Zero-free regions of radar ambiguity functions and moments

Philippe Jaming (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: zero-free region; ambiguity functions

Domaines: Analyse classique [math.CA]

Philippe Jaming. Zero-free regions of radar ambiguity functions and moments. 2006. ⟨hal-00080459v2⟩