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1.
从分数傅里叶变换(FRFT)的定义出发,理论分析了联合分数变换相关器(JFRTC)的分数相关特性.从所得JFRTC的数学表达式中可以看出,将FRFT应用到联合变换相关器(JTC)中得到的JFRTC具有与传统JTC不同的性质.对于传统JTC,一旦输入平面上参考图像与目标图像之间的距离给定,相关输出峰的位置即确定,而JFRTC的相关输出峰的位置则可以由分数级次p1和p2来自由调节,这个特性在实际模式识别中非常有用.另一方面,JFRTC的相关输出峰值在大多数情况下低于传统JTC的相关峰值,却是JFRTC的一大缺点.最后,从FRFT的比例性质出发,给出了FRFT谱畸变不变的实现条件,并由此预言了JFRTC畸变不变模式识别的功能.  相似文献   

2.
We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in an ad hoc manner to time-dependent forces. A modified FFPE (MFFPE) is rigorously derived, being valid for a family of dichotomously alternating force fields. This MFFPE is numerically validated for a rectangular time-dependent force with zero average bias. For this case, subdiffusion is shown to become enhanced as compared to the force free case. We question, however, the existence of any physically valid FFPE for arbitrary varying time-dependent fields that differ from this dichotomous varying family.  相似文献   

3.
分数傅里叶变换计算全息   总被引:1,自引:0,他引:1  
盛兆玄  孙新利 《光学技术》2008,34(1):156-158
在计算全息和分数傅里叶变换的基础上提出了不对称分数傅里叶变换计算全息和双随机相位不对称分数傅里叶变换计算全息。在这种方法中,首先用一随机相位函数乘以输入图像信息,然后沿x方向实施α级次的一维分数傅里叶变换,再乘以第二个随机相位函数,最后,沿y方向实施β级次的一维分数傅里叶变换。采用迂回位相编码法对变换后的结果编码,绘出计算全息图。为了恢复原始图像,需要知道变换级次和随机相位函数。利用这种方法进行图像加密,使加密图像的密钥由原来两重增加到四重,从而提高了系统的保密性能。  相似文献   

4.
Weimin Jin  Caijie Yan 《Optik》2007,118(1):38-41
The optical image encryption based on multichannel fractional Fourier transform (FRT) and double random phase encoding technique is proposed. Optical principles of encoding and decoding are analyzed in detail. With this method, one can encrypt different parts of input image, respectively. The system security can be improved to some extent, not only because fractional orders and random phase masks in every channel can be set with freedom, but also because the system parameters among all channels are independent. Numerical simulation results of optical image encryption based on four channel FRT and double random phase encoding are given to verify the feasibility of the method.  相似文献   

5.
From continuous time random walks to the fractional fokker-planck equation   总被引:1,自引:0,他引:1  
We generalize the continuous time random walk (CTRW) to include the effect of space dependent jump probabilities. When the mean waiting time diverges we derive a fractional Fokker-Planck equation (FFPE). This equation describes anomalous diffusion in an external force field and close to thermal equilibrium. We discuss the domain of validity of the fractional kinetic equation. For the force free case we compare between the CTRW solution and that of the FFPE.  相似文献   

6.
Lv Longjin  Fu-Yao Ren  Wei-Yuan Qiu 《Physica A》2010,389(21):4809-1752
In this paper, in order to establish connection between fractional derivative and fractional Brownian motion (FBM), we first prove the validity of the fractional Taylor formula proposed by Guy Jumarie. Then, by using the properties of this Taylor formula, we derive a fractional Itô formula for H∈[1/2,1), which coincides in form with the one proposed by Duncan for some special cases, whose formula is based on the Wick Product. Lastly, we apply this fractional Itô formula to the option pricing problem when the underlying of the option contract is supposed to be driven by a geometric fractional Brownian motion. The case that the drift, volatility and risk-free interest rate are all dependent on t is also discussed.  相似文献   

7.
朱邦和  韩利  谢鸿伟  刘树田 《光子学报》1999,28(10):910-914
本文通过理论分析和计算机仿真研究了分数傅里叶变换的级次对分数相关峰值特性的影响并优化了分数相关的级次。结果表明分数相关输出在旁辩和峰值宽度方面与传统相关相比有了较大的改善,因而可以提高目标探测的灵敏性。  相似文献   

8.
In this study, the modified Kudryashov method is used to construct new exact solutions for some conformable fractional differential equations. By implementing the conformable fractional derivative and compatible fractional complex transforms, the fractional generalized reaction duffing (RD) model equation, the fractional biological population model and the fractional diffusion reaction (DR) equation with quadratic and cubic nonlinearity are discussed. As an outcome, some new exact solutions are formally established. All solutions have been verified back into its corresponding equation with the aid of maple package program. We assure that the employed method is simple and robust for the estimation of the new exact solutions, and practically capable for reducing the size of computational work for solving a various class of fractional differential equations arising in applied mathematics, mathematical physics and biology.  相似文献   

9.
Xiaoyun Jiang  Mingyu Xu 《Physica A》2010,389(17):3368-3374
In this paper a time fractional Fourier law is obtained from fractional calculus. According to the fractional Fourier law, a fractional heat conduction equation with a time fractional derivative in the general orthogonal curvilinear coordinate system is built. The fractional heat conduction equations in other orthogonal coordinate systems are readily obtainable as special cases. In addition, we obtain the solution of the fractional heat conduction equation in the cylindrical coordinate system in terms of the generalized H-function using integral transformation methods. The fractional heat conduction equation in the case 0<α≤1 interpolates the standard heat conduction equation (α=1) and the Localized heat conduction equation (α→0). Finally, numerical results are presented graphically for various values of order of fractional derivative.  相似文献   

10.
We investigate the relationships between models of power-law long-range interactions and mechanics based on fractional derivatives. We present the fractional Lagrangian density which gives the Euler–Lagrange equation that serves as the equation of motion for fractional-power-law long-range interactions. We derive this equation by the fractional variational method. In addition, we derive a Noether-like current from the fractional Lagrangian density.  相似文献   

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