Intermittent Clutter Removal Approach for Wind Profiler Data Based on Fractional Fourier Transform

Through the analysis of the target characteristics and according to the intermittent clutter bursting and short duration characteristics, a new method for the clutter recognition based on the fractional Fourier transform (FRFT) is proposed. This method is predicated on the fact that the FRFT perfectly localizes a chirp signal as an impulse when the angle parameter of the transform matches the chirp rate of the chirp signal. The method involves detecting the presence of the intermittent clutter and correctly estimating its orientation in the time-frequency plane, removing the intermittent clutter in the fractional domain, and completing wind estimation by the power spectrum. By testing the artificial WPR-like signal and data measured from the field, we verify that the FRFT-based method is very effective.     

Key Frame Extraction of Surveillance Video Based on Fractional Fourier Transform

With the vigorous development of national infrastructure construction and public information construction, video surveillance systems have gradually penetrated various fields. The current key frame extraction technology has inadequate target details and inaccurate judgment of local actions. Addressing this problem, a key frame extraction method based on fractional Fourier transform is proposed. This method obtained the phase spectra information of different orders by performing fractional Fourier transform on the surveillance video frames. Next, the method designed an adaptive algorithm based on the golden section point to select the transformation order.Then, the phase spectrum information of two adjacent frames was used to characterize the changes in the global and local motion states of the target. The final step was to extract key frames based on this. Experimental results show that, compared with the previous methods, the key frames extracted by the method proposed in this paper can correctly capture the changes in the global and local motion states of the target.     

Improved Spectral Representation for Birdcall Based on Fractional Fourier Transform

A novel spectral representation based on fractional Fourier transform (FrFT) is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart,and the spectrum gathering method is used to show the energy distribution related to the pitch frequency. The fixed transform order and adaptive orders for FrFT are tested. The fixed order can be obtained empirically or calculated according to the known chirp rate. The adaptive optimal orders are determined by using ambiguity function. Experimental results with birdcalls show that the FrFT-based spectrogram with an optimal transform order has higher resolution than its STFT-based counterpart,and the better performance can be achieved if adaptive orders are used.     

Rejection of Linear FM Interference in DSSS System Based on Fractional Fourier Transform

A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the receiver with an interference exciser is also presented. Based on the property that the fractional Fourier transform of a signal is equivalent to rotating the signal in the time-frequency plane, the received signal is transform into a certain fractional Fourier domain, this transform will result in the least spectrum overlap between the signal and interference. Then, a narrowband filter is exploited to extract most of the interference energy. The performance analyses show that remarkable improvements in signal-to-noise ratio (SNR) and biterror-ratio (BER) are obtained.     

Adaptive Short-Time Fractional Fourier Transform Based on Minimum Information Entropy

Traditional short-time fractional Fourier transform(STFrFT) has a single and fixed window function, which can not be adjusted adaptively according to the characteristics of frequency and frequency change rate. In order to overcome the shortcomings, the STFrFT method with adaptive window function is proposed. In this method, the window function of STFrFT is adaptively adjusted by establishing a library containing multiple window functions and taking the minimum information entropy as the criterion, so as to obtain a time-frequency distribution that better matches the desired signal. This method takes into account the time-frequency resolution characteristics of STFrFT and the excellent characteristics of adaptive adjustment to window function, improves the time-frequency aggregation on the basis of eliminating cross term interference,and provides a new tool for improving the time-frequency analysis ability of complex modulated signals.     

Novel Way to Suppress Reverberation Based on Fractional Fourier Transform

A novel method of anti-reverberation based on the fractional Fourier transformation is presented. By virtue of the fact that it has a good focus property in the fractional Fourier domain, the linearly frequency modulation (LFM) signal can be seperated from the reverberation through a swept-frequency filter. With the actual reverberation data and the LFM pulse for seperation, the good results are obtained : the reverbareation is largely removed, and relatively the better performance is shown under the lower signal reverberation ratio (SRR). Based on the theorical analyses and simulation results, two schemes for detecting targets are provided: one is the detection of the LFM echo from the target with a threshold by means of this method directly; the other is to detect the target by means of other methods, with this method performing pre-process to increase SRR, which need enoughlarge SRR.     

