On time-frequency localization

The idea behind a time-frequency representation is often connected with that of some form of localization on the plane. This point of view is faced with a number of limitations, which all express uncertainty relations between time and frequency. In the case of “chirps”, there exist however adapted representations which can localize very accurately on specific trajectories, and whose construction can be simply justified on the basis of geometric arguments. As a corollary, such joint descriptions, in both time and frequency, allow for an interpretation of the corresponding localization curves in terms of “instantaneous frequencies”