基于多项式调频Fourier变换的信号分量提取方法

为了从含有噪声的混合信号中有效提取各个信号分量, 提出一种基于多项式调频Fourier变换的分量提取方法. 通过研究Fourier变换和分数阶Fourier变换的信号能量积累方式及变换基函数的时频表示, 提出利用时频平面上的多项式调频曲线族代替Fourier变换和分数阶Fourier 变换的调频直线族, 将变换的适用范围扩展到非线性调频信号. 采用粒子群智能优化算法搜索调频曲线族的最优多项式参数, 使混合信号中的某一分量在多项式调频Fourier域上能量谱集中. 最后对能量谱集中的分量进行窄带滤波, 并利用多项式调频逆Fourier变换重构信号分量. 仿真实验结果表明, 该方法不仅能够提取混合信号中的线性调频分量, 还能够实现非线性调频分量的能量谱集中、信号分离和时频特征提取.     

简明分数阶傅里叶变换及其对线性调频信号的检测和参数估计

针对低信噪比下线性调频信号的检测问题,提出了一种简明分数阶傅里叶变换方法。该变换借助chirp相乘和傅里叶变换对时频平面上的频率轴进行旋转,以获取信号在各个角度下频率轴上的频谱分布。对时频分布呈直线状的线性调频信号,简明分数阶傅里叶变换能在特定角度上将信号能量聚集成尖锐的强能量峰,从而提高信噪比,实现对线性调频信号的可靠检测和参数估计。数值仿真和实验验证结果表明,简明分数阶傅里叶变换可对较低信噪比的线性调频信号实现有效检测,并由变换域峰值的位置对信号参数进行准确估计。相比于传统的分数阶傅里叶变换方法,简明分数阶傅里叶变换的复杂度更低,离散计算效率更高,在对噪声掩盖下的线性调频信号进行检测和参数估计时能更好地满足实时处理的要求。     

简明分数阶傅里叶变换及其对线性调频信号的检测和参数估计

针对低信噪比下线性调频信号的检测问题,提出了一种简明分数阶傅里叶变换方法。该变换借助chirp相乘和傅里叶变换对时频平面上的频率轴进行旋转,以获取信号在各个角度下频率轴上的频谱分布。对时频分布呈直线状的线性调频信号,简明分数阶傅里叶变换能在特定角度上将信号能量聚集成尖锐的强能量峰,从而提高信噪比,实现对线性调频信号的可靠检测和参数估计。数值仿真和实验验证结果表明,简明分数阶傅里叶变换可对较低信噪比的线性调频信号实现有效检测,并由变换域峰值的位置对信号参数进行准确估计。相比于传统的分数阶傅里叶变换方法,简明分数阶傅里叶变换的复杂度更低,离散计算效率更高,在对噪声掩盖下的线性调频信号进行检测和参数估计时能更好地满足实时处理的要求。      

基于短时分数阶傅里叶变换域滤波的多项式相位信号时频检测

针对低信噪比下多个多项式相位信号提出了一种基于短时分数阶滤波的时频检测方法。分数阶傅里叶变换作为一种线性变换,能够实现线性调频信号检测与分离。而多项式相位信号在短时间内可以由线性调频信号提供良好的近似,故可以采用短时分数阶傅里叶变换实现多线性调频分量的检测与分离。对每个短时信号的时频分析进行叠加组合,即得到多个多项式相位信号的时频分析检测。计算机模拟仿真证明了此方法的有效性。     

线性过阻尼分数阶Langevin方程的共振行为

通过将广义Langevin方程中的系统内噪声建模为分数阶高斯噪声,推导出分数阶Langevin方程, 其分数阶导数项阶数由系统内噪声的Hurst指数所确定.讨论了处于强噪声环境下的线性过阻尼分数阶 Langevin方程在周期信号激励下的共振行为,利用Shapiro-Loginov公式和Laplace变换, 推导了系统响应的一、二阶稳态矩和稳态响应振幅、方差的解析表达式.分析表明,适当参数下, 系统稳态响应振幅和方差随噪声的某些特征参数、周期激励信号的频率及系统部分参数的变化出现了 广义的随机共振现象.     

