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.

Generalized Parseval’s Theorem on Fractional Fourier Transform for Discrete Signals and Filtering of LFM Signals

This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality with lower and upper bounds associated with FRFT parameters, named as generalized Parseval’s theorem by us. These results theoretically provide potential valuable applications in filtering, and examples of filtering for LFM signals in FRFT domains are demonstrated to support the derived conclusions.

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.

Fractional Fourier domain hopped communication method based on chirp modulation for underwater acoustic channels

To improve the data rate of underwater acoustic frequency-hopped communications, frequency hopping is applied to different orders of fractional Fourier domain (FrFD), to enable non-intrusive, bandwidth-limited acoustic communications. An FrFD frequency-hopped communication method based on chirp modulation, namely multiple chirp shift keying-FrFD hopping (MCSK-FrFDH), is proposed for underwater acoustic channels. Validated by both simulations and experimental results, this method can reach a bandwidth efficiency twice more than conventional frequency-hopped methods with the same data rate and anti-multipath capability, suggesting that the proposed method achieves a better performance than the traditional frequency hopped communication in underwater acoustic communication channels. Results also show that in practical scenarios, the MCSK-FrFDH system with longer symbol length performs better at the low signal-to-noise ratio (SNR), while the system with larger frequency sweeping range performs better at a high SNR.

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.

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.

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.

A Matrix Formulation of Discrete Chirp Fourier Transform Algorithms

This work presents a computational matrix framework in terms of tensor signal algebra for the formulation of discrete chirp Fourier transform algorithms. These algorithms are used in this work to estimate the point target functions （impulse response functions） of multiple-input multiple-output （MIMO） synthetic aperture radar （SAR） systems. This estimation technique is being studied as an alternative to the estimation of point target functions using the discrete cross-ambiguity function for certain types of environmental surveillance applications. The tensor signal algebra is presented as a mathematics environment composed of signal spaces, finite dimensional linear operators, and special matrices where algebraic methods are used to generate these signal transforms as computational estimators. Also, the tensor signal algebra contributes to analysis, design, and implementation of parallel algorithms. An instantiation of the framework was performed by using the MATLAB Parallel Computing Toolbox, where all the algorithms presented in this paper were implemented.

An Efficient Radar Detection Method of Maneuvering Small Targets

Detection of maneuvering small targets has always been an important yet challenging task for radar signal processing.One primary reason is that target variable motions within coherent processing interval generate energy migrations across multiple resolution bins,which severely deteriorate the parameter estimation performance.A coarse-to-fine strategy for the detection of maneuvering small targets is proposed.Integration of small points segmented coherently is performed first,and then an optimal inter-segment integration is utilized to derive the coarse estimation of the chirp rate.Sparse fractional Fourier transform(FrFT)is then employed to refine the coarse estimation at a significantly reduced computational complexity.Simulation results verify the proposed scheme that achieves an efficient and reliable maneuvering target detection with-16dB input signal-to-noise ratio(SNR),while requires no exact a priori knowledge on the motion parameters.

基于分数阶傅里叶变换和图像加权熵的chirp scaling算法

针对传统的基于傅里叶变换和匹配滤波实现的chirp scaling(CS)成像算法中多普勒参数随斜距变化以及成像分辨率低的问题,提出利用分数阶傅里叶变换(FRFT)对CS成像算法进行优化。首先建立斜视合成孔径雷达(SAR)回波信号模型,理论推导利用FRFT代替匹配滤波进行信号压缩。针对方位向最优旋转角的搜索问题,对得到的图像基于加权最小熵建立代价函数,利用动量法的梯度下降优化算法进行迭代计算,最终得到分辨率更高的SAR图像。为验证算法的有效性,分别在点目标仿真数据和实测SAR数据集上进行实验。结果表明,与传统CS成像算法相比,该算法的成像结果成像主瓣宽度更窄、旁瓣更低、成像更加清晰。

Cyclic beamforming using fractional Fourier transform domain cyclostationarity

A minimum mean-squared error （MSE） beamforming algorithm employing the optimum fractional Fourier transform （Opt-FrFT） domain second-order cyclostationarity is proposed. This method can efficiently filter out the compact desired chirp signal, with a consequence that the cyclically uncorrelated interferences and stationary （colored） Gaussian noise are greatly suppressed in the Opt- FrFT domain. This improves the MSE minimization cyclic beamformer by reducing effectively the Opt-FrFY domain signal-noise cross terms in the presence of finite data length de-correlation operation. Simulation results show that the new method works well under a wide range of signal-to-noise ratio （SNR） and signal-to-interference ratio （SIR）.

