Digital Computation of Linear Canonical Transforms

We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take ~ N log N time, where N is the time-bandwidth product of the signals. The only essential deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus, the algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy.     

基于自适应分数阶傅里叶变换的线性调频信号检测及参数估计

该文提出了一种基于最小均方算法的自适应计算分数阶傅里叶变换的方法并将该方法应用到多分量chirp信号的检测与估计之中。该方法通过对连续型分数阶傅里叶反变换进行离散化采样,得到适合数值计算的离散形式,进而通过适当的选择输入向量和目标函数构造自适应滤波器,经过最小均方算法进行训练后所得的滤波器权系数即为分数阶傅里叶变换的结果。仿真实验表明,该方法可以用来计算分数阶傅里叶变换及对chirp信号进行检测和参数估计,且计算延时相对较小。     

基于尺度变换的宽带线性调频信号时差/尺度差估计算法

提出了一种基于尺度变换的宽带线性调频信号时差和尺度差的快速算法.根据两路接收到的线性调频信号间调频率之比为尺度差的平方的特点,利用分数阶傅里叶变换分别估计出两路信号的调频率,即可获得尺度差的估计.将估计的尺度差对一路信号进行伸缩,并计算伸缩后信号与另一接收信号的时域相关,根据相关峰的位置估计出时差.相比于传统基于宽带互模糊函数的方法,该方法避免了二维搜索宽带互模糊函数的峰值,只需若干次快速傅里叶变换即可实现,能够显著降低运算量.仿真结果显示该方法在高信噪比下逐渐接近克拉美-罗下界.     

基于分数傅里叶四阶中心矩的尺度差/时差估计

针对大瞬时宽带线性调频信号的时差/尺度差在低信噪比下估计精度下降和算法运算量大的问题。本文利用时频轴旋转、魏格纳分布和模糊函数的关系推导出分数阶傅里叶四阶中心矩和尺度差的关系式,通过寻找两路信号的分数阶傅里叶四阶中心矩在角度域的位置,即可获得尺度差的估计值。将估计的尺度差对一路信号进行伸缩,并计算伸缩后信号与另一接收信号的时域相关,根据相关峰的位置估计出时差,并对本文算法抗噪性进行定性推导。仿真结果表明,相比于分数阶傅里叶尺度变换时差/尺度差估计算法,本文算法提高了在低信噪比下时差/尺度差估计精度,并对算法抗噪性定量分析得出本文算法抗噪性更好。      

基于分数阶Fourier变换的机载SAR运动目标检测

该文首先建立了机载合成孔径雷达(SAR)对运动目标的回波信号模型,阐述了其本质为线性调频信号的特点。根据这种特点,提出了一种基于分数阶Fourier变换的机载SAR运动目标检测新方法,有效地消除了线性调频信号的时频耦合特性对信号检测的影响。与双线性时频分布类算法相比,分数阶Fourier变换是线性变换,在多运动目标存在的情况下,不会受到交叉项的影响。仿真结果验证了算法的有效性。     

非线性CS算法的前斜视SAR成像

针对SAR的前途斜视工作模式,该文建立了雷达信号的回波模型,详细分析了回波信号的瞬时方位频率和瞬时多普勒频率及距离Chirp斜率对方位频率的影响。然后结合经典的CS算法,提出了一种基于前斜视的改进CS算法,并利用该方法进行了仿真试验。理论分析和仿真结果表明,该方法更符合斜视SAR的几何关系,能有效地进行距离压缩、距离徒动校正和方位聚焦,改善了成像质量。     

Eigenfunctions of linear canonical transform

The linear canonical transform (the LCT) is a useful tool for optical system analysis and signal processing. It is parameterized by a 2×2 matrix {a, b, c, d}. Many operations, such as the Fourier transform (FT), fractional Fourier transform (FRFT), Fresnel transform, and scaling operations are all the special cases of the LCT. We discuss the eigenfunctions of the LCT. The eigenfunctions of the FT, FRFT, Fresnel transform, and scaling operations have been known, and we derive the eigenfunctions of the LCT based on the eigenfunctions of these operations. We find, for different cases, that the eigenfunctions of the LCT also have different forms. When |a+d|<2, the eigenfunctions are the scaling, chirp multiplication of Hermite functions, but when |a+d|=2, the eigenfunctions become the chirp multiplication, chirp convolution of almost-periodic functions, or impulse trains. In addition, when |a+d|>2, the eigenfunctions become the chirp multiplication and chirp convolution of self-similar functions (fractals). Besides, since many optical systems can be represented by the LCT, we can thus use the eigenfunctions of the LCT derived in this paper to discuss the self-imaging phenomena in optics. We show that there are usually varieties of input functions that can cause the self-imaging phenomena for an optical system     

基于离散多项式相位变换和分数阶傅里叶变换的加速目标检测算法

 本文提出了一种离散多项式相位变换(DPT)和分数阶傅里叶变换(FRFT)相结合的LFM检测方法.首先,分析了经典DPT算法中调频分辨率与互相关时延、积累脉冲长度以及积累性能之间的相互关系,指出时延较小的DPT算法与经典DPT算法相比,检测性能提高约3dB,但调频率估计误差大.其次,针对这一问题,提出在DPT基础上,利用FRFT进一步提高调频率估计精度,当输入信噪比大于-11dB时,在分数阶域引入一维牛顿迭代法可提高运算速度;最后,给出了算法复杂度和估计误差的理论分析并用实验结果验证了算法的有效性.     

Chirp Scaling算法中的相位补偿因子研究

该文从SAR回波的二维频谱表达式入手,研究了适合高波段SAR的CS(Chirp Scaling)类算法和一种适合超宽带(Ultra Wideband,UWB)SAR成像的非线性CS算法,通过对算法推导中的近似性分析,重新刻画了SAR成像,即SAR成像是利用回波频谱特性构造频域或时域相位补偿因子的过程,尤其是对UWB SAR回波,相位补偿因子的精确性直接影响着目标聚焦性能。仿真实验表明,补偿三阶以上二维相位耦合的非线性CS算法能够在一定的测绘带内满足UWB SAR点目标的理想聚焦;同时,该算法在UWB SAR实测数据处理中也已得到成功应用。     

Precision SAR processing using chirp scaling

A space-variant interpolation is required to compensate for the migration of signal energy through range resolution cells when processing synthetic aperture radar (SAR) data, using either the classical range/Doppler (R/D) algorithm or related frequency domain techniques. In general, interpolation requires significant computation time, and leads to loss of image quality, especially in the complex image. The new chirp scaling algorithm avoids interpolation, yet performs range cell migration correction accurately. The algorithm requires only complex multiplies and Fourier transforms to implement, is inherently phase preserving, and is suitable for wide-swath, large-beamwidth, and large-squint applications. This paper describes the chirp scaling algorithm, summarizes simulation results, presents imagery processed with the algorithm, and reviews quantitative measures of its performance. Based on quantitative comparison, the chirp scaling algorithm provides image quality equal to or better than the precision range/Doppler processor. Over the range of parameters tested, image quality results approach the theoretical limit, as defined by the system bandwidth     

The effect of pulse phase errors on the chirp scaling SARprocessing algorithm

The chirp scaling (CS) SAR processing algorithm uses the linear FM property of the transmitted pulses to provide accurate range cell migration correction. However, when the transmitted pulse is not linear FM, or if the FM rate is not known exactly, processing errors due to chirp scaling will result. This paper presents the resulting processing error in the CS algorithm, given pulse phase errors that exceed those expected in SAR systems. The registration and phase error that result in chirp scaling are negligible for typical or stable pulse phase errors, or can be avoided if phase modulation coefficients are estimated from the replica. A fast Fourier transformed pulse replica is sufficient to form the range matched filter in the CS algorithm, giving slightly better range resolution than the range/Doppler (R/D) algorithm     

Parameter Estimation of LFM Signals Based on Scaled Ambiguity Function

A method based on the scaled ambiguity function for parameter estimation of LFM signals under noncooperative conditions is presented. In the proposed algorithm, the scaling principle is employed to remove the linear frequency migration brought by the coupling between the time variable and the lag variable. Afterward, the Fourier transform is performed for feature extraction of LFM signals on the centroid frequency versus chirp rate plane. The method avoids centroid frequency information loss, which is almost inevitable in the Radon-ambiguity transform. Furthermore, fractional lower-order statistics and the scaled ambiguity transform are combined to improve the performance in practical impulsive noise environments. Simulation results show that the fractional lower-order scaled ambiguity transform is robust for both Gaussian and impulsive noise, and it achieves significant performance improvement in a heavy noise environment.     

