基于FrFT和RVM的变压器局部放电模式识别

快速准确识别局部放电类型对于保证变压器安全稳定运行具有重要意义。针对局部放电信号模式识别中面临的最优特征参数提取和分类器设计难题,提出一种基于分数阶傅里叶变换(fractional Fourier transform,FrFT)和相关向量机(relevance vector machine,RVM)的局部放电模式识别方法。首先将FrFT引入局部放电信号分析领域,利用FrFT将局部放电信号转换至分数域并对其进行多尺度分析,在扩充信息提取维度的同时,提取可反映不同局部放电信号波形差异的14维特征构成特征向量;然后将特征向量作为输入,建立RVM模型进行最优特征选择和分类判决函数的联合优化,从而实现对不同局部放电信号的分类识别。建立电晕放电、沿面放电和气隙放电试验模型并采集局部放电超声信号开展试验,结果表明所提方法对于每种局部放电信号均能获得较高的识别精度,平均正确识别率相对于常规支持向量机(support vector machine,SVM)分类方法提升超过2.7%。

基于FrFT-FH架构LPD通信波形设计与性能分析

针对Chirp基调制信号在分数阶傅里叶变换域特征明显,信号周期易被检测等问题,提出一种能够实现多域隐蔽的低检测概率(low probability of detection,LPD)波形构造方法。该方法采用分数阶傅里叶变换跳频(fractional Fourier transform-frequency hopping,FrFT-FH)架构,在不改变Chirp信号扩频增益的前提下,通过时宽分割和重组(time width division and reorganization,TDR),降低信号在分数阶傅里叶变换域和周期域的能量聚敛特性。仿真结果表明,相较于现有LPD波形只能实现单一特征域隐蔽的问题,所提波形在不影响系统通信性能的前提下,面对频域检测、分数阶傅里叶变换域检测、周期域检测多种检测手段,在10 dB信噪比条件下的信号检测概率均低于0.2,满足系统在不同特征域下的LPD需求。

基于FRFT的低信噪比LFM信号参数快速估计算法

基于分数阶傅里叶变换(Fractional Fourier Transform,FRFT)对线性调频(Linear Frequency Modulated,LFM)信号参数进行估计,问题关键是确定FRFT最佳阶数,根据误差迭代思想提出新的参数估计算法,该算法利用归一化带宽和旋转角的转化关系,由估计误差推算角度差值,有效降低了运算量,不需要调频斜率正负的先验信息,改进的对数搜索算法可以进一步提高参数估计结果的稳定性和可靠性。仿真结果表明,信噪比在-8 dB以上时该方法在高效率的前提下仍具有良好的参数估计性能,平均估计误差在1%以内,估计结果接近Cramer-Rao下限,满足工程实时处理需求。

Fractal Surface Synthesis Based on Two Dimensional Discrete Fourier Transform

The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fractal dimension and scale factor） and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface （Sq） is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height（Sz）, the skewness（Ssk） and the kurtosis（Sku） are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.

基于FrFT-Keystone运动补偿的OFDM声纳高速微弱目标相参积累检测算法

针对水下目标探测中使用的正交频分复用信号,提出了一种针对高速微弱目标的相参积累算法,以解决多脉冲积累下由目标机动引起的较大相位变化和由水下环境中信噪比低导致的相参积累增益不足的问题。所提算法利用分数阶傅里叶变换来估计目标的运动参数并进行补偿,并结合Keystone变换,实现对高速微弱目标的多脉冲相参积累。理论推导和仿真实验结果表明,所提算法能够有效补偿高速目标脉冲间的相位移动,并在低信噪比环境下取得较好的能量积累效果。

