About the positivity of trigonometric polynomials with positive samples

摘要

In this paper we focus on the class of trigonometric polynomials that have positive samples at frequency points that are multiples of 2π/N. It has previously been shown that this cannot guarantee the positivity of a polynomial trigonometric. We discuss some aspects that can affect the positivity: the influence of sample scattering, the weight of the number of samples and the effect of minor changes to the samples. Usually, scattering the samples increases the chance that the polynomial trigonometry will not be positive. The number of samples is not very important, and its weight almost disappears when the variance of the samples is small. If the values of the samples change very little, the positivity of the polynomial trigonometric is not affected.