Eigenvectors of the DFT and discrete fractional fourier transform based on the bilinear transform

Orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, are crucial to define the discrete fractional Fourier transform. In this work we determine the eigenvectors of the DFT matrix inspired by the bilinear transform. The bilinear transform maps the analog space to the discrete sample and it maps jw in the analog s-domain to the unit circle in the discrete z-domain one-to-one without aliasing, it is appropriate to use in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian like eigenvectors of the DFT matrix and confirm the results with extensive simulations.