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     

Real-time motion compensation, image formation and image enhancement of moving targets in ISAR and SAR using S-methodbased approach

The commonly used technique for inverse synthetic aperture radar (ISAR)/synthetic aperture radar signal analysis is a two-dimensional Fourier transform (FT), which results in an image of the target's reflectivity mapped onto a range and cross-range plane. However, in cases where the line-of-sight projections of the target's point velocities change or there is uncompensated movement within the coherent integration time, the FT produces blurred images. For target recognition applications, mainly those in military surveillance and reconnaissance operations, a blurred ISAR image has to be refocused quickly so that it can be used for real-time target identification. Two standard techniques used for improvement of blurred ISAR images are motion compensation and the use of quadratic time-frequency representations. Both are computationally intensive. The authors present an effective quadratic time-frequency representation, the S-method. This approach performs better than the Fourier transform method by drastically improving images of fast manoeuvring targets and by increasing the SNR in both low and high noise environments. These advantages are a result of the S-method's ability to automatically compensate for quadratic and all even higher-order phase terms. Thus, targets with constant acceleration will undergo full motion compensation and their point scatterers will each be localised. It should be noted that the source of the quadratic term can come not only from acceleration, but also from non-uniform rotational motion and the cosine term in wide-angle imaging. The method is also computationally simple, requiring only slight modifications to the existing FT-based algorithm. The effectiveness of the S-method is demonstrated through application to simulated and experimental data sets.     

Fourier transform of a linear distribution with triangular supportand its applications in electromagnetics

A three-dimensional Fourier transform (FT) of a linear function with triangular support is derived in its coordinate-free representation. The Fourier transform of this distribution is derived in three steps. First, the 2-D FT of a constant (top hat) function is obtained. Next, the distribution is generalized to a linearly varying function. Finally, the formulation is extended to a coordinate-free representation which is the 3-D FT of the 2-D function defined over a surface. This formulation is applied to the near-field computation, yielding accurate numerical solutions     

An isomorphic Fourier transform analysis of AWGs and FBGs

We present a previously unknown equivalence relationship between the spectral transfer functions of arrayed-waveguide gratings and fiber Bragg gratings (FBGs). We find that both devices can be characterized using a functionally identical Fourier transform (FT) integral; the single difference being that the FT lies within a simple hyperbolic function for the FBG case. Thus, the mode of operation of one device informs and yields insights into the operation of the other device     

一端固定的双站SAR体制下基于距离补偿的毫米波快速成像算法

本文提出了一种一端固定的双站SAR(OS-BiSAR)体制下基于距离补偿的毫米波快速成像算法.在图像重构过程中,该算法通过保留回波模型中的幅度衰减因子来补偿信号传播衰减,并根据目标回波方程特性对接收阵列维执行了卷积操作,最后通过快速傅里叶变换(FFT)以及相干累加等步骤求解出最终目标图像.仿真分析和实验结果表明,与OS...     

Unified fractional Fourier transform and sampling theorem

The fractional Fourier transform (FRT) is an extension of the ordinary Fourier transform (FT). Applying the language of the unified FT, we develop FRT expressions for discrete and continuous signals, introducing a particular form of periodicity: chirp-periodicity. The FRT sampling theorem is derived as an extension of its ordinary counterpart     

基于运动参数非搜索高速机动目标检测

该文提出一种新的高速机动目标检测与参数估计算法。首先,通过二阶Keystone变换(KT)消除距离频率与慢时间的二次耦合,并计算对称瞬时自相关函数(SIAF)。其次,对SIAF不同维依次进行尺度逆傅里叶变换(SIFT)、尺度傅里叶变换(SFT)和快速傅里叶变换(FFT)实现能量积累,在新的参数空间进行峰值检测得到径向速度模糊数和径向加速度估计值。最后,根据估计的参数构造补偿函数对距离徙动和多普勒扩散进行补偿,并通过KT算法实现目标检测和距离、模糊径向速度的估计,结合补偿的径向速度模糊数计算出不模糊径向速度。 由于不需要进行参数搜索,并且SIFT和SFT均能通过FFT快速实现,因此算法计算量得到大幅度减小。仿真实验验证了该算法的有效性。     

