对比值均值,得到多尺度局部能量对比特征矩阵,通过此特征矩阵和自适应阈值分离得到仅保留了跳频信号时频信息的时频矩阵P。然后从P中提取时频跳变信息,精确估计跳频信号的跳频周期、起跳时间和跳变频率。仿真结果表明,与传统局部对比度（local contrast measure,LCM）法及形态学滤波法相比,本文算法具有更好的跳频信号提取效果和更高的参数估计精度,其有效性与实用性在DSP+FPGA的硬件系统上得到了测试验证。     

基于R半径DFT信号时频灰度特征的辐射源识别

针对通信辐射源的个体识别问题,提出一种基于R半径离散傅里叶变换(DFT)对寄生调制信号的DFT采样圆内以及采样圆外零极点进行时频灰度特征提取的新方法。以零点特征提取为例,在寄生调制信号的幅频特性于零点处表现为谷值的基础上,结合R半径DFT变换,生成时频二维灰度图,并通过边缘检测对增强后的时频二维灰度图进行图像断点检测,以完成对寄生调制信号的特征提取,通过在不同模拟发射机下寄生调制信号所携带的零点位置半径不同,说明寄生调制信号发射自不同的辐射源。仿真实验结果表明,该方法提取出的两辐射源特征差异明显,稳定性高,可靠性好,能够快速有效地完成辐射源的个体识别。     

基于小波时频分析的心音异常信号检测

利用小波时频分析知识,结合Choi－Williams分布及重排对正常心音信号和异常心音信号进行能量分布分析,运用matlab编程可以计算得到正常心音和异常心音信号不同的时频分布结构,从而可以很清晰的区分心音信号是否正常。时频分布操作简单,信号蕴含信息很强,可以通过连续观测结果分析,清楚的发现异常心音信号出现的时刻,从而进行及早的预判和相应治疗,对于心脏相关疾病的预防具有很好的指导作用。     

基于级联变换的光学和SAR图像配准算法

针对光学和SAR(Synthetic Aperture Radar)图像配准中存在明显辐射和几何差异的问题,提出了一种基于级联变换的多源遥感图像配准方法.首先,利用灰度变换提取光学和SAR图像间的稳定结构特征,去除辐射差异性;然后,提出一种新的加权对数极坐标变换算法,解决图像间全局几何差异性,保证算法的尺度和旋转不变性,并初步得到整体的平移量;最后,通过局部几何变换,得到一系列的匹配点对,构建薄板样条模型,实现图像的精确配准.实验验证了算法去除辐射差异性和获得全局几何变换参数的能力,与传统的多源图像配准算法相比,基于级联变换的配准算法鲁棒性好,配准精度高.     

结合图像处理与时频分析的直扩/跳频信号参数估计

为实现扩频带宽大于跳频间隔、干扰信号强度较大及存在信道噪声时直扩/跳频(DS/FH)信号参数精确估计,提出了一种结合图像处理算法与时频分析技术的DS/FH信号参数估计方法。该方法首先利用时频分析算法提取DS/FH信号的时频分布图,然后结合干扰分量在时频图中的图像特征,利用图像处理的开运算与闭运算剔除了图像中的孤立干扰点及"空洞"干扰点。特别地,为抑制复杂的毛刺干扰信号提出了一种迭代相关匹配算法。最后通过分析图像像素位置与时频参数的对应关系完成DS/FH信号的参数估计。仿真实验表明,该方法可以有效消除干扰信号的影响,准确快速提取混合扩频信号的时频参数。     

一种基于时频原子特征的雷达辐射源信号识别方法

提出了一种全新的基于时频原子特征的雷达辐射源信号识别方法.训练阶段,在过完备时频原子库的基础上,以类区分度为度量,提取少数最能区分不同类别信号的时频原子作为一组固定的特征;识别阶段,以原子和信号的内积的绝对值作为分类器的输入特征,采用有监督模糊自适应共振网络进行辐射源的自动识别.对5类典型雷达辐射源信号的实验结果表明,...