Skip to main content

Time-Frequency Representations of Broad-Band Signals

  • Conference paper
Wavelets

Part of the book series: inverse problems and theoretical imaging ((IPTI))

Abstract

Joint time-frequency analyses were first devoted to the study of quasi-monochromatic signals for which familiar notions of time and frequency translations exist. In the axiomatic formulation of the problem, this situation has led to the strong requirement of covariance of the representation by the group of time and frequency translations. However, if the resulting representations are very interesting when applied to quasi-monochromatic signals, they lose meaning in the general case due to flagrant time localization anomalies. This latter point is illustrated in section II.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

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.

References

  1. J.Ville, Cables et transmissions, n°l, pp. 60–74, 1948.

    Google Scholar 

  2. P.Flandrin, in this volume.

    Google Scholar 

  3. E.P.Wigner, Phys.Rev. 40, 749–759, 1932.

    Article  ADS  Google Scholar 

  4. P.Bertrand and J.Bertrand, Rech. Aerosp. n°5, 277–283, 1985.

    Google Scholar 

  5. J.Bertrand and P.Bertrand, Found. Phys. 17, 397–405, 1987.

    Article  ADS  MathSciNet  Google Scholar 

  6. J.Bertrand and P.Bertrand, C.R.Acad.Sc. Paris, 299, 635–638, 1984.

    Google Scholar 

  7. A.Unterberger, Comm. in Part. Diff. Eq., 9, 1179–1236, 1984.

    Article  Google Scholar 

  8. A.Grossmann and J.Morlet, SIAM J. Math. Anal., 15, 723–736, 1984.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bertrand, J., Bertrand, P. (1990). Time-Frequency Representations of Broad-Band Signals. In: Combes, JM., Grossmann, A., Tchamitchian, P. (eds) Wavelets. inverse problems and theoretical imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75988-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-75988-8_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53014-5

  • Online ISBN: 978-3-642-75988-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics