Skip to main content

Abstract

In this chapter the spaces of periodic polynomial splines, which are introduced in Sect. 3.2.2, are discussed in more details. It is shown that the periodic exponential splines generate a specific form of harmonic analysis in these spaces. A family of generators of the spaces of periodic splines is presented.

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 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

References

  1. A. Aldroubi, M. Unser, M. Eden, Cardinal spline filters: stability and convergence to the ideal sinc interpolator. Signal Process. 28(2), 127–138 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  2. G. Battle, A block spin construction of ondelettes. I. lemarié functions. Commun. Math. Phys. 110(4), 601–615 (1987)

    Article  MathSciNet  Google Scholar 

  3. P. G. Lemarié. Ondelettes à localisation exponentielle. J. Math. Pures Appl. (9), 67(3), 227–236 (1988)

    Google Scholar 

  4. P. Neittaanmäki, V. Rivkind, V. Zheludev, A wavelet transform based on periodic splines and finite element method, ed. by M. Kvectorrívectorzek, P. Neittaanmäki, R. Stenberg, Finite Element Methods (Jyväskylä, 1993), vol. 164 of Lecture Notes in Pure and Appl. Math. (New York, Dekker, 1994), pp. 325–334

    Google Scholar 

  5. P. Neittaanmäki, V. Rivkind, V. Zheludev, Periodic spline wavelets and representation of integral operators. Preprint 177, University of Jyväskylä, Department of Mathematics (1995)

    Google Scholar 

  6. C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (The University of Illinois Press, Urbana, IL, 1949)

    MATH  Google Scholar 

  7. V. Zheludev, An operational calculus connected with periodic splines. Soviet. Math. Dokl. 42(1), 162–167 (1991)

    MathSciNet  Google Scholar 

  8. V. Zheludev, Periodic splines and the fast Fourier transform. Comput. Math. Math. Phys. 32(2), 149–165 (1992)

    MATH  MathSciNet  Google Scholar 

  9. V. Zheludev, Periodic splines, harmonic analysis, and wavelets, ed. by Y. Y. Zeevi, R. Coifman, Signal and Image Representation in Combined Spaces, vol. 7 of Wavelet Anal. Appl. (Academic Press, San Diego, CA, 1998), pp. 477–509

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amir Z. Averbuch .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Averbuch, A.Z., Neittaanmaki, P., Zheludev, V.A. (2014). Periodic Polynomial Splines. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8926-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-8926-4_4

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-8925-7

  • Online ISBN: 978-94-017-8926-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics