The fast computation of multi-angle discrete fractional Fourier transform

The discrete fractional Fourier transform (DFRFT) plays an important role in processing time-varying signals. Nevertheless, directly computing the DFRFT involves high complexity, particularly when addressing multi-angle DFRFT scenarios. This article presents a method to compute multi-angle DFRFTs through the execution of a single complex DFRFT, exploiting several properties of the DFRFT. We first calculate the DFRFTs with rotation angles 0 and α. Subsequently, when dealing with the DFRFTs of two real signals with rotation angles α and β, which is so-called the multi-angle DFRFTs, our method only need one complex DFRFT and some additional manipulations with complexity O(M), which reduce the computational complexity efficiently. Furthermore, the proposed method is also applicable to the processing of two dimensional (2D) signals. Additionally, as a generalized form of the DFRFT, the fast computation of the multi-angle discrete affine Fourier transform (DAFT) is also considered. Finally, the simulation results confirm that the proposed methods can effectively reduce the computational complexity without compromising precision.