Mathematics – Classical Analysis and ODEs
Scientific paper
2005-09-02
Applied and Computational Harmonic Analysis (25/04/2007) doi:10.1016/j.acha.2007.04.001
Mathematics
Classical Analysis and ODEs
Scientific paper
10.1016/j.acha.2007.04.001
In 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.
Bonami Aline
Garrigos Gustavo
Jaming Philippe
No associations
LandOfFree
Discrete radar ambiguity problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Discrete radar ambiguity problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete radar ambiguity problems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-193328