基于矢量线阵的目标低频线谱提取方法

主动声呐系统常采用线性调频信号探测水下目标。利用分数阶傅里叶变换处理线性调频回波时,可在低信噪比和强混响背景下获得目标参数的有效估计。主动声呐系统常通过增大发射信号的时间带宽积来提升系统的距离分辨力和速度分辨力,但却带来了计算复杂度的显著增加,尤其是奈奎斯特采样下基于分数阶傅里叶变换的回波处理方法,导致数据处理时间难以满足功耗和体积受限的无人水下航行器平台的实时性要求。针对此问题,该文提出分数阶傅里叶变换的带通采样实现方法,通过对线性调频信号时频特性直线在分数阶域的投影进行修正,使利用分数阶傅里叶变换方法处理带通采样的回波数据时,可获得正确的目标参数估计。计算机仿真数据和无人水下航行器湖试数据处理结果验证了分数阶傅里叶变换的带通采样实现方法的正确性,数据处理时间能够满足无人水下航行器平台处理的实时性要求。     

低信噪比线性调频信号目标的方位估计

线性调频(LFM)信号目标的方位估计是水声探测研究的重要内容,在进行方位估计时,若存在强干扰信号源与强背景噪声,阵元接收信号的信噪比会显著降低,严重影响LFM信号目标方位估计结果的准确性.针对该问题,提出了一种简明分数阶滤波方法,并将其与常规波束形成方法(CBF)相结合来实现低信噪比条件下LFM信号目标的方位估计.简明分数阶傅里叶变换能在正交角度上将LFM信号的能量聚集在特定频点处并形成明显的能量峰,利用该特性,可对阵列各阵元接收的低信噪比LFM信号在简明分数阶域聚集的能量峰进行最佳滤波,以滤除干扰信息及背景噪声.对滤波输出进行逆简明分数阶傅里叶变换可得到增强信干比和信噪比的阵元域信号,进一步用于目标方位估计,就能获得更加准确的目标方位。数值仿真结果和海试实验数据处理结果验证表明,本文所提出的方法可有效抑制干扰和背景噪声,并对低信噪比LFM信号进行准确、稳健的方位估计。      

水下连续波有源探测的回波检测算法

研究线性调频连续波在水下探测中的信号模型、回波信号的检测和目标参数估计方法,通过分析回波信号与发射信号间的差拍信号,提出差拍-分数阶傅里叶变换结构的处理算法。为了减少分数阶傅里叶变换二维搜索时的计算量,首先使用Radon-Ambiguity变换估计差拍信号的调频斜率,再做相应阶次的分数阶傅里叶变换。数值仿真说明提出的算法能够有效消除线性调频连续波的距离-速度耦合现象,准确估计目标参数。通过湖上试验比较线性调频脉冲信号和线性调频连续波的处理增益,提出的算法处理的连续波比匹配滤波方法处理的脉冲信号处理增益大13 dB。研究结果表明该算法在连续波水下探测中可行有效,不仅能够准确估计目标参数,还具有良好的检测性能。      

非线性调频信号激励下非线性系统的最优共振响应

非线性调频(NLFM)信号在雷达、通信、信号处理中应用广泛,该类信号所激励下的非线性系统响应有着丰富的信息,通过共振来增强NLFM信号具有一定实际意义与价值.本文主要研究了受到不同类型NLFM信号所激励的非线性系统共振现象,提出了实时尺度变换方法来处理高频NLFM信号,克服人为选择造成信号输出响应较差的缺点.同时,提出实时谱放大因子作为共振评价指标,准确评价NLFM信号激励下的系统共振响应,讨论系统参数对系统最优共振响应的影响,参数选择在合理的区间内即可实现最优共振响应,不仅实现信号特征的大幅增强,还保持信号时频特征的连续性.最后,将实时尺度变换方法和固定尺度变换方法进行对比,说明所提方法处理NLFM信号的优越性.     

浅海双基地有源探测调频信号直达波消除

双基地有源探测常采用长脉宽探测信号以获取更高的时间增益,容易导致回波弱信号被强直达波信号掩蔽而影响回波检测.针对长调频信号直达波的干扰,提出基于分数阶傅里叶变换(FrFT)的直达波消除方法.该方法利用调频信号在时频分布上的稀疏性,通过对接收信号进行分数阶傅里叶变换分离直达波和回波信号然后在变换域对直达波信号进行去除.远...     

