DISCRETE FRACTIONAL HARTLEY AND FOURIER-TRANSFORMS

This paper is concerned with the definitions of the discrete fractiona l Hartley transform (DFRHT) and the discrete fractional Fourier transf orm (DFRFT), First, the eigenvalues and eigenvectors of the discrete F ourier and Hartley transform matrices are investigated. Then, the resu lts of the eigendecompositions of the transform matrices are used to d efine DFRHT and DFRFT, Also, an important relationship between DFRHT a nd DFRFT is described, and numerical examples are illustrated to demon strate that the proposed DFRFT is a better approximation to the contin uous fractional Fourier transform than the conventional defined DFRFT, Finally, a filtering technique in the fractional Fourier transform do main is applied to remove chirp interference.