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 f and g that enter the definition are both Gaussians.