  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.
