A novel discrete fractional Fourier transform

Author

Ran, Tao ; Xianjun, Ping ; Yu, Shen ; Xinghao, Zhao

Author_Institution

Dept. of Electron. Eng., Beijing Inst. of Technol., China

fYear

2001

fDate

2001

Firstpage

1027

Lastpage

1030

Abstract

The definition of the fractional Fourier transform (FRFT) is described. Several discrete FRFT methods developed previously are reviewed briefly. A novel discretization method for FRFT is presented in this paper. It has some advantages such as being easily understood and implemented compared with the previous DFRFT methods. Especially, it needs a small amount of computation because only a diagonal matrix has to be recomputed when the rotational angle is changed. In addition, it does not need to consider the match between eigenvalues and eigenvectors, or to orthogonalize the DFT Hermite eigenvectors. A few simulation results for some typical signals are provided to verify the correctness of the proposed method

Keywords

Hermitian matrices; bandlimited signals; discrete Fourier transforms; eigenvalues and eigenfunctions; signal sampling; time-frequency analysis; transfer function matrices; DFRFT; Hermite eigenvectors; Hermite functions; band-limited signal; computer simulations; diagonal matrix; discrete FRFT methods; discrete fractional Fourier transform; discretization method; eigenvalues; orthogonalize; rotational angle; signal processing; signal sampling; time-frequency analysis; Computational modeling; Discrete Fourier transforms; Eigenvalues and eigenfunctions; Fourier transforms; Kernel; Optical filters; Signal analysis; Signal processing algorithms; Time frequency analysis; Wavelet transforms;

fLanguage

English

Publisher

ieee

Conference_Titel

Radar, 2001 CIE International Conference on, Proceedings

Conference_Location

Beijing

Print_ISBN

0-7803-7000-7

Type

conf

DOI

10.1109/ICR.2001.984885

Filename

984885