Skip to main content

Trigonometric Wavelets for Time-Frequency-Analysis

  • Chapter
Approximation Theory, Wavelets and Applications

Part of the book series: NATO Science Series ((ASIC,volume 454))

Abstract

We present here a new solution for the problem of periodic time—frequency—localized signal analysis. Working on polynomials with Fourier coefficients included in bands similar to octaves, we can vary the actual position and length of those bands and also the localization of the bases in the time domain by the choice of parameters. Having simple, fast and numerically stable algorithms, this concept can be easily applied to various practical tasks.

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover 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. Chui, C.K. and Mhaskar, H.N. (1993) On trigonometric wavelets, Constr. Approx. 9: 167–190.

    Article  MathSciNet  MATH  Google Scholar 

  2. Daubechies, I. (1992) Ten Lectures on Wavelets, SIAM, Philadelphia.

    MATH  Google Scholar 

  3. Davis, P.J. (1979) Circulant matrices, Wiley Interscience, New York.

    MATH  Google Scholar 

  4. Lemarié P. G. and Meyer, Y. (1986) Ondelettes et bases hilbertiennes, Rev. Mat. Iberoamericana 2: 1–18.

    Article  MathSciNet  Google Scholar 

  5. Perrier, V. and Basdevant, C. (1989) Periodic Wavelet Analysis, a tool for inhomogeneous field investigation, Theory and Algorithms, Rech. Aérospat., 3: 53–67.

    MathSciNet  Google Scholar 

  6. Prestin, J. and Quak, E. (1993) Trigonometric Interpolation and Wavelet Decomposition, submitted.

    Google Scholar 

  7. Prestin, J. and Selig, K. (1994) Interpolatory and Orthonormal Trigonometric Wavelets, submitted.

    Google Scholar 

  8. Privalov, A.A. (1991) On an orthogonal trigonometric basis, Math. Sbornik 182: 384–394.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Selig, K. (1995). Trigonometric Wavelets for Time-Frequency-Analysis. In: Singh, S.P. (eds) Approximation Theory, Wavelets and Applications. NATO Science Series, vol 454. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8577-4_30

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-8577-4_30

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4516-4

  • Online ISBN: 978-94-015-8577-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics