Measuring time-frequency information content using the Reényi entropies

R. G. Baraniuk, P. Flandrin, A. J E M Janssen, O. J J Michel

Research output: Contribution to journalArticlepeer-review

344 Scopus citations


The generalized entropies of Rényi inspire new measures for estimating signal information and complexity in the time-frequency plane. When applied to a time-frequency representation (TFR) from Cohen's class or the affine class, the Rényi 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 and cross-component and transformation invariances, that make them natural for time-frequency analysis. This paper comprises a detailed study of the properties and several potential applications of the Rényi entropies, with emphasis on the mathematical foundations for quadratic TFRs. In particular, for the Wigner distribution, we establish that there exist signals for which the measures are not well defined.

Original languageEnglish (US)
Pages (from-to)1391-1409
Number of pages19
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - May 2001


  • Complexity
  • Rényi entropy
  • Time-frequency analysis
  • Wigner distribution

ASJC Scopus subject areas

  • Information Systems
  • Electrical and Electronic Engineering


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