TIME-FREQUENCY LOCALIZATION VIA THE WEYL CORRESPONDENCE

A technique of producing signals whose energy is concentrated in a given region of the time-frequency plane is examined. The degree to which a particular signal is concentrated is measured by integrating the Wigner distribution over the given region. This procedure was put forward by Flandrin, and has been used for time-varying filtering in the recent work of Hlawatsch, Kozek, and Krattenthaler. In this paper, the associated operator is studied. Estimates for the eigenvalue decay and the smoothness and decay of the eigenfunctions are established.