Integral bounds for radar ambiguity functions and Wigner distributions

Elliott Lieb

Research output: Contribution to journalArticlepeer-review

81 Scopus citations

Abstract

An upper bound is proved for the Lp norm of Woodward's ambiguity function in radar signal analysis and of the Wigner distribution in quantum mechanics when p > 2. A lower bound is proved for 1 ≤ p < 2. In addition, a lower bound is proved for the entropy. These bounds set limits to the sharpness of the peaking of the ambiguity function or Wigner distribution. The bounds are best possible and equality is achieved in the Lp bounds if and only if the functions f and g that enter the definition are both Gaussians.

Original languageEnglish (US)
Pages (from-to)594-599
Number of pages6
JournalJournal of Mathematical Physics
Volume31
Issue number3
DOIs
StatePublished - Jan 1 1990

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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