NASA NTRS1973
The purpose of this study was to determine the optimum points of evaluation of data compressed by means of polynomial smoothing. It is shown that a set y of m statistically independent observations Y(t sub 1), Y(t sub 2), ... Y(t sub m) of a quantity X(t), which can be described by a (n-1)th degree polynomial in time, may be represented by a set Z of n statistically independent compressed observations Z (tau sub 1), Z (tau sub 2),...Z (tau sub n), such that The compressed set Z has the same information content as the observed set Y. the times tau sub 1, tau sub 2,.. tau sub n are the zeros of an nth degree polynomial P sub n, to whose definition and properties the bulk of this report is devoted. The polynomials P sub n are defined as functions of the observation times t sub 1, t sub 2,.. t sub n, and it is interesting to note that if the observation times are continuously distributed the polynomials P sub n degenerate to legendre polynomials. The proposed data compression scheme is a little more complex than those usually employed, but has the advantage of preserving all the information content of the original observations.