Integral bounds for radar ambiguity functions and Wigner distributions
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.
KeywordsCoherent State Integral Bound Wigner Distribution Ambiguity Function Sharp Constant
Unable to display preview. Download preview PDF.
- 4.E. H. Lieb, “Gaussian kernels have only Gaussian maximizers,” to be published in Invent. Math. (1990).Google Scholar
- 10.L. Leindler, “On a certain converse of Hölder’s inequality. II,” Acta Math. Szeged. 33, 217–223 (1972).Google Scholar
- 11.A. J. E. M. Janssen, “Wigner weight functions and Weyl symbols of nonnegative definite linear operators,” Philips J. Res. 6, 7–42 (1989).Google Scholar