Zero-free Regions of 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 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 obtaina function that is orthogonal to the original function.