Measuring time-frequency information content using the Renyi entropies

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.