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。     

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。      

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...     

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。      

基于分数阶傅里叶变换混响抑制的目标回波检测方法

提出了一种声呐发射信号为线性调频信号时,基于分数阶傅里叶变换混响抑制的目标回波信号检测方法。通过计算混响的缓慢时变包络,对混响进行时间域的平稳化处理。对平稳化的混响信号滑动窗截取,对截取信号进行分数阶傅里叶变换,然后在分数阶傅里叶域进行滤波处理,再进行逆分数阶傅里叶变换恢复出时间域信号,最后输出该信号的能量。当滑动窗截取到目标回波信号时,窗内的混响噪声得到抑制,系统输出目标回波的能量,从而实现混响背景下的信号检测。通过计算机仿真和湖试实验结果,表明所提方法可以准确的在混响背景下检测到目标回波信号,并且在混响噪声背景条件下相比于匹配滤波器具有更好的检测性能。      

分数阶反卷积的高分辨力目标亮点提取

提出了一种采用分数阶反卷积的目标亮点提取方法对目标亮点进行高分辨力提取。该方法依据分数阶域卷积公式,引入反卷积理论去除窗函数的影响,实现了时频域去模糊,提升了时频分辨力。仿真和实验数据表明,基于反卷积的短时分数阶傅里叶变换对线性调频信号的频域分辨力高于分数阶傅里叶变换,可提高时频域上检测线性调频信号的性能。从而实现时频域上目标亮点的高分辨力提取,提升目标亮点间时延差的估计精度。与传统方法相比基于分数阶反卷积的目标亮点提取方法具有更高的分辨力,且对混响有一定的抑制作用。     

基于逐次滤波Radon-Ambiguity变换的多线性调频信号时频检测

Radon-Ambiguity变换是一种检测低信噪比下线性调频信号的有力工具。但在多信号环境下,强线性调频信号分量的Radon-Ambiguity变换对弱线性调频信号分量的Radon-Ambiguity变换有较强的抑制作用。同时Radon-Ambiguity变换对具有相同调频斜率和不同初始频率的线性调频信号分量不能实现识别与区分。提出了一种基于逐次滤波Radon-Ambiguity变换的时频表示方法可以有效地检测出多种情况下的多个线性调频信号。仿真试验证明了此方法可以有效地去除噪声、多信号之间交叉项的影响,在低信噪比下也十分有效。     

线性调频信号激励过阻尼双稳系统的随机共振现象研究

线性调频信号是工程中常见的一种信号, 由于其为非周期信号, 无法以频域信噪比作为衡量其是否产生随机共振的测量手段, 故鲜有文献研究以线性调频信号为激励信号的随机共振现象. 本文利用线性调频信号在最优分数阶Fourier变换域上的能量聚集性, 首次提出以最优分数阶Fourier变换域上定义的信噪比作为测量手段, 研究了线性调频信号叠加高斯白噪声激励过阻尼双稳系统的随机共振现象, 且发现了以线性调频信号为激励信号时产生的新现象, 即随着信号频率的增大, 随机共振将逐渐减弱, 并给出了合理的解释.仿真的结果与理论分析一致, 验证了本文所提出方法的有效性. 关键词： 线性调频信号 分数阶Fourier变换 随机共振     

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.     

Multi component LFM signal detection and parameter estimation based on EEMD–FRFT

This paper studied multi component LFM signal detection and parameter estimation under the noise circumstance of various signal-to-noise ratios. Based on the analysis of fractional Fourier transform detection and parameter estimation on simple component LFM signal, this paper proposed the method of multi component LFM signal detection and parameter estimation based on EEMD–FRFT (Ensemble Empirical Mode Decomposition–Fractional Fourier transform), and this method was that with the EEMD algorithm, from the frequency domain decompose the analyzable signal to narrow-bandwidth components, whose center frequency changed from high to low, then accurately estimate the parameter and detect the signal of each component out of the pseudo-component with FrFT. This method solved the problem of mode aliasing of signal decomposition; meanwhile, the problem of detecting the multi component LFM signal would be simplified as the problem of one-dimensional search in small scope, which could reduce the amount of operation and improved the detection accuracy. A simulation computation for multi component LFM signal of various SNR (signal-to-noise ratios) was made and the result showed that the error of parameter estimation was less than 5% in the case of SNR not less than −10 dB.     

