Discrete fractional Fourier transform: Vandermonde approach
  Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier transform from the discrete Fourier transform in a completely analogous manner. To achieve this, we have used a very simple method based on the Vandermonde matrices, to obtain rational and irrational powers of the discrete Fourier transform matrices. 
H\'ector M. Moya-Cessa and Francisco Soto-Eguibar
math.GM