A unified framework for the fractional Fourier transform

The paper investigates the possibility for giving a general definition of the fractional Fourier transform (FRT) for all signal classes [one-dimensional (1-D) and multidimensional, continuous and discrete, periodic and aperiodic]. Since the definition is based on the eigenfunctions of the ordinary Fourier transform (FT), the preliminary conditions is that the signal domain/periodicity be the same as the FT domain/periodicity. Within these classes, a general FRT definition is formulated, and the FRT properties are established. In addition, the multiplicity (which is intrinsic in a fractional operator) is clearly developed. The general definition is checked in the case in which the FRT is presently available and, moreover, to establish the FRT in new classes of signals     

Discrete framelet transform based OFDM system using N-FRAT mapping over Rayleigh fading channel

This article proposes an N-finite Radon transform (N-FRAT) and a discrete framelet transform (FT) for the design of a new orthogonal frequency division multiplexing (OFDM) system. In the proposed system, the inverse FT (IFT) and FT were used instead of the inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) to realize multicarrier modulation and demodulation techniques, respectively. Simultaneously, it was suggested that the N-FRAT technique operate as a data mapper instead of the conventional phase shift keying (PSK) and quadrature amplitude mapping (QAM), which are usually used with the traditional OFDM system. The usage of the N-FRAT and FT in the proposed system led to an increase in the orthogonality between the subcarriers due to the application of IFFT in the N-FRAT, which was added to improve the orthogonality and time–frequency localization properties of the FT. Furthermore the proposed structure improved the bandwidth efficiency through the elimination of the cyclic prefix compared to the traditional system. The proposed system was simulated and compared with other OFDM systems, such as FFT based OFDM using N-FRAT mapping (N-FRAT-FFT-OFDM), FT based OFDM using QAM mapping (QAM-FT-OFDM), and FFT based OFDM using QAM mapping (QAM-FFT-OFDM). The simulation was performed over frequency selective fading channel using MATLAB technical programming language. The results of simulations showed that the new structure outperformed the other three systems by reducing the inter-symbol interference (ISI) and inter-carrier interference (ICI), which then improved the bit error rate (BER) performance.     

Application-oriented comparison of the methods for AC/DC converter harmonics analysis

Fourier transform (FT) is the most widely used tool for voltage and current waveform analysis. Nevertheless, it has certain drawbacks for time-varying signals analysis. Therefore, a need for another analysis technique appears. windowed FT, wavelet transform, and modulated lapped transform were considered in this paper. Comparison based on practical application shows the advantages of the last one. As an example, it has been applied for ac/dc converter input current harmonics analysis.     

On Convolution and Product Theorems for FRFT

The fractional Fourier transform (FRFT), which is considered as a generalization of the Fourier transform (FT), has emerged as a very efficient mathematical tool in signal processing for signals which are having time-dependent frequency component. Many properties of this transform are already known, but the generalization of convolution theorem of Fourier transform for FRFT is still not having a widely accepted closed form expression. In the recent past, different authors have tried to formulate convolution theorem for FRFT, but none have received acclamation because their definition do not generalize very appropriately the classical result for the FT. A modified convolution theorem for FRFT is proposed in this article which is compared with the existing ones and found to be a better and befitting proposition.     

Linear recursive operator's response using the discrete Fouriertransform

A classic problem in signal processing is that of analysing empirical data in order to extract information contained within that data. The primary goal of this article is to employ the discrete Fourier transform (DFT) techniques for approximating, to a prescribed accuracy, the response of a shift-invariant recursive linear operator to a finite-length excitation. In this development, the required properties of the Fourier transform (FT) are first reviewed with particular attention directed toward the stable implementation of shift-invariant recursive linear operators. This is found to entail the decomposition of such operators into their causal and anticausal component operators. Subsequently, relevant issues related to the approximation of the FT by the DFT are examined. This includes the important properties of the non-uniqueness of mapping between a sequence and a given set of DFT coefficients. In the unit-impulse response approximation, DFT is shown to provide a useful means for approximating the unit-impulse response of a linear recursive operator. This includes making a partial fraction expansion of the operator's frequency-response. The error incurred in using the DFT for effecting the unit-impulse response approximation is then treated. This error analysis involves the introduction of one-sided exponential sequences and their truncated mappings that arise in a natural fashion when employing the DFT. These concepts form the central theme of the article     

A Convolution and Correlation Theorem for the Linear Canonical Transform and Its Application

As a generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) plays an important role in many fields of optics and signal processing. Many properties for this transform are already known, but the correlation theorem, similar to the version of the Fourier transform (FT), is still to be determined. In this paper, firstly, we introduce a new convolution structure for the LCT, which is expressed by a one dimensional integral and easy to implement in filter design. The convolution theorem in FT domain is shown to be a special case of our achieved results. Then, based on the new convolution structure, the correlation theorem is derived, which is also a one dimensional integral expression. Last, as an application, utilizing the new convolution theorem, we investigate the sampling theorem for the band limited signal in the LCT domain. In particular, the formulas of uniform sampling and low pass reconstruction are obtained.     

SAR imaging of moving targets using polynomial Fourier transform

The polynomial Fourier transform (FT) is employed as a tool for the SAR imaging of moving targets. An efficient algorithm is proposed that can be used for radar images containing both moving and stationary targets. The proposed algorithm can be used in the form of the second-order polynomial FT, but it can also be extended to higher-order and order-adaptive polynomial FT forms.     

用傅里叶变换光谱法记录激光腔内吸收光谱的研究

介绍了初步建立起来的傅里叶变换激光腔内吸收光谱仪（ＦＴ－ＩＣＬＡＳ）装置，讨论了这一探测分子光谱学的方法相对于传统的光栅光谱的激光腔内吸收光谱方法的优点     

基于三阶多项式傅里叶变换的SAR地面加速运动目标参数估计与成像

该文主要针对加速运动目标的参数估计及成像问题,推导了加速度目标的SAR回波频谱,分析了回波相位三次项估计和补偿对运动参数估计和SAR成像的必要性。提出一种利用Hough变换估计距离走动率和径向速度、相位补偿法校正距离徙动效应,并基于三阶多项式傅里叶变换(LPFT)对三次相位估计的新方法。利用Hough变换,在不明显增加计算量的前提下,达到加速运动目标的运动参数精确估计和精确聚焦成像的目的。最后通过仿真数据验证了该算法的有效性。     

基于二次速度估计的距离像运动补偿

为解决频率步进雷达高分辨距离像的运动补偿问题,推导了其成像原理,分析了运动目标的回波相位特性,提出一种基于二次速度估计的距离像补偿算法。首先对回波信号的互相关函数进行快速傅里叶变换(FFT)以获得速度、距离粗估计值,其次采用基于谱包络最小波形熵的修正离散Chirp-Fourier变换(MDCFT)在合理区间内进行参数的精确估计,最后分析其补偿性能。该算法通过对回波互相关函数进行FFT为MDCFT缩小参数搜索区间,将极大简化计算。仿真结果证明了该算法的可行性与有效性。     

A three-dimensional DFT algorithm using the fast Hartley transform

A three-dimensional (3-D) Discrete Fourier Transform (DFT) algorithm for real data using the one-dimensional Fast Hartley Transform (FHT) is introduced. It requires the same number of one-dimensional transforms as a direct FFT approach but is simpler and retains the speed advantage that is characteristic of the Hartley approach. The method utilizes a decomposition of the cas function kernel of the Hartley transform to obtain a temporary transform, which is then corrected by some additions to yield the 3-D DFT. A Fortran subroutine is available on request.     

基于方位波数域聚束模式PFA的运动补偿新方法研究

该文在对聚束模式SAR数据进行极坐标算法(PFA)形式成像的过程中,通过研究载机运动误差对散射点方位向波数表达式的影响,给出了一种基于方位波数域进行运动误差估计及相关补偿的新方法。该方法首先应用距离匹配滤波和方位dechirp实现对原始数据的2维调频率去斜处理,同时经过距离FFT和极坐标算法的操作将原来极坐标下的数据重采样到直角坐标系下的2维波数域,最后对数据进行距离和方位的分块误差估计及补偿。这种方法能很好地针对运动误差造成的方位二次及高次误差相位项进行精确补偿,同时也能处理误差相位的空变性问题,因此可以获得相对传统时域补偿方法更好的图像聚焦效果。实测数据的处理和分析,验证了该文所述方法的有效性,证明了与传统时域运动补偿方法相比的优越性。     

微弱LFM信号的FrFT检测能力分析

基于分数阶傅里叶变换（FrFT）检测线性调频（LFM）信号广泛应用于雷达、通信、声呐和电子战领域,但缺乏对检测灵敏度的定量分析。为此,研究了FrFT对微弱LFM信号的检测能力。根据FrFT思想和二元假设检验理论,推导了检测概率和虚警概率的数学表达式。由于表达式是关于LFM信号频谱的函数,因此区分快变信号和慢变信号对LFM的频谱进行了合理近似。基于接收机工作特性曲线分析了FrFT检测LFM信号的灵敏度。仿真比较了FrFT与传统傅里叶变换（FT）对微弱LFM信号的检测能力,结果表明FrFT对LFM信号的检测灵敏度和信号累积能力均优于FT。