两个简单的分数傅立叶变换光学装置

给出两个可实现分数傅立叶变换新的简单光学装置，利用光学标度分数傅立叶变换和矩阵光学的方法，得到实现分数傅立叶变换的条件。并与Lohmann的两个光学基本单元比较分析。最后给出简单的数值模拟。     

基于分数阶傅里叶变换的混叠电磁信号分离研究

在现代电子侦察领域中,随着电磁信号接收环境的日益复杂以及电子防御措施的完善,对信号进行分选和识别的工作变得更加复杂。由于在同一时间内,接收机能够接收到多个信号,导致从这几个混和重叠的信号中检测并分离出来每个信号及其相应的特点参数十分困难。针对电磁环境中存在的干扰源信号混叠的问题,基于分数阶傅里叶变换对传统混叠电磁信号参数估计算法进行改进,并设计出相应的分离方法。通过仿真实验证明,新的方法具有更好的信号参数估计性能,且具备更强的噪声抑制能力。     

A New Tensor Factorization Based on the Discrete Simplified Fractional Fourier Transform

Tensor analysis approaches are of great importance in various fields such as computation vision and signal processing. Thereinto, the definitions of tensor-tensor product(t-product)and tensor singular value decomposition(t-SVD) are significant in practice. This work presents new t-product and t-SVD definitions based on the discrete simplified fractional Fourier transform(DSFRFT). The proposed definitions can effectively deal with special complex tenors, which further motivates the transform based tensor analysis approaches. Then, we define a new tensor nuclear norm induced by the DSFRFT based t-SVD. In addition, we analyze the computational complexity of the proposed t-SVD, which indicates that the proposed t-SVD can improve the computational efficiency.     

Chirp-Rate Resolution of Fractional Fourier Transform in Multi-component LFM Signal

Distinguishing close chirp-rates of different linear frequency modulation (LFM) signals under concentrated and complicated signal environment was studied. Firstly, detection and parameter estimation of multi-component LFM signal were used by discrete fast fractional Fourier transform (FrFT). Then the expression of chirp-rate resolution in fractional Fourier domain (FrFD) was deduced from discrete normalize time-frequency distribution, when multi-component LFM signal had only one center frequency. Furthermore, the detail influence of the sampling time, sampling frequency and chirp-rate upon the resolution was analyzed by partial differential equation. Simulation results and analysis indicate that increasing the sampling time can enhance the resolution, but the influence of the sampling frequency can be omitted. What’s more, in multi-component LFM signal, the chirp-rate resolution of FrFT is no less than a minimal value, and it mainly dependent on the biggest value of chirp-rates, with which it has an approximately positive exponential relationship.     

分数阶Fourier变换在SAR动目标检测中的应用

基于分数阶Fourier变换与时频分布的关系，利用合成孔径雷达运动目标回波信号本质上为线性调频信号的特点，在分数阶Fourier域对运动目标进行检测和多普勒参数估计，并通过理论分析和计算机仿真证明了该方法的有效性。     

基于FRFT的小波包调制信号的识别研究

该文基于正交频分复用调制和小波包调制信号的调制原理,利用分数阶傅立叶变换的时频旋转特性,探讨了在高斯信道、瑞利信道和频率选择信道下小波包调制信号的识别.仿真实验结果表明,该方法具有良好的识别性能,不需要任何信道参数,能较好的实现盲信道的小波包调制识别.     

分数阶Fourier变换在信号处理中的应用研究

本文综述了分数阶Fourier变换的定义、数值化实现方法及其应用。重点比较了三种数值化实现方法的优缺点,详细阐释了离散采样型数值化方法的实现过程。此外,本文对分数阶Fourier变换在数字水印、信号检测与参数估计和生理信号去噪等信号处理中的应用做了概述,系统阐释其算法原理与处理过程。最后,总结了分数阶Fourier变换在时变、非平稳等复杂信号处理中表现出的优势,并展望了今后的研究发展方向。     

基于相位信息的分数傅里叶变换域超宽带接收机

现有的超宽带接收机在多径分离方面存在一定的限制,为了避免上述问题,提出了一种基于相位信息的分数傅里叶变换域超宽带接收机设计方案.采用Chirp信号作为超宽带脉冲波形,并利用其在分数傅里叶变换域上能量聚集的特性在接收端进行信号滤波,得到多径分量;同时,根据分数傅里叶变换的时移性质,利用多径到达时间及多径到达相位的估计得到模板多径处的相位校正因子;最后,将接收到的信号与相位校正因子结合起来,并利用相关判决得到对数据信息的估计.仿真结果表明,通过对相位信息的校正可以得到比传统接收机更好的系统误码性能;而且由于符号间干扰对系统的影响并不严重,可以实现高数据速率的信号传输.     

