Infinite Series, Limits, Relationships and Aliasing

Abstract

This paper presents a coherent approach to the evaluation of limits of certain
infinife serieì and to the establishrnènt of relationships which exist between such series. The approach is based on the connection which exists between the Discrete Fourier Trarisform and the phenomenon of aliasing as expressed by the Poisson sum formula. One of the limits which follows naturally from the method described in this paper is for the well known Leibnitz series which converges to æ. The interpretation of certain infinite sums as aliased spectra allows many interesting relationships between series to be derived and some new results are presented which may be of interest to communications theory.