Acceleration target detection based on LFM radar

In radar systems, the echo signal caused by an accelerated target can be similarly considered as linear frequency modulation (LFM) signal. In high signal-to-noise ratio (SNR), discrete polynomial-phase transform (DPT) algorithm can be used to detect the echo signal, as it has low computation complexity and high real-time performance. However, in low SNR, the DPT algorithm has a large mean square error of the rate of frequency modulation and a low detection probability. In order to detect LFM signal in low SNR, this paper proposes a detection method, segment discrete polynomial-phase transform (SDPT), which means, at first, dividing the whole echo pulses into several segments with same duration in time domain, and then, using coherent accumulation method of DFT to segments, at last, processing this signal with DPT in intra-segment. In the case of a large number of segments, the SDPT can improve the output SNR. In addition, in a certain SNR, to the target signal with big sampling interval, large acceleration and less segments, this paper proposes an algorithm to detect the LFM signal generated from the combination of an improved DPT (IDPT) and fractional Fourier transform (FRFT). The output SNR of this algorithm is connected with the length of time delay. In the simulation, when the length of the time delay is 0.2 N, the output SNR is 2.5 dB more than that which results from directly using DPT. Finally, the detection performance and algorithm complexity of the proposed algorithm were analyzed, and the simulated and measured data verify the effectiveness of the algorithm.     

水下回波处理中分数阶傅里叶变换的带通采样实现方法

利用球形压电陶瓷自身所具有的耐压能力,采用径向极化空气背衬压电球壳换能器作为声学接收敏感元件,设计并制作了一种球形耐压水听器。首先对其低频开路接收灵敏度和谐振频率等声学特性进行了分析和有限元仿真,然后对其强度和稳定性等耐压性能进行了分析和有限元仿真,最后对其声学性能和耐压能力进行了测试。测试表明,该球形耐压水听器的直径为36 mm,工作频段为50 Hz10 kHz,低频接收灵敏度为􀀀198:4 dB(0 dB=1 V/Pa),等效自噪声谱级为46.5 dB@1 kHz,其耐压深度可达3000 m。该耐压水听器为大深度水听器设计提供了参考,在深水声学领域具有重要的应用价值。     

Improved space time prewhitener for linear frequency modulation reverberation using fractional Fourier transform

This letter presents an improved space time prewhitening method for linear frequency modulation (LFM) reverberation. The proposed method transforms the reverberation to fractional Fourier domain to whiten using fractional Fourier transform. The linear varying frequency in LFM reverberation is focused on a stationary frequency, and the adjacent block signal is used as the reference signal of prewhitening. Finally, experiment results with real reverberation data verify that the proposed method improves the detection performance of active sonar in shallow sea significantly.     

变分模态分量降噪后重构的水声弱信号检测

针对能量检测法在低信噪比下对非合作水声探测信号的检测性能显著下降的问题,提出了一种组合变分模态分解和小波变换降噪重构的信号检测方法。以信号分解出的各个本征模态函数的近似熵与互相关系数比值作为分量分类参数,将所得分量分为信号分量、含噪信号分量与噪声分量,然后利用第二代小波变换对含噪信号分量降噪后与信号分量组成重构信号,最后对重构信号进行检测。数值仿真结果表明该方法可以在无先验信息的情况下对CW和LFM信号自适应降噪,信噪比0 dB以下时CW信号重构后信噪比提升约12 dB,宽带LFM信号信噪比提升约8～9 dB,有效提升了低虚警概率下信号的检测概率。湖试结果表明,虚警概率为0.1时检测概率可提升至0.9以上,验证了该方法的有效性。     

Application of multi-scale chirplet path pursuit and fractional Fourier transform for gear fault detection in speed up and speed-down processes

Demodulation is very important for gear fault detection. However, the demodulation is substantially complicated by the non-stationary nature of the signal during the speed-up and speed-down processes. As such, we propose a new technique to detect gear faults under such conditions based on the multi-scale chirplet path pursuit (MSCPP) algorithm and the fractional Fourier transform (FrFT) method. With the MSCPP algorithm, the instantaneous frequency of the signal component with the largest energy in the multi-components gear vibration signal can be estimated. Then according to the estimated instantaneous frequency, the vibration signal segment whose instantaneous frequency curve approximated as either an ascending or descending linear segment can be obtained from the original gear vibration signal. In other words, the vibration signal segment that can be regarded as a multi-component linear frequency modulated (LFM) signal is extracted. As the FrFT is suitable for multi-component LFM signal analysis, it is then applied to demodulating this vibration signal segment and hence detecting local gear faults based on the revealed modulation phenomenon. The effectiveness of the proposed method has been demonstrated by both simulation and experimental data.     

基于分数阶傅里叶变换的水下目标宽带回波精确提取

线性调频信号可能将成为水下目标强度宽带测试的一种主要信号形式。本文在分析水中目标回声构成特点的基础上,探讨了一种滤除界面反射精确提取目标回波的方法。利用线性调频信号在一定分数阶傅立叶域呈现高度聚集的特性,将线性调频信号作为收发合置换能器的发射信号,在适当的分数阶傅立叶域中,目标回波和界面反射波如果表现为两个可分离的谱峰,就可以用窄带滤波的方法去除界面反射。本文给出了算法仿真及水池试验结果,即使对于和线性调频回波相距很近的界面反射,仍然可以有效去除,精确提取出目标回波。     

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.