Skip to main content
Springer Nature Link
Log in

Measuring of Time-Frequency Representation (TFR) Content – Using the Kapur’s Entropies

  • Conference paper
Contemporary Computing (IC3 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 94))

Included in the following conference series:

  • 1185 Accesses

Abstract

The generalized entropies of Kapur 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 kapur’s entropies confirm closely to the concept of complexity as discussed in theorem 2.2.1 and 2.2.2. In this paper, we study the properties of the Kapur’s entropies, with emphasis on the mathematical foundations for quadratic TFRs. In particular, for the Wigner distribution we establish some results that there exist signals for which the measures are not well defined.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Williams, W.J., Brown, M.L., Hero, A.O.: Uncertainty, information, and time-frequency distributions. In: Proceeding of SPIE Int. Soc. Opt. Eng., vol. 1566, pp. 144–156 (1991)

    Google Scholar 

  2. Orr, R.: Dimensionality of signal sets. In: Proc. SPIE Int. Soc. Opt. Eng., vol. 1565, pp. 435–446 (1991)

    Google Scholar 

  3. Cohen, L.: What is a multi component signal? In: Proc. IEEE Int. Conf. Acoust., speech, Signal Processing, vol. V, pp. 113–116 (1992)

    Google Scholar 

  4. Cohen, L.: Time-Frequency Analysis. Prentice-Hall, Englewood Cliffs (1995)

    Google Scholar 

  5. Baraniuk, R.G., Flandrin, P., Michel, O.: Information and complexity on the time- frequency plane. In: 14 EME Collogue GRETSI, pp. 359–362 (1993)

    Google Scholar 

  6. Flandrin, P., Baraniuk, R.G., Michel, O.: Time-Frequency complexity and information. In: Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, vol. III, pp. 329–332 (1994)

    Google Scholar 

  7. Shannon, C.E.: A mathematical theory of communication. Bell Sys. Tech. J. 27, 379–423 (1948)

    MATH  MathSciNet  Google Scholar 

  8. Renyi’s, A.: On measures of entropy and information. In: Proc. 4th Berkeley Symp. Math. Stat. and Prob., vol. 1, pp. 547–561 (1961)

    Google Scholar 

  9. Williams, W.J.: Reduced interference distributions. Proc. IEEE Biological Applications and Interpretations 84, 1264–1280 (1996)

    Google Scholar 

  10. Baraniuk, R.G., Janssen, A.J.E.M.: Measuring time-frequency information content using the Renyi’s entropies. IEEE Transactions on Information Theory 47(4), 1391–1409 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kapur, J.N.: Generalization entropy of order α and type β. The Mathematical Seminar 4, 78–84 (1967)

    MathSciNet  Google Scholar 

  12. Ash, R.: Information Theory. Interscience Publishers, New York (1965)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Professor, Deptt. of Stat., Maharishi Dayanand University, Rohtak

    Priti Gupta

  2. Sr. Lecturer in Mathematics, Delhi College of Tech.& Mgt., Palwal

    Vijay Kumar

Authors
  1. Priti Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vijay Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Computer Sciences, University of Florida, 32611, Gainesville, FL, USA

    Sanjay Ranka

  2. University of Florida, Gainesville, Fl, USA

    Arunava Banerjee

  3. Department of Computer Science and Engineering, Indian Institute of Technology, 110016, New Delhi, INDIA

    Kanad Kishore Biswas

  4. Computer Science, College of Engineering and Science, Louisiana Tech University, LA 71272, Ruston, USA

    Sumeet Dua

  5. University of Florida, Gainesville, FL, USA

    Prabhat Mishra

  6. Department of Computer Science & Engineering, Indian Institute of Technology, 208016, Kanpur, India

    Rajat Moona

  7. National Tsing Hua University, Hsin-Chu, Taiwan, R.O.C.

    Sheung-Hung Poon

  8. Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong

    Cho-Li Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gupta, P., Kumar, V. (2010). Measuring of Time-Frequency Representation (TFR) Content – Using the Kapur’s Entropies. In: Ranka, S., et al. Contemporary Computing. IC3 2010. Communications in Computer and Information Science, vol 94. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14834-7_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14834-7_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14833-0

  • Online ISBN: 978-3-642-14834-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics