离散分数阶傅里叶变换快速算法的DSP详细实现

为满足在数字信号处理器DSP(digital signal processor)上进行离散分数阶傅里叶变换DFRFT(discrete fractional fourier transform) 实时计算的要求，通过对多种DFRFT计算方法进行比较,选择Ozaktas提出的DFRFT快速算法进行基于DSP的详细实现处理。在对该快速算法进行理论分析的基础上，将快速算法的计算过程进行优化配置，并给出完整的计算量统计结果。在保证精度要求的情况下，提出的详细实现方法将快速算法的实数乘法计算量减至最小。工程实际应用表明：该方法满足DSP运算精度和实时性要求。     

一种基于混沌和分数阶傅里叶变换的数字水印算法

基于混沌序列及离散分数阶傅里叶变换,提出了一种基于混沌和分数阶傅里叶变换的数字水印算法,并对算法及抗攻击性能进行了仿真分析.结果表明,该算法简单有效,对JPEG压缩、噪声、滤波等攻击具有良好的鲁棒性. 关键词： 数字水印 混沌 分数阶傅里叶变换 鲁棒性     

基于分数阶傅里叶变换的弹载SAR成像算法

针对弹载合成孔径雷达(SAR)回波信号的多普勒参数随斜距变化大及传统脉冲压缩成像算法分辨率低的问题,本文提出了一种基于分数阶傅里叶变换(FrFT)的弹载SAR成像算法.首先建立弹载SAR末制导阶段回波信号模型,然后通过局部最优处理来测量回波信号的调频率,并以此计算FrFT的最优阶次,在最优阶次下分别对回波信号进行距离向和方位向的FrFT,从而得到成像区域的SAR图像,最后分别采用传统脉冲压缩成像算法与本文基于FrFT的成像算法进行仿真和实测对比实验.实验结果表明,该算法能够对目标区域精确成像;由于在成像处理过程中,对每个距离向和方位向的回波信号进行独立的局部最优处理,因此该算法更适应于弹载SAR的非线性飞行轨迹,大大提高了弹载SAR的成像性能.该研究成果在目标探测与识别,精确制导等领域中具有重要的应用价值.     

基于分数阶傅里叶变换的模式测控一体化方法

提出了一种基于分数阶傅里叶变换的模式测控一体化方法。利用分数阶傅里叶变换光路对光纤模式耦合态进行空间调制和相位调制,以实现模式的有效分解。与双重傅里叶变换（F²）法以及空间和频谱成像（S²）法相比,采用的分数阶傅里叶变换法,通过改变分数阶参数,控制模式的空间分布以及模式间的叠加状态,更易于分解出高阶模式。基于分数阶傅里叶变换的模式测量方法可在更广泛空间,研究模式的空间和相位叠加以及模式分解,也可退化为F²法和S²法。     

基于全光时域分数阶傅里叶变换的光脉冲最小损伤传输新方法

提出了一种基于全光分数阶傅里叶变换(optical fractional fourier transformation,OFRFT)的关于色散和自相位调制对光脉冲传输影响的分析方法,并基于该方法给出了一种新的光脉冲在光纤中传输最小损伤的方法,通过在发射端将输入的高斯光脉冲做OFRFT然后再送入到光纤中去传输,可以提高光脉冲抵抗色散和非线性的能力,仿真发现当色散占主要作用的时候,负阶数的分数阶傅里叶变换可以很大程度上减小光脉冲的展宽;当自相位调制作用占主要的时候,正阶数的分数阶傅里叶变换可以消除自相位调制作 关键词： 光脉冲传输 分数阶傅里叶变换 色散 自相位调制     

水下目标几何声散射回波在分数阶傅里叶变换域中的特性

水下目标散射回波在时域、频域混叠在一起, 而且受声波入射角度的影响严重, 在不同的入射角度下表现出很大的差异, 需要建立全方位入射角度下回波分量的理论分析模型. 本文推导了目标几何声散射分量在分数阶傅里叶变换域中随入射角度变化的解析表达式; 确定了目标几何声散射回波分量在最佳分数阶傅里叶变换域中的全方位模型, 从理论上证明了目标回波的几何特征形式; 给出了离散分数阶傅里叶变换对声散射分量的分辨能力和计算精度与发射信号带宽和观测时间之间的关系. 实验数据处理表明, 建立的分数阶傅里叶变换域的全方位模型与目标几何特征是一致的, 对未知入射角度下的目标识别提供了理论依据.     

