The discrete multiple-parameter fractional Fourier transform  

作　　者：LANG Jun, TAO Ran& WANG Yue Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China 

出　　处：《Science China(Information Sciences)》2010年第11期2287-2299,共13页中国科学（信息科学）（英文版）

基　　金：supported by the National Natural Science Foundation of China for Distinguished Young Scholars(Grant No. 60625104);the National Key Basic Research Program Founded by MOST (Grant Nos. 2009CB724003,2010CB731902);the National Natural Science Foundation of China (Grant No. 60890072);the Research Fundfor the Doctoral Program of Higher Education (Grant No. 1010036620602);Beijing Outstanding Doctoral thesis (Grant No. 1320037010901)

摘　　要：As a generalization of the Fourier transform （FT）, the fractional Fourier transform （FRFT） has many applications in the areas of optics, signal processing, information security, etc. Therefore, the efficient discrete computational method is the vital fundament for the application of the fractional Fourier transform. The multiple-parameter fractional Fourier transform （MPFRFT） is a generalized fractional Fourier transform, which not only includes FRFT as special cases, but also provides a unified framework for the study of FRFT. In this paper, we present in detail the discretization method of the MPFRFT and define the discrete multiple-parameter fractional Fourier transform （DMPFRFT）. Then, we utilize the tensor product to define two-dimensional multiple-parameter fractional Fourier transform （2D-MPFRFT） and the corresponding two-dimensional discrete multiple-parameter fractional Fourier transform （2D-DMPFRFT）. Finally, as an application, a novel image encryption method based on 2D-DMPFRFT is proposed. NumeAs a generalization of the Fourier transform （FT）, the fractional Fourier transform （FRFT） has many applications in the areas of optics, signal processing, information security, etc. Therefore, the efficient discrete computational method is the vital fundament for the application of the fractional Fourier transform. The multiple-parameter fractional Fourier transform （MPFRFT） is a generalized fractional Fourier transform, which not only includes FRFT as special cases, but also provides a unified framework for the study of FRFT. In this paper, we present in detail the discretization method of the MPFRFT and define the discrete multiple-parameter fractional Fourier transform （DMPFRFT）. Then, we utilize the tensor product to define two-dimensional multiple-parameter fractional Fourier transform （2D-MPFRFT） and the corresponding two-dimensional discrete multiple-parameter fractional Fourier transform （2D-DMPFRFT）. Finally, as an application, a novel image encryption meAs a generalization of the Fourier transform （FT）, the fractional Fourier transform （FRFT） has many applications in the areas of optics, signal processing, information security, etc. Therefore, the efficient discrete computational method is the vital fundament for the application of the fractional Fourier transform. The multiple-parameter fractional Fourier transform （MPFRFT） is a generalized fractional Fourier transform, which not only includes FRFT as special cases, but also provides a unified framework for the study of FRFT. In this paper, we present in detail the discretization method of the MPFRFT and define the discrete multiple-parameter fractional Fourier transform （DMPFRFT）. Then, we utilize the tensor product to define two-dimensional multiple-parameter fractional Fourier transform （2D-MPFRFT） and the corresponding two-dimensional discrete multiple-parameter fractional Fourier transform （2D-DMPFRFT）. Finally, as an application, a novel image encryption method based on 2D-DMPFRFT is proposed. NumeAs a generalization of the Fourier transform （FT）, the fractional Fourier transform （FRFT） has many applications in the areas of optics, signal processing, information security, etc. Therefore, the efficient discrete computational method is the vital fundament for the application of the fractional Fourier transform. The multiple-parameter fractional Fourier transform （MPFRFT） is a generalized fractional Fourier transform, which not only includes FRFT as special cases, but also provides a unified framework for the study of FRFT. In this paper, we present in detail the discretization method of the MPFRFT and define the discrete multiple-parameter fractional Fourier transform （DMPFRFT）. Then, we utilize the tensor product to define two-dimensional multiple-parameter fractional Fourier transform （2D-MPFRFT） and the corresponding two-dimensional discrete multiple-parameter fractional Fourier transform （2D-DMPFRFT）. Finally, as an application, a novel image encryption me

关 键 词：multiple-parameter fractional Fourier transform fractional Fourier transform image encryption information security 

分 类 号：TN911.72[电子电信—通信与信息系统]