Maximum signal energy concentration in a time-frequency domain

An approach which operates directly in the time-frequency plane is proposed to address the problem of finding the signal whose time-frequency energy distribution is most concentrated in a given time-frequency domain of any shape. The solution is shown to be that of an eigenequation depending on both the considered domain and the chosen distribution. Explicit solutions are derived for elliptic domains in the Wigner-Ville case, and connections with classical approaches are pointed out