Representation of uniformly sampled signals in the Hermite transform domain

The problem of the representation of uniformly sampled signals in the Hermite transform basis is revisited. Namely, due to the application of Gauss-Hermite quadrature in the calculation of transformation coefficients, the discrete Hermite transform assumes that the analyzed signal is sampled at the points proportional to the roots of the Hermite polynomial of the corresponding order. Since the most of discrete signals are sampled according to the sampling theorem, there is a particular interest for the representation of such signals. A form of the Hermite transform is defined based on the sampling theorem formula for the reconstruction of continuous-time signals from the samples of their discrete counterparts.