Measuring time-frequency information content using the Reényi entropies

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

doi:10.1109/18.923723

Measuring time-frequency information content using the Reényi entropies

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

Houston Methodist

Research output: Contribution to journal › Article › peer-review

426 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	1391-1409
Number of pages	19
Journal	IEEE Transactions on Information Theory
Volume	47
Issue number	4
DOIs	https://doi.org/10.1109/18.923723
State	Published - May 2001

Keywords

Complexity
Rényi entropy
Time-frequency analysis
Wigner distribution

ASJC Scopus subject areas

Information Systems
Electrical and Electronic Engineering

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10.1109/18.923723

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title = "Measuring time-frequency information content using the Re{\'e}nyi entropies",

abstract = "The generalized entropies of R{\'e}nyi 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 R{\'e}nyi 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 R{\'e}nyi 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 = "Complexity, R{\'e}nyi entropy, Time-frequency analysis, Wigner distribution",

author = "Baraniuk, {R. G.} and P. Flandrin and Janssen, {A. J E M} and Michel, {O. J J}",

note = "Funding Information: Manuscript received September 29, 1998; revised October 10, 2000. This work was supported by the National Science Foundation under Grants MIP-9457438 and CCR-997318, the Office of Naval Research under Grants N00014-95-1-0849 and N00014-99-1-0813, the NATO Collaborative Research Programme under Grant GRG-950202, and by URA 1325 CNRS. The material in this paper was presented in part at the IEEE International Conference on Acoustics, Speech, and Signal Processing, Adelaide, Australia, May 1994, and at the IEEE International Symposium on Information Theory, Whistler, BC, Canada, September 1995.",

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N1 - Funding Information: Manuscript received September 29, 1998; revised October 10, 2000. This work was supported by the National Science Foundation under Grants MIP-9457438 and CCR-997318, the Office of Naval Research under Grants N00014-95-1-0849 and N00014-99-1-0813, the NATO Collaborative Research Programme under Grant GRG-950202, and by URA 1325 CNRS. The material in this paper was presented in part at the IEEE International Conference on Acoustics, Speech, and Signal Processing, Adelaide, Australia, May 1994, and at the IEEE International Symposium on Information Theory, Whistler, BC, Canada, September 1995.

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AB - 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.

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Measuring time-frequency information content using the Reényi entropies

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Keywords

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