分数阶Fourier域中多分量chirp信号的遮蔽分析

本文从分数阶Fourier变换与时频分布的关系入手,在离散分数阶Fourier变换算法基础上导出了单分量chirp信号分数阶Fourier谱强度的近似表达,并依据分数阶Fourier变换的线性性质,得到了调频率不同的两分量chirp信号间分数阶Fourier谱相互遮蔽的量化结果,给出了图例分析,并进行了仿真验证.通过本文的分析可以知道分数阶Fourier域中调频率不同的多分量chirp信号间的相互遮蔽主要取决于各自的幅度、调频率和采样时间.当多分量chirp信号幅度、调频率确定后,可以通过延长采样时间来降低各分量间的相互遮蔽.

分数阶Fourier变换对多分量Chirp信号中心频率的分辨能力

研究了当多个同调频率的Chirp信号相近时,分数阶Fourier变换(FRFT)对中心频率的分辨能力问题。从FRFT在数值计算中对中心频率的估计区间出发,推导出了对中心频率的分辨能力表达式,根据偏微分方程进一步分析了采样时间、采样频率和信号调频率对分辨能力的影响。计算机仿真结果表明,当采样频率为400 MHz,采样时间为2μs;信号调频率的大小不超过100MHz/μs时,FRFT对中心频率的最小分辨力与调频率约成凹形抛物线关系,并且大于2 MHz.

基于修正Chirp-fourier变换的数字水印算法

提出了一种基于修正Chirp-fourier变换的数字水印算法,该算法直接在空域中,嵌入Chirp信号作为水印信息,用修正Chirp-fourier变换对这一特定结构的水印信息进行盲检测。仿真结果表明,该算法透明性好、检测速度快,在对常见的图像处理过程中具有鲁棒性。

分级计算迭代在Radon-Ambiguity变换和分数阶Fourier变换对chirp信号检测及参数估计的应用

该文在分析Radon-Ambiguity变换(RAT)和分数阶Fourier变换对chirp信号的检测和参数估计的基础上,建立了多分量chirp信号检测和参数估计系统模型,提出了分级计算迭代方法,大大减少了计算量,提高了运算速度。

基于Chirp-Fourier变换的LFM信号的参数估计

本文从匹配Fourier变换的角度给出了Chirp -Fourier变换的定义、意义和离散实现。分析表明 ,LFM信号的Chirp -Fourier变换的峰值对应的坐标即为其初始频率和调频斜率 ,所以应用Chirp -Fourier变换可以估计LFM信号的参数。仿真试验表明 ,应用Chirp -Fourier变换不但可以有效地估计LFM信号的参数 ,而且有很好的抗噪声干扰能力。

一种新的分数阶Fourier域的Chirp类水印方案

提出了一种新的分数阶Fourier域Chirp类数字水印方案,该方案利用分数阶Fourier变换基函数的正交性和旋转相加性,在不同的分数阶Fourier域嵌入Chirp水印,并利用分数阶Fourier域Chirp信号的聚集性进行盲检测。接着结合该水印嵌入方案,利用分数阶Fourier变换的旋转相加性和酉性,推导出分数阶Fourier域水印容量的计算公式。仿真实验表明该算法由于可以选择嵌入在不同分数阶Fourier域,使得嵌入方法灵活安全,同时算法的不可见性好,对高斯白噪声干扰、裁剪及其它常见图像处理过程具有一定的鲁棒性。

高斯脉冲调制Chirp信号分数阶Fourier变换的解析表示

分数阶Fourier变换是Fourier变换的一种广义形式,揭示了信号从时域到频域变化过程中所呈现的特征,运用FrFT分析Chirp信号具有极佳的能量积聚效果。介绍分数阶Fourier变换的基本定义,给出高斯脉冲Chirp信号的FrFT以及最优化高斯脉冲Chirp信号分析角度,对于该类信号的低噪声检测与参数估计具有良好的应用前景。

基于修正离散Chirp-Fourier变换的ISAR成像算法

针对逆合成孔径雷达(ISAR)对机动目标成像的问题,提出了一种新的机动目标ISAR成像算法。该算法基于机动目标散射点的多普勒频率近似于线性调频(LFM)信号的特征,利用修正离散Chirp Fourier变换对LFM信号进行检测和参数估计,通过结合CLEAN技术进行多次迭代有效地克服了散射点分量间的相互影响,可获得较为理想的成像效果。给出了应用该方法的具体步骤,并用仿真数据验证了该方法的有效性。

图像在Chirp-Fourier域的能量分布与Chirp水印算法研究

分析了图像在Chirp-Fourier域的能量分布,给出空域Chirp水印嵌入参数选取与Chirp-Fourier域水印检测时的处理方法。仿真结果表明,按照给出的参数嵌入水印,水印算法的透明性好,检测快,对常见的图像处理鲁棒性较强。