GP Algorithm-Based Fourier Transform Infrared Spectrum Trend Term Removal Model

Trend term removal is a key step in Fourier transform infrared spectroscopy(FTIR) data pre-processing. The most commonly used least squares (LS) method, although satisfying the real-time requirement, has many problems such as highly correlated initial values of the expression parameters, the need to pre-estimate the trend term shape, and poor fitting accuracy at low signal-to-noise ratios. In order to achieve real-time and robust trend term removal, a new trend term removal method using genetic programming (GP) in symbolic regression is constructed in this paper, and the FTIR simulation interference results and experimental measurement data for common volatile organic compounds (VOCs) gases are analyzed. The results show that the genetic programming algorithm can both reduce the initial value requirement and greatly improve the trend term accuracy by 20%–30% in three evaluation indicators, which is suitable for gas FTIR detection in complex scenarios.     

基于最优FRWT的非平稳信号去噪新方法

研究非平稳信号的去噪,提出一种基于最优分数阶小波变换（FRWT）的信号去噪方法.该方法根据输出信号信噪比采用遗传算法寻找FRWT的最优分数阶值,实现非平稳信号的去噪.以带噪语音信号为例的去噪实验结果表明,采用新方法的去噪效果明显提高.     

基于分数阶Fourier变换的Chirp-COTR-UWB系统窄带干扰抑制

对基于Chirp的正交码发送参考超宽带（Chirp—COTR—UWB）系统进行研究,推导了窄带单音干扰和窄带BPSK干扰条件下接牧机干扰输出分量的表达式,证明了窄带平稳干扰信号经过去斜脉冲压缩后将被展宽成两个具有不同中心频率的非平稳线性调频干扰。采用分数阶Fourier变换的时频分析方法对线性调频干扰进行抑制,并对该系统抗干扰性能进行了仿真分析。结果表明采用FrFT时频方法可有效抑制Chirp—COTR—UWB信号中的窄带干扰,并改善系统的抗干扰性能,     

基于小波变换的SAR幅度图像压缩算法

针对合成孔径雷达信号处理的幅度图像压缩问题,提出一种基于小波变换的幅度图像压缩方法,对幅度图像进行离散小渡变换,实现幅度图像的多级分解,达到良好的压缩效果.使用星载合成孔径雷达RADARSAT的图像作为测试图像进行实验,压缩比CR=10∶1,峰值信噪比PSNR=31.86 dB.仿真实验结果验证了所提出算法的有效性和实用性.     

Novel LFM Jammer Suppression Algorithm for DSSS in FRFT Domain

A novel algorithm is proposed to resolve the defects in the traditional linear frequency modulation (LFM) jamming suppression algorithm in the fractional Fourier transform (FRFT) domain. The traditional LFM jamming suppression algorithm in the FRFT domain has some defects. For example, the exact threshold is difficult to set and both the signal-to-noise ratio (SNR) loss and spectrum leakage are serious in strong jamming-to-signal ratio (JSR) situations. Windowing, overlapping and inverse windowing techniques are used in the FRFT domain to reduce the spectrum leakage and the SNR loss. Under the condition that only the direct sequence spread spectrum (DSSS) signal and white Gaussian noise are present, the amplitude of the received signal after FRFT is assumed to be Rayleigh distributed. Based on the distribution characteristic, hypothesis testing is used to suppress the jamming spectrum using the algorithm. Simulation results show that the performance of proposed algorithm is better than that of the conventional algorithms, especially in a strong jamming and multi component LFM jamming environment.     

基于WVHT 的合成孔径雷达运动目标检测与成像

目的针对合成孔径雷达（ＳＡＲ）的运动目标检测和成像提出了一种通用、完整的ＷｉｇｎｅｒＶｉｌｅＨｏｕｇｈ变换（ＷＶＨＴ）．方法基于线积分,将ＷＶＤ和Ｈｏｕｇｈ变换结合起来,推导出ＷＶＨ变换,并利用计算机仿真的ＳＡＲ回波数据对该新ＷＶＨ变换作了验证．结果与结论计算机仿真结果证明了该变换的正确性和有效性．和传统的ＷＶＤＨＴ方法相比,这种基于ＷＶＨＴ的ＳＡＲ运动目标检测和成像的新方法,可以将多目标回波的ｃｈｉｒｐ信号从时间域直接转换到参数域,同时完成了ＷＶＤＨＴ方法中的交叉项抑制和运动参数的估计,进而对多目标成像,简化了处理过程．这种新ＷＶＨ变换还可以应用于其它场合的ｃｈｉｒｐ信号检测中．