一种特殊构型的双站SAR的CS实现

针对发射机位于地球同步卫星的双站SAR这种新型成像雷达体制,建立了信号的回波模型,并推导了在这一模型下的Chirp Scaling算法实现.通过大场景点阵目标的仿真证明,该算法处理速度快,无需插值即可实现对SAR原始数据的二维匹配滤波操作进而实现良好的SAR图像效果,可适用于高精度发射机位于同步卫星的双站SAR的成像处理.     

A short discussion on the exact compensation of the SARrange-dependent range cell migration effect

Efficient and precise compensation of the range cell migration (RCM) effect is a key point for a fast and accurate synthetic aperture radar (SAR) data processor. In particular the range-dependent nature of the range cell migration effect complicates the compensation operation. It has been recently shown that an exact compensation of the range-dependent RCM (RDRCM) phenomenon can be carried out either by applying the chirp scaling algorithm or the chirp z-transform procedure. This paper investigates the relationship between the two methods. In particular, it is shown that the chirp z-transform based approach represents a particular implementation of the chirp scaling algorithm. A final discussion is dedicated to show how the chirp z-transform and the chirp scaling procedure can be applied within a SAR data processing algorithm     

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.     

基于ChirpScaling算法的星载SAR成像处理实现方法

本文提出一种基于ＣｈｉｒｐＳｃａｌｉｎｇ（ＣＳ）算法的星载合成孔径雷达成像处理实现方法，该算法与目前国际上通用的距离－多普勒算法相比，由于避免了插值运算，且能够精确地进行距离徒动校正，使得成像质量优于精的ＲＤ算法。     

A new method for the compensation of the SAR range cell migrationbased on the chirp z-transform

Precision synthetic aperture radar (SAR) data processing requires the compensation of the range-dependent range cell migration (RDRCM) phenomenon. This paper describes a new method that permits the compensation of the RDRCM effect using a nonstandard Fourier transform (FT). This operation is applied, in the two-dimensional Fourier domain, to the range signal spectrum and allows the compensation of the azimuth frequency-dependent scaling factor due to the RDRCM. The nonstandard FT is performed via a chirp z-transform that is carried out with one convolution operation and two phase multiplications     

高分辨星载SAR改进ChirpScaling成像算法

本文提出了一种用于星载合成孔径雷达(SAR)的改进Chirp Scaling成像处理算法.本文分析了三种星载SAR距离模型,根据误差最小的斜视等效距离模型,推导了改进Chirp Scaling算法,给出了实现步骤.该算法适用于大距离徙动高分辨率星载SAR精确成像.并且基于改进的Chirp Scaling算法,分析了多普勒参数误差对成像质量的影响.最后通过计算机仿真,验证了算法的有效性.     

Fractional Fourier transform of the Gaussian and fractional domain signal support

The fractional Fourier transform (FrFT) provides an important extension to conventional Fourier theory for the analysis and synthesis of linear chirp signals. It is a parameterised transform which can be used to provide extremely compact representations. The representation is maximally compressed when the transform parameter, /spl alpha/, is matched to the chirp rate of the input signal. Existing proofs are extended to demonstrate that the fractional Fourier transform of the Gaussian function also has Gaussian support. Furthermore, expressions are developed which allow calculation of the spread of the signal representation for a Gaussian windowed linear chirp signal in any fractional domain. Both continuous and discrete cases are considered. The fractional domains exhibiting minimum and maximum support for a given signal define the limit on joint time-frequency resolution available under the FrFT. This is equated with a restatement of the uncertainty principle for linear chirp signals and the fractional Fourier domains. The calculated values for the fractional domain support are tested empirically through comparison with the discrete transform output for a synthetic signal with known parameters. It is shown that the same expressions are appropriate for predicting the support of the ordinary Fourier transform of a Gaussian windowed linear chirp signal.     

临近空间慢速运动平台SAR基于CS成像算法的运动补偿

分析了临近空间慢速运动平台合成孔径雷达（SAR）中平台运动误差对接收信号的影响,指出在成像的运动补偿处理当中,可以将距离向误差分解成空不变项和空变项,并采用一阶和二阶运动补偿的方法对两种误差项进行校正补偿。为了将测量的运动误差数据应用到高分辨成像中,本文采用了一种与Chirp Scaling（CS）相结合的运动补偿方法。最后通过对仿真数据进行分析,验证了本方法的可行性。