Optimization and selection of time-frequency transforms for wave-packet analysis in ultrafast spectroscopy.

The analysis of quantum beats in time-resolved spectroscopic signals is becoming a task of primary importance because it is now clear that they bring crucial information about chemical reactivity, transport, and relaxation processes. Here we describe how to exploit the wide family of time-frequency transform methodologies to obtain information not only about the frequency but also about the dynamics of the oscillating components contributing to the overall beating signal. Several linear and bilinear transforms have been considered, and a general and easy procedure to judge in a non-arbitrary way the performances of different transforms has been outlined.