一种分数阶傅里叶变换快速算法的研究

介绍了分数阶傅里叶变换的定义,接着提出了一种分数阶傅里叶变换的快速算法,其中分数阶傅里叶变换快速算法分三步进行:线性调频信号乘法,线性调频信号卷积,另一个线性调频信号乘法,从而利用FFT来计算FRFT。这种算法思想直观,结果与连续FRFT的输出接近。最后用具体的信号作了计算机仿真,并给出Matlab仿真结果图。     

基于多重分数阶傅里叶变换ISAR快速成像算法

关于机动目标的逆合成孔径雷达成像技术在诸多应用领域扮演着重要的角色,但其应用一直存在一个严重问题——时变多普勒频率,它会在信号回波中引入高阶相位项,如调频率项,如果不对其进行精确补偿,最终获得的ISAR图像质量会出现明显恶化.针对上述问题,大量算法相继被提出用以实现调频率的估计,但是这些算法往往存在运算量大以及传递误差...     

A Generalized Reverse Block Jacket Transform

Jacket matrices motivated by the center weight Hadamard matrices have played important roles in signal processing, communication, image compression, cryptography, etc. In this paper we propose a notation called block Jacket matrix which substitutes elements of the matrix into common matrices or even block matrices. Employing the well-known Pauli matrices which are very important in many subjects, block Jacket matrices with any size are investigated in detail, and some recursive relations for fast construction of the block Jacket matrices are obtained. Based on the general recursive relations, several special block Jacket matrices are constructed. To decompose high order block Jacket matrices, a fast decomposition algorithm for the factorable block Jacket matrices is suggested. After that some properties of the block Jacket matrices are investigated. Finally, several remarks are presented. These remarks are associated with comparisons between the Clifford algebra and the block Jacket matrices, generations of orthogonal and quasi-orthogonal sequences, and relations of the block Jacket matrices to the orthogonal transforms for signal processing. Since the Pauli matrices are actually infinitesimal generators of $SU(2)$ group, the proposed construction and decomposition algorithms for the block Jacket matrices are available in the signal processing, communication, quantum signal processing and information theory.      

分数傅里叶变换产生分数泰伯效应

讨论了如何使用分数傅里叶变换来产生分数泰伯效应，导出了要产生这种双重变换的光学条件，变换后的周期、变换比例因子和级联运算法则，并进行了实验验证。这种双重变换有助于光学系统的设计、分析和计算。最后给出了应用实例     

The Fractional Wave Packet Transform

We introduce the concept of the Fractional Wave Packet Transform(FRWPT), based on the idea of the Fractional Fourier Transform(FRFT) and Wave Packet Transform(WPT). We show a version of the resolution of the identity and some properties of FRWPT connected with those of FRFT and WPT.     

分数阶傅里叶变换

最近分数阶傅里叶交换引起光学界的广泛关注，本文介绍分数阶傅里叶交换的概念、性质、光学解释和实现、与其它变换的关系及应用等。     

Two New Convolutions for the Fractional Fourier Transform

In this paper we introduce two novel convolutions for the fractional Fourier transforms, and prove natural algebraic properties of the corresponding multiplications such as commutativity, associativity and distributivity, which may be useful in signal processing and other types of applications. We analyze a consequent comparison with other known convolutions, and establish necessary and sufficient conditions for the solvability of associated convolution equations of both the first and second kind in \(L^1({\mathbb {R}})\) and \(L^2 ({\mathbb {R}})\) spaces. An example satisfying the sufficient and necessary condition for the solvability of the equations is given at the end of the paper.     

分数阶Fourier变换及其应用

本文介绍了一种崭新的信号分析工具－分数阶Ｆｏｕｒｉｅｒ变换（ＦＲＦＴ）。本文在简单介绍了ＦＲＦＴ的几种不同的引入途径和其基本性质之后，在时－频平面对ＦＲＦＴ进行了研究，用经典的Ｆｏｕｒｉｅｒ变换的观点对ＦＲＦＴ进行了解释，并推导了ＦＲＦＴ与Ｒａｄｏｎ－Ｗｉｇｎｅｒ变换的关系。最后，根据ＦＦＲＴ的特点，提出了它在时频信号分析中的两种新的应用途径。     

