Measuring time-frequency information content using the Renyi entropies

Author

Baraniuk, Richard G. ; Flandrin, Patrick ; Janssen, Augustus J E M ; Michel, Olivier J J

Author_Institution

Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA

Volume

47

Issue

4

fYear

2001

fDate

5/1/2001 12:00:00 AM

Firstpage

1391

Lastpage

1409

Abstract

The generalized entropies of Renyi 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 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 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 Renyi 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

Keywords

Wigner distribution; computational complexity; entropy; signal representation; time-frequency analysis; Cohen´s class; Renyi entropies; Wigner distribution; accounting invariances; affine class; complexity; cross-component invariances; generalized entropies; quadratic TFR; signal information; time-frequency analysis; time-frequency information content; time-frequency plane; time-frequency representation; transformation invariances; Acoustic materials; Collaborative work; Entropy; Frequency domain analysis; Helium; Particle measurements; Shape measurement; Signal processing; Signal resolution; Time frequency analysis;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.923723

Filename

923723