Uncertainty Principles for Radar Ambiguity Functions and Moments

In this article, we give an estimate of the zero-free region around the origin of the ambiguity function of a one-dimensional signal u in terms of the moments of u. This is done by proving an uncertainty relation between the first zero of the Fourier transform of a non-negative function and the moments of the function. As a corollary, we also give an estimate of how much a function needs to be translated to obtain a function that is orthogonal to the original function. The paper is completed with a proof of the local uncertainty principe for the ambiguity function.