分数傅里叶变换计算全息图

提出了分数傅里叶变换计算全息图 (FRTCGH)。采用分数傅里叶变换的快速算法和罗曼Ⅲ型迂回位相编码方法设计并制作了一个物体不同分数阶的分数傅里叶变换计算全息图 ,用罗曼Ⅰ型分数傅里叶变换光学系统再现原物体 ,得到了物体清晰的像。分析了FRTCGH和再现图像随分数阶变化的规律 ,讨论了分数傅里叶变换计算全息图与菲涅耳计算全息图之间的关系。     

基于分数阶Hilbert变换的多路加密

基于分数阶Hilbert变换的单边带通信可以同时将分数阶旋转角度作为加密密钥,从而保证通信安全。但基于分数阶Hilbert变换的单边带通信加密技术只能让信号使用一个加密密钥。为了达到增大密钥空间以更有效地保证信息安全的目的,采用多通道滤波器组分路处理的方法,在减少了系统计算复杂度的基础上增大了密钥空间。     

多参数离散分数傅里叶变换的应用

离散分数傅里叶变换是离散傅里叶变换的推广,文中将离散分数傅里叶变换推广到了带有N个参数的多参数分数傅里叶变换.并将它应用于数字图像加密解密过程中.给出了加密解密模型,实验结果表明本方法保密性能高,实现简单,具有广泛的应用前景.     

基于分数阶Fourier变换的反辐射导弹检测技术

针对反辐射导弹的检测问题,主要是消除载机信号的干扰.本文研究了单频信号和线性调频信号的分数阶Fourier变换模函数的时移特性.研究表明,单频信号和线性调频信号的FRFT模函数具有不同的时移特性.分数阶Fourier变换是线性变换,不存在交叉项,采用分数阶Fourier变换搜索匹配动目标信号,使其能量汇聚.根据以上特点本文提出了一种基于观测信号以及其时延信号的分数阶Fourier变换模之差的反辐射导弹检测方法.此方法可以有效的消除载机信号的干扰,并且对背景噪声幅度有一定的抑制作用.仿真结果表明,在低信噪比下能有效的检测出反辐射导弹.     

Fractional Fourier-Radial Transform for Digital Image Recognition

This paper presents a new system for pattern recognition in digital images, called Fractional Fourier-Radial Transform, invariant to translation, scale and rotation (TSR invariant) taking advantage of the well-known properties of some integral transform as Fourier Transform, Mellin Transform and the Radial Hilbert Transform. The main contribution of this work is the use of the Fractional Fourier Transform to avoid, or reduce the overlap between results due to the optimal order selection for each reference image, assuming α = β for computing optimization, which helps to get a higher difference between the reference images spectrum. This system was tested using different species of phytoplankton obtaining a level of confidence of at least 92.68% invariant to position, size, and rotation, supporting scale variations of ±20%. The mean of the highest confidence values for the scale variation correlations is 98.47%, for rotation variation correlations is 100%, and for the rotation and scale variation correlations is 98.15%. The testing dataset images are selected due to their morphology complexity; they have a real pattern to be recognized instead of using a test-book data set.

     

快速傅里叶变换深能级瞬态谱测试系统

提出了一套快速傅里叶变换深能级瞬态谱（FFT-DLTS）测试系统,分析了该系统的硬件构成和软件流程,并给出了一个实例分析。最后,将FFT-DLTS与常规DLTS作了对比。     

Closed-Form Analytical Expression of Fractional Order Differentiation in Fractional Fourier Transform Domain

In this paper, a closed-form analytical expression for fractional order differentiation in the fractional Fourier transform (FrFT) domain is derived by utilizing the basic principles of fractional order calculus. The reported work is a generalization of the differentiation property to fractional (noninteger or real) orders in the FrFT domain. The proposed closed-form analytical expression is derived in terms of the well-known confluent hypergeometric function. An efficient computation method has also been derived for the proposed algorithm in the discrete-time domain, utilizing the principles of the discrete fractional Fourier transform algorithm. An application example of a low-pass finite impulse response (FIR) fractional order differentiator in the FrFT domain has also been investigated to show the practicality of the proposed method in signal processing applications.     