分数傅里叶变换啁啾滤波

针对常规傅里叶变换所不能解决的啁啾噪声滤除问题，利用Wigner分布函数分析分数傅里叶变换的空域和频域特性，提出在分数傅里叶变换域进行啁啾滤波的方法。并将该方法应用到图像处理中，对分数傅里叶变换滤除一维和二维图像的啁啾噪声进行了计算机仿真，获得了满意的效果，结果表明该方法在图像处理中的有效性。     

Fractional Gabor transform

A fractional Gabor transform (FRGT) is proposed. This new transform is a generalization of the conventional Gabor transform (GT) based on the Fourier transform to the windowed fractional Fourier transform (FRFT). The FRGT provides analyses of signals in both the real space and the FRFT frequency domain simultaneously. The space-FRFT frequency pattern can be rotated as the fractional order changes. The FRGT has an additional freedom, compared with the conventional GT, i.e., the transform order. The FRGT may offer a useful tool for guiding optimal filter design in the FRFT domain in signal processing.     

一阶光学系统分数傅里叶变换的相空间分析

在维格纳相空间中,通过将一阶光学系统的传输矩阵分解为坐标旋转、比例缩放和啁啾矩阵的组合,得到了一阶光学系统在空域的分数傅里叶表示.结果表明:任意一阶光学系统均可表示为经过比例缩放和二次相位调制的分数傅里叶变换.通过将输入输出光场在相空间中作π/2角旋转,得到了一阶光学系统在频域的传输矩阵和衍射积分公式,进而得到了一阶光学系统在频域的分数傅里叶表示.比较空域和频域一阶光学系统的相空间变换矩阵,说明2个系统本质上属同一变换在不同基坐标下的表示,并推导出了光学系统在空域和频域具有相同分数傅里叶变换的条件.     

水下目标几何声散射回波在分数阶傅里叶变换域中的特性

水下目标散射回波在时域、频域混叠在一起, 而且受声波入射角度的影响严重, 在不同的入射角度下表现出很大的差异, 需要建立全方位入射角度下回波分量的理论分析模型. 本文推导了目标几何声散射分量在分数阶傅里叶变换域中随入射角度变化的解析表达式; 确定了目标几何声散射回波分量在最佳分数阶傅里叶变换域中的全方位模型, 从理论上证明了目标回波的几何特征形式; 给出了离散分数阶傅里叶变换对声散射分量的分辨能力和计算精度与发射信号带宽和观测时间之间的关系. 实验数据处理表明, 建立的分数阶傅里叶变换域的全方位模型与目标几何特征是一致的, 对未知入射角度下的目标识别提供了理论依据.     

Short-time fractional Fourier methods for the time-frequency representation of chirp signals

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.     

Stochastic resonance in a single-mode laser driven by quadratic pump noise and amplitude-modulated signal

This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by quadratic pump noise and amplitude-modulated signal. A new linear approximation approach is advanced to calculate the signal-to-noise ratio. In the linear approximation only the drift term is linearized, the multiplicative noise term is unchangeable. It is found that there appears not only the standard form of stochastic resonance but also the broad sense of stochastic resonance, especially stochastic multiresonance appears in the curve of signal-to-noise ratio as a function of coupling strength λ between the real and imaginary parts of the pump noise.     

The performance of methods based on the fractional Fourier transform for detecting marine mammal vocalizations

The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species.     

The concise fractional Fourier transform and its application in detection and parameter estimation of the linear frequency-modulated signal

A concise fractional Fourier transform(CFRFT) is proposed to detect the linear frequency-modulated(LFM) signal with low signal to noise ratio(SNR).The frequency axis in time-frequency plane of the CFRFT is rotated to get the spectrum of the signal in different angles using chirp multiplication and Fourier transform(FT).For LFM signal which distributes as a straight line in time-frequency plane,the CFRFT can gather the energy in the corresponding angle as a peak and improve the detection SNR,thus the LFM signal of low SNR can be detected.Meanwhile,the location of the peak value relates to the parameters of the LFM signal.Numerical simulations and experimental results show that,the proposed method can be used to efficiently detect the LFM signal masked by noise and to estimate the signal's parameters accurately.Compared with the conventional fractional Fourier transform(FRFT),the CFRFT reduces the transform complexity and improves the real-time detection performance of LFM signal.