Inequalities pp 625-630 | Cite as

Integral bounds for radar ambiguity functions and Wigner distributions

  • Elliott H. Lieb


An upper bound is proved for the L p 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 L P bounds if and only if the functions/ and g that enter the definition are both Gaussians.


Coherent State Integral Bound Wigner Distribution Ambiguity Function Sharp Constant 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  1. 1.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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