A CLASS OF AFFINE WIGNER FUNCTIONS WITH EXTENDED COVARIANCE PROPERTIES

Affine Wigner functions are phase space representations based on the affine group in place of the usual Weyl-Heisenberg group of quantum mechanics. Such representations are relevant to the time-frequency analysis of real signals. An interesting family is singled out by the requirement of covariance with respect to each solvable three-parameter group containing the affine group. Explicit forms are given in each case and properties such as unitarity and localization are discussed. Some particular distributions are recovered.