VHDL Implementation of the Fast Wavelet Transform

In this paper, a VHDL implementation of a decomposition unit based on Mallat's fast Wavelet Transform, which utilizes a two-channel subband coder, is described. The units were simulated, synthesized, and optimized using Mentor^? design tools. The final design was verified with VHDL test benches and Matlab image processing tools. Results of the decomposition for color images validate the design. Utilizing a clock frequency of 25 MHz, a time period of 45 ms was estimated for the decomposition process of a 640 × 480 color image, which makes it feasible for real time video compression. The size of the layout was found to be within 2.5 × 2.5 mm, which suggests a 40 pin-package tiny frame. Paul Salama received the B.Sc. in Electrical Engineering (First Class Honors) from the University of Khartoum in 1991, and the M.S.E.E. and the Ph.D. degrees from Purdue University in 1993 and 1999, respectively. He is currently an Associate Professor at the Department of Electrical and Computer Engineering, Purdue School of Engineering and Technology, Indiana University Purdue University Indianapolis (IUPUI). His research interests include image and video compression, image processing, Transmission of compressed Video, Ill posed problems, and medical imaging. Dr. Salama is a member of SPIE, Tau Beta Pi, and Eta Kappa Nu. Maher E. Rizkalla received his Ph.D. in Electrical Engineering from Case Western Reserve University, Cleveland, Ohio in 1985. From Jan. 1985 to Sep. 1986, he was a Visiting Scientist at Argonne National Laboratory, Argonne, IL while being a Visiting Assistant Professor at Purdue University Calumet. Since 1986 he has been with the Department of Electrical and Computer Engineering, Purdue School of Engineering and Technology, Indiana University Purdue University Indianapolis (IUPUI), where he is Professor of Electrical and Computer Engineering. His research interests include solid-state electronics, VLSI design as applied to DSP, electromagnetics, and engineering education. He has published over 100 papers in these areas. He received the outstanding teaching awards in the ECE Department and in the School five times and was the Professor of the Year at Purdue Calumet in 1986. He is the recipient of one NSF grant, and two FIPSE grants, and is COPI of a number of industrial and equipment grants. Dr. Rizkalla is a Senior Member, IEEE, and a Professional Engineer (PE) registered in the State of Indiana. Michael Eckbauer received the M.S.E.E. degree in Electrical Engineering from Indiana University Purdue University Indianapolis (IUPUI) in December 2002. He is currently with GE Medical Systems in Waukesha, Wisconsin.     

Fast Complexified Quaternion Fourier Transform

In this paper, we consider the extension of the Fourier transform to biquaternion-valued signals. We introduce a transform that we call the biquaternion Fourier transform (BiQFT). After giving some general properties of this transform, we show how it can be used to generalize the notion of analytic signal to complex-valued signals. We introduce the notion of hyperanalytic signal. We also study the Hermitian symmetries of the BiQFT and their relation to the geometric nature of a biquaternion-valued signal. Finally, we present a fast algorithm for the computation of the BiQFT. This algorithm is based on a (complex) change of basis and four standard complex FFTs.     

Interpolating Between Periodicity and Discreteness Through the Fractional Fourier Transform

Periodicity and discreteness are Fourier duals in the same sense as operators such as coordinate multiplication and differentiation, and translation and phase shift. The fractional Fourier transform allows interpolation between such operators which gradually evolve from one member of the dual pair to the other as the fractional order goes from zero to one. Here, we similarly discuss the interpolation between the dual properties of periodicity and discreteness, showing how one evolves into the other as the order goes from zero to one. We also discuss the concepts of partial discreteness and partial periodicity and relate them to fractional discreteness and periodicity.     

假彩色编码分数傅里叶变换彩虹全息图

提出了假彩色编码分数傅里叶变换彩虹全息图 ,并对其再现像的位置、大小、编码色的设计进行了讨论。基于再现像的位置、大小与记录系统分数阶有关 ,其编码颜色既与狭缝位置又与记录系统和再现系统的分数阶有关的特性 ,可建立一种新的防伪全息术。     

多重分数傅里叶变换全息防伪术

基于分数傅里叶变换全息图 (FRTH)的记录和再现的特殊性 ,提出一种记录多重全息图的新方法 ,可发展一种多重FRTH防伪术。即利用简单的分数傅里叶变换系统 ,并改变其分数阶 ,就可以很方便地在一块感光板上分别记录多个物体 (或同一物体的不同部分 )在不同位置上的不同阶的FRTH。制作了多重分数傅里叶变换全息图 ,讨论了其防伪特性 ,并获得了满意的再现结果