New methods for fast computation of fractional Fourier transform

We present a FRFT high-resolution computation (zoom-FRFT) method, which can zoom-in on any interested portion of fractional spectrum by setting spectrum range and output number M. In addition, for solving lower efficiency of zoom-FRFT for small M, a FRFT single-point fast computation (SP-FRFT) method based on Homer rule is presented and its further reduction is made for zero-point computation. It can be used to increase computational efficiency for small M, and compute un-uniform output samples. Finally, two methods are verified by the simulations.