Representation of tails of periodic and infinite-range signals: Towards a treatment for truncation

Two types of signals are considered: infinite-range signals and periodic signals. Tails of infinite-range signals can be described with an asymptotic power series (having terms of the type x−n with n≥2). For tails of periodic signals an asymptotic series [having terms of the type sin−n(πx/p) with p=period and n≥2] is derived from the asymptotic power series for the infinite-range signals using Poisson summation. It is shown that for practical purposes the tails of a signal can be described quite satisfactorily with only a few terms of the series. On this basis nonmeasurable parts of tails of both symmetric and asymmetric signals can be estimated reliably and thus the effects of the unavoidable signal truncation can be counteracted.