Separability, positivity, and minimum uncertainty in time–frequency energy distributions

Abstract

Gaussian signals play a very special role in classical time–frequency analysis because they are solutions of apparently unrelated problems such as minimum uncertainty, and positivity and separability of Wigner–Ville distributions. We investigate here some of the logical connections which exist between these different features, and we discuss some examples and counterexamples of their extension to more general joint distributions within Cohen’s class and the affine class.