PCG-Based Exercise Fatigue Detection Method Using FRFT-Based Fusion Model

Accurate detection of exercise fatigue based on physiological signals is vital for reason-able physical activity.As a non-invasive technology,phonocardiogram(PCG)signals possess arobust capability to reflect cardiovascular information,and their data acquisition devices are quiteconvenient.In this study,a novel hybrid approach of fractional Fourier transform(FRFT)com-bined with linear and discrete wavelet transform(DWT)features extracted from PCG is proposedfor PCG multi-class classification.The proposed system enhances the fatigue detection performanceby combining optimized FRFT features with an effective aggregation of linear features and DWTfeatures.The FRFT technique is employed to convert the 1-D PCG signal into 2-D image which issent to a pre-trained convolutional neural network structure,called VGG-16.The features from theVGG-16 were concatenated with the linear and DWT features to form fused features.The fusedfeatures are sent to support vector machine(SVM)to distinguish six distinct fatigue levels.Experi-mental results demonstrate that the proposed fused features outperform other feature combinationssignificantly.

基于FrFT的组合预测模型在地铁基坑沉降监测中的应用

针对极限学习机(ELM)模型在地铁基坑沉降预测领域存在的参数选取困难问题,本文引入粒子群(PSO)算法对ELM模型的关键参数进行寻优,结合分数阶傅里叶变换(FrFT),提出一种基于FrFT与PSO-ELM模型的地铁基坑沉降组合预测模型。首先,采用FrFT对地铁基坑沉降数据进行多尺度分解,得到若干结构简单的子序列;其次,引入粒子群算法对ELM模型进行全局寻优,提升ELM预测性能,对于各子序列,使用提出的PSO-ELM模型分别进行建模预测;最后,叠加各子序列结果作为预测结果。使用某地铁基坑沉降监测数据进行预测实验,对比GM(1,1)模型、ELM网络模型、长短期记忆(LSTM)模型与本文组合预测模型的实验结果,证明本文提出的组合预测模型的预测精度较对比模型明显提升,从而验证了本文模型能够有效挖掘数据中存在的规律性与趋势性信息,同时解决参数选取困难的问题,为相关结构变形监测与预测提供了一定借鉴。

基于FRFT与盲分离的扩频通信网络跳频信号时差估计

针对扩频通信网络跳频信号时差估计结果误差过高,导致信号定位追踪能力下降,多领域内信号传播停滞的问题,为增强扩频通信网络跳频信号的传播效率,提高辐射源跟踪和定位系统的信号探测能力,提出基于分数阶傅立叶变换(FRFT:Fractional Fourier Transform)与盲分离的扩频通信网络跳频信号时差估计算法的方法。采用盲分离方法获取满足跳频信号时差估计条件的两条信道,即平坦衰落信道和频率选择性衰落信道,利用FRFT估计两条信道特征,分别将平坦衰落信道特征和频率选择性衰落信道特征与最大似然块检测算法结合,实现扩频通信网络跳频信号的时差估计。实验结果表明,该方法无论是在正常环境中,还是在噪声干扰环境中,其均方根误差均处于较低水平、估计成功率均处于较高水平。

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 he 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.

Order selection in fractional Fourier transform based beamforming

Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional power spectra（FrFT moment） of the linear chirp signal.This method can adaptively determine the optimum FrFT order by maximizing the second-order central FrFT moment.This makes the desired chirp signal substantially concentrated whereas the noise is rejected considerably.This improves the mean square error minimization beamformer by reducing effectively the signal-noise cross terms due to the finite data length de-correlation operation.Simulation results show that the new method works well under a wide range of signal to noise ratio and signal to interference ratio.

Existence detection of blanket jamming based on fractal characteristics in FRFT domain

This paper addresses the existence detection of blanket jamming based on fractal features in fractional Fourier transform （FRET） domain. Firstly, the existences of fractal features of three typical jamming signals are analyzed, and box dimension and information dimension are employed to describe fractal features quantitatively. Then the differences of fractal characteristics between blanket jamming and white Gaussian noise （WGN） in FRFT domain are described, and a detector to detect the jamming is proposed. At last, simulations are done to verify that the algorithm is effective preferable.

INTERFERENCE MITIGATING BASED ON FRACTIONAL FOURIER TRANSFORM IN TRANSFORM DOMAIN COMMUNICATION SYSTEM

The method of FRactional Fourier Transform (FRFT) is introduced to Transform Domain Communication System (TDCS) for signal transforming in the paper after theoretical analysis. The method yields optimal Basis Function (BF) by FRFT with optimal transform angle. The TDCS using the proposed method has wider usable spectrum, stronger robustness and better ability of anti non-stationary jamming than using usual methods, such as Fourier Transform (FT), Auto Regressive (AR), Wavelet Transform (WT), etc. The main simulation results are as follows. First, the Bit Error Rate (BER) Pb is close to theoretical bound of no jamming no matter in single tone or in linear chirp interference. Second, the interference-to-signal ratio J /E is at least 12dB more than that of Direct Spread Spectrum System (DSSS) under the same BER if the spectrum hopping-to-signal ratio is 1:20 in chirp plus hopping interfering. Third, the Eb /N 0(when estimation difference is 90% between trans- mitter and receiver) is about 3.5dB or about 0.5dB (when estimation difference is 10% between transmitter and receiver) more than that of theoretical result when no estimation difference un-der Pb=10-2.

Quasi-LFM radar waveform recognition based on fractional Fourier transform and time-frequency analysis

Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.

Novel uncertainty relations associated with fractional Fourier transform

In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special ease of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains.

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 bit-error-ratio (BER) are obtained.

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.

基于FRFT的单基地MIMO雷达稳健波束形成算法

以单基地多输入多输出(multiple input multiple output,MIMO)雷达系统为研究对象,针对线性调频(linear frequency modulation,LFM)形式的正交频分复用(orthogonal frequency division multiplexing,OFDM)信号,提出了一种新的稳健自适应波束形成算法。所提算法首先利用LFM信号的特性,对匹配滤波后的雷达回波信号进行分数阶傅里叶变换(fractional Fourier transform,FRFT),经化简得到峰值点作为阵列的观测值。而后,利用观测值构建接收信号的协方差矩阵,并使用Capon谱估计方法重构干扰加噪声数据协方差矩阵。最后,通过求解优化问题估计实际导向矢量,从而得到阵列的最优权值。通过计算机仿真实验,验证了所提算法的有效性。

A fine acquisition algorithm based on fast three-time FRFT for dynamic and weak GNSS signals

As high-dynamics and weak-signal are of two primary concerns of navigation using Global Navigation Satellite System(GNSS)signals,an acquisition algorithm based on threetime fractional Fourier transform(FRFT)is presented to simplify the calculation effectively.Firstly,the correlation results similar to linear frequency modulated(LFM)signals are derived on the basis of the high dynamic GNSS signal model.Then,the principle of obtaining the optimum rotation angle is analyzed,which is measured by FRFT projection lengths with two selected rotation angles.Finally,Doppler shift,Doppler rate,and code phase are accurately estimated in a real-time and low signal to noise ratio(SNR)wireless communication system.The theoretical analysis and simulation results show that the fast FRFT algorithm can accurately estimate the high dynamic parameters by converting the traditional two-dimensional search process to only three times FRFT.While the acquisition performance is basically the same,the computational complexity and running time are greatly reduced,which is more conductive to practical application.

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.

AN OPTIMAL INFORMATION HIDING ALGORITHM FOR SPEECH IN THE FRACTIONAL FOURIER TRANSFORM DOMAIN

With the increasing requirement of military and security, the technology of information hiding for speech becomes a hotspot and difficulty in the fields of speech signal processing and in-formation security, which is developing rapidly. In order to stand against the stegano-analysis, the paper proposed an optimal information hiding algorithm for speech in the Fractional Fourier Transform (FrFT) domain based on the Minimum Mean Square Error (MMSE) criterion. The results of simulation and experiments show that speech modified by the proposed algorithm has no remarkable changes both in time and frequency domains, which can effectively resist the time and frequency analysis, Otherwise, the algorithm is robust to general signal process attack, and the difference is imperceptible between the original and modified speech.