The analysis of the discrete fractional Fourier transform algorithms

The discrete formal FRFT is difficult to obtained by the directly sampling the continuous FRFT because the kernel function of the continuous fractional Fourier transform (FRFT) exhibits drastic oscillation and the oscillation amplitude has the distinct difference from the different order of the FRFT. Discrete FRFT has been intensively investigated recently and many definitions of the discrete FRFT have emerged. Firstly, the multiplicity of discrete FRFT is presented and the discrete FRFT are classified in term of its definition mode. Some of discrete FRFT are demonstrated which kind of the continuous FRFT they correspond to. Secondly, the problem of the discrete FRFT is analyzed and digital simulations are presented to verify the conclusion.