In [2] we have considered a class of integral transforms which generalizs the classical Fourier tranform. We are able now to define a class of discrete tranformations which can be considered as a generalization of the discrete Fourier transform. Furthermore, when our result is considered in connnection with the particular kernel associated with th Fourier transform, the fast Fourier transform algorithm can be used in order to approximate the Hermite-Fourier coefficients of a class of functions *