An extended poisson type sum formula for general transforms and aliasing error bound for the generalized sampling theorem

Abstract

The Poisson sum formula is of importance in expres-ing the samples of the infinite Fourier integral as a finite limit integral. In this paper we extend the Poisson sum formula for other more general integral transforms like the Hankel (Bessel) transform. Such a generalization seems to be the most feasible route for finding an upper bound for the aliasing error of the generalized sampling theorem, which is reported here for a special but important class of Hankel transforms