Quantum entangled fractional Fourier transform based on the IWOP technique

In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Reservoir information extraction using a fractional Fourier transform and a smooth pseudo Wigner-Ville distribution

Currently, it is difficult for people to express signal information simultaneously in the time and frequency domains when analyzing acoustic logging signals using a simple-time or frequency-domain method. It is difficult to use a single type of time-frequency analysis method, which affects the feasibility of acoustic logging signal analysis. In order to solve these problems, in this paper, a fractional Fourier transform and smooth pseudo Wigner Ville distribution （SPWD） were combined and used to analyze array acoustic logging signals. The time-frequency distribution of signals with the variation of orders of fractional Fourier transform was obtained, and the characteristics of the time-frequency distribution of different reservoirs under different orders were summarized. Because of the rotational characteristics of the fractional Fourier transform, the rotation speed of the cross terms was faster than those of primary waves, shear waves, Stoneley waves, and pseudo Rayleigh waves. By choosing different orders for different reservoirs according to the actual circumstances, the cross terms were separated from the four kinds of waves. In this manner, we could extract reservoir information by studying the characteristics of partial waves. Actual logging data showed that the method outlined in this paper greatly weakened cross-term interference and enhanced the ability to identify partial wave signals.

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WFRFT的噪声式隐蔽传输方案研究

隐蔽无线通信旨在实现通信双方信息的隐藏传输,以保证信息的安全性。提出一种基于加权分数傅里叶变换的混沌扩频噪声式信号隐蔽通信方法,该方法利用改进后的Logistic映射产生的两个不同的混沌序列对隐蔽信号进行符号扩频,再对其进行加权分数傅里叶变换生成噪声式隐蔽信号。发送方将隐蔽信号与公开信号叠加到一起一同传输,同步等问题交由公开信号解决,而经过处理的隐蔽信号具有低能量和类高斯特性,能够很好地与背景噪声混淆在一起,具有较强的隐蔽性和抗截获能力。仿真结果表明,所提出的方法具有较好的隐蔽性能,仿真误码率与理论推导一致,并且功率比取值在0.007~0.01之间时,可以使隐蔽信号和公开信号都能达到较好的误码率。

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。

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.

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.

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.

Joint Timing and Frequency Synchronization for OFDM based on Fractional Fourier Transform

In this paper a joint timing and frequency synchronization method based on Fractional Fourier Transform （FIFT） is proposed for Orthogonal Frequency-Division Multiplexing （OFDM） system. The combination of two chirp signals with opposite chirp rates are used as the training signal, the received training signal with timing and frequency offset is transformed by FrFT and the two peaks representing two chirps in FrFT domain are detected, then the position coordinates of the two peaks are precisely corrected and substituted into an equation group to calculate timing and frequency offset simultaneously. This method only needs one FrFT calculation to implement synchronization, the computational complexity is equal to that of FFT and less than that of correlation or maximum likelihood calculation of existing methods, and estimation range of frequency offset is Large, greater than half the signal bandwidth, while the simulation results show that even at low SNR it can accurately estimate timing and frequency offset and the estimation error is less than that of existing methods.

基于多级联混沌加密的MP-WFRFT安全通信方法

为提高无线通信物理层安全传输性能,提出一种基于多级联混沌加密的多参数加权分数傅里叶变换(MP-WFRFT)安全通信方法。通过基于Logistic映射和Henon-Sine映射的多级联混沌系统实现比特数据的第1轮置乱加密和符号数据的第2轮相位加密,利用MP-WFRFT的星座裂变特性进行数据第3轮星座加密。三重加密方案极大提升了通信系统的保密性,有效防止了暴力攻击。相比传统的低维混沌加密方法,基于Logistic映射和Henon-Sine映射的多级联混沌具备更大的密钥空间,且系统运动轨迹更为复杂。针对多级联混沌加密方案在数据加密中的应用,提出了新的比特置乱和改进的移位星座旋转方法实现数据安全。仿真结果和分析表明:所提三重加密方案在不影响传输性能的情况下能够有效地对信息进行安全传输,非合作接收方在混沌密钥仅存在10^(-15)偏差的情况下误比特率始终保持在0.5左右。

Digital watermarking for still image based on discrete fractional fourier transform

Presents a digital watermarking technique based on discrete fractional Fourier transform (DFRFT), discusses the transformation of the original image by DFRFT, and the modification of DFRFT coefficients of the original image by the information of watermark, and concludes from experimental results that the proposed technique is robust to lossy compression attack.

Research Progress of the Sampling Theorem Associated with the Fractional Fourier Transform

Sampling is a bridge between continuous-time and discrete-time signals,which is import-ant to digital signal processing.The fractional Fourier transform(FrFT)that serves as a generaliz-ation of the FT can characterize signals in multiple fractional Fourier domains,and therefore can provide new perspectives for signal sampling and reconstruction.In this paper,we review recent de-velopments of the sampling theorem associated with the FrFT,including signal reconstruction and fractional spectral analysis of uniform sampling,nonuniform samplings due to various factors,and sub-Nyquist sampling,where bandlimited signals in the fractional Fourier domain are mainly taken into consideration.Moreover,we provide several future research topics of the sampling theorem as-sociated with the FrFT.

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.

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。

New Eigenmodes of Propagation in Quadratic Graded Index Media and Complex Fractional Fourier Transform

By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalues of propagation in quadratic graded-index medium over a definite distance are the same as the eigenvalues of the α-th CFFT, which means that our definition of the α-th CFFT is physically meaningful.

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%。

From fractional Fourier transformation to quantum mechanical fractional squeezing transformation

By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional squeezing transformation（FrST） which satisfies additivity.By virtue of the integration technique within the ordered product of operators（IWOP） we derive the unitary operator responsible for the FrST,which is composite and is made of e^iπa＋a/2 and exp[iα/2（a^2 ＋a^＋2）.The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.

Imaging Analysis by Means of Fractional Fourier Transform

Starting from the diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified image of input function.

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.