The generalized entropies of Renyi inspire new measures for estimating sign
al information and complexity in the time-frequency plane. When applied to
a time-frequency representation (TFR) from Cohen's class or the affine clas
s, the Renyi entropies conform closely to the notion of complexity that we
use when visually inspecting time-frequency images. These measures possess
several additional interesting and useful properties, such as accounting an
d cross-component and transformation invariances, that make them natural fo
r time-frequency analysis. This paper comprises a detailed study of the pro
perties and several potential applications of the Renyi entropies, with emp
hasis on the mathematical foundations for quadratic TFRs. in particular, fo
r the Wigner distribution, we establish that there exist signals for which
the measures are not well defined.