A novel discrete fractional Fourier transform

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.