Discrete radar ambiguity problems

Simple item page
dc.creatorBonami, Aline
dc.creatorGarrigos, Gustavo
dc.creatorJaming, Philippe
dc.date2005-09-02
dc.date.accessioned2026-07-07T08:14:56Z
dc.date.available2026-07-07T08:14:56Z
dc.descriptionIn this paper, we pursue the study of the radar ambiguity problem started in \cite{Ja,GJP}. More precisely, for a given function $u$ we ask for all functions $v$ (called \emph{ambiguity partners}) such that the ambiguity functions of $u$ and $v$ have same modulus. In some cases, $v$ may be given by some elementary transformation of $u$ and is then called a \emph{trivial partner} of $u$ otherwise we call it a \emph{strange partner}. Our focus here is on two discrete versions of the problem. For the first one, we restrict the problem to functions $u$ of the Hermite class, $u=P(x)e^{-x^2/2}$, thus reducing it to an algebraic problem on polynomials. Up to some mild restriction satisfied by quasi-all and almost-all polynomials, we show that such a function has only trivial partners. The second discretization, restricting the problem to pulse type signals, reduces to a combinatorial problem on matrices of a special form. We then exploit this to obtain new examples of functions that have only trivial partners. In particular, we show that most pulse type signals have only trivial partners. Finally, we clarify the notion of \emph{trivial partner}, showing that most previous counterexamples are still trivial in some restricted sense.
dc.identifierhttps://arxiv.org/abs/math/0509031
dc.identifierhttp://arxiv.org/abs/math/0509031
dc.identifierApplied and Computational Harmonic Analysis (25/04/2007) doi:10.1016/j.acha.2007.04.001
dc.identifierdoi:10.1016/j.acha.2007.04.001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133311
dc.subjectClassical Analysis and ODEs
dc.subject42B10;81S30;94A12
dc.titleDiscrete radar ambiguity problems
dc.typetext

Files

Collections

arXiv