分数阶傅里叶变换结合高峰均比抑制算法对CO-OFDM系统的影响分析

针对相干光正交频分复用系统中出现的高峰值平均功率比问题,提出分数阶傅里叶变换与高峰值平均功率比抑制算法相结合的方法.计算表明:随着分数阶傅里叶变换阶数的减小,信号的峰值平均功率比逐渐降低;与抑制算法结合后可进一步降低系统的峰值平均功率比,并解决抑制算法影响系统性能的问题.从结合的兼容性、抑制高峰值平均功率比效果及改善引入抑制算法后对系统的负面影响三方面进行仿真分析,结果表明:采用选择性映射算法与分数阶傅里叶变换结合后,旋转因子同为4时,峰值平均功率比高于6.6dB的概率较单一选择性映射算法低104;选取高峰值平均功率比抑制情况相近时,结合算法的时间复杂度比单一选择性映射算法降低了8倍;采用限幅算法与分数阶傅里叶变换结合的仿真情况也较单一限幅算法有很大提高,表明该算法结合的兼容性良好.     

用于光学图象加密的分数傅里叶变换双相位编码

作者提出了一种用于图象加密的基于分数傅里叶变换的双相位编码技术.该方法由于密钥比传统的编码技术增加两重,因而其安全性有所改进.     

基于分数阶Fourier变换的数字图像实值加密方法

构造了一种新的保实化的分数阶Fourier变换,提出了一种基于该变换的数字图像实值加密方法。利用保实分数阶Fourier变换的保实特性和阶数可加性等完成了数字图像的加密与解密,明文和密文分别位于空域和由密钥决定的保实分数阶Fourier变换域中,具有较强的抗统计破译能力。密图是一个实值图像,便于显示和存储。仿真实验结果表明,该加密方法密钥简单,无数据膨胀,对参数敏感度高,具有一定的鲁棒性和安全性。在信息安全领域具有良好的研究前景和实用价值。     

不对称离散分数傅里叶变换实现数字图像的加密变换

利用不对称分数傅里叶变换的特性,提出了一种图像加密变换的新方法。对图像的x,y方向分别实施不同级次的一维分数傅里叶变换,得到加密图像。解密方法就是对变换后的图像实施对应级次的分数傅里叶逆变换,只有当x,y方向的逆变换级次分别与原变换级次都相同或者满足周期条件时,才能恢复原图像。加密变换有效地提高了图像加密和防伪力度。数值计算验证了方法的正确性和可行性。     

Single phase encoding method based on the fractional Fourier transform

We propose a single phase encoding scheme for encrypting image by using fractional Fourier transform. Single phase mask is designed in order to be symmetrical about certain direction, which can be used in the process of both encryption and decryption. A conjugate mask is not required in the image decryption process, which is very convenient for the practical application in optics. Moreover, the optical implementation of the image encryption and decryption is given. The implementing structure is composed of lens and spherical mirror. Numerical simulations have demonstrated the validity and security of the encryption algorithm.     

Displacement measurement based on joint fractional Fourier transform correlator

A displacement measurement technology based on joint fractional Fourier transform is firstly proposed. Contrast to conventional displacement measurement based on joint Fourier transform correlator, the position of cross correlation peak in the proposed technology could be fixed arbitrarily according to the order of fractional Fourier transform. The optical setup in the proposed technology is more flexible and easier to implement. Simulation and experiment results are given out to verify the analysis.     

Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function

In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. In this paper, we propose a new approach for image encryption based on the multiple-parameter discrete fractional Fourier transform and chaotic logistic maps in order to meet the requirements of the secure image transmission. In the proposed image encryption scheme, the image is encrypted by juxtaposition of sections of the image in the multiple-parameter discrete fractional Fourier domains and the alignment of sections is determined by chaotic logistic maps. This method does not require the use of phase keys. The new method has been compared with several existing methods and shows comparable or superior robustness to blind decryption.     

Asymmetric multiple-image encryption based on the cascaded fractional Fourier transform

A multiple-image cryptosystem is proposed based on the cascaded fractional Fourier transform. During an encryption procedure, each of the original images is directly separated into two phase masks. A portion of the masks is subsequently modulated into an interim mask, which is encrypted into the ciphertext image; the others are used as the encryption keys. Using phase truncation in the fractional Fourier domain, one can use an asymmetric cryptosystem to produce a real-valued noise-like ciphertext, while a legal user can reconstruct all of the original images using a different group of phase masks. The encryption key is an indivisible part of the corresponding original image and is still useful during decryption. The proposed system has high resistance to various potential attacks, including the chosen-plaintext attack. Numerical simulations also demonstrate the security and feasibility of the proposed scheme.     

Fully phase-encrypted memory using cascaded extended fractional Fourier transform

In this paper, we implement a fully phase-encrypted memory system using cascaded extended fractional Fourier transform (FRT). We encrypt and decrypt a two-dimensional image obtained from an amplitude image. The full phase image to be encrypted is fractional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating through phase conjugation, the conjugate of the encrypted image. A lithium niobate crystal has been used as a phase contrast filter to reconstruct the decrypted phase image, alleviating the need of alignment in the Fourier plane making the system rugged.     

Image encryption based on the multiple-order discrete fractional cosine transform

A novel scheme for image encryption based-on the multiple-order discrete fractional cosine transform (MODFrCT) is proposed. The DFrCT has a similar relationship with the discrete fractional Fourier transform (DFrFT). Not only has the DFrCT many useful properties similar to the conventional discrete cosine transform, but it also has another property, namely its fraction, or its transform order. The image to be encrypted is transformed with the multiple-order DFrCT using a random row cipher key vector and a random column key vector successively, and the corresponding cipher key vectors of decryption are also very sensitive. The transmission of the encrypted image with the algorithm of the multiple-order DFrCT is faster due to its reality. The digital simulation results proved the validity and safety of this algorithm.     

Joint extended fractional Fourier transform correlator

Based on the conventional correlation and fractional correlation, the extended fractional correlation (EFC) is presented. And based on the configuration of the nonconventional joint transform correlator, we propose the joint extended fractional Fourier transform correlator (JEFRTC). The properties of the extended fractional cross correlation peak (EFCCP) in theory are analyzed. A sound conclusion is drawn that the width of EFCCP is narrower than that of fractional correlation peak under some conditions. This JEFRTC can permit lower precision of the systemic parameters when implemented with optical configuration. That will improve correlator’s character discriminability.     

Image encryption algorithm based on the multi-order discrete fractional Mellin transform

A multi-order discrete fractional Mellin transform (MODFrMT) is constructed and directly used to encrypt the private images. The MODFrMT is a generalization of the fractional Mellin transform (FrMT) and is derived by transforming the image with multi-order discrete fractional Fourier transform (MODFrFT) in log-polar coordinates, where the MODFrFT is generalized from the closed-form expression of the discrete fractional Fourier transform (DFrFT) and can be calculated by fast Fourier transform (FFT) to reduce the computation burden. The fractional order vectors of the MODFrMT are sensitive enough to be the keys, and consequently key space of the encryption system is enlarged. The proposed image encryption algorithm has significant ability to resist some common attacks like known-plaintext attack, chosen-plaintext attack, etc. due to the nonlinear property of the MODFrMT. Additionally, Kaplan-Yorke map is employed in coordinate transformation process of the MODFrMT to further enhance the security of the encryption system. The computer simulation results show that the proposed encryption algorithm is feasible, secure and robust to noise attack and occlusion.