Discrete fractional Fourier transform based on new nearly tridiagonal commuting matrices

Based on discrete Hermite-Gaussian like functions, a discrete fractional Fourier transform (DFRFT) which provides sample approximations of the continuous fractional Fourier transform was defined and investigated recently. In this paper, we propose a new nearly tridiagonal matrix which commutes with the discrete Fourier transform (DFT) matrix. The eigenvectors of the new nearly tridiagonal matrix are shown to be better discrete Hermite-Gaussian like functions than those developed before. Furthermore, by appropriately combining two linearly independent matrices which both commute with the DFT matrix, we develop a method to obtain even better discrete Hermite-Gaussian like functions. Then, new versions of DFRFT produce their transform outputs more close to the samples of the continuous fractional Fourier transform, and their application is illustrated.