Skip to main content
SpringerLink
Log in

A New Approach to Irregular Sampling of Band-Limited Functions

  • Chapter
Recent Advances in Fourier Analysis and Its Applications

Part of the book series: NATO ASI Series ((ASIC,volume 315))

Abstract

This is a report on joint work in progress [10,11,12] on irregular sampling by H. G. Feichtinger, University of Vienna, and the author.

This work was supported by a faculty research grant of The University of Connecticut.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

Similar content being viewed by others

References

  1. A. Beurling: Local harmonic analysis with some applications to differential operators. In “Some Recent Advances in the Basic Sciences”, p. 109–125, Belfer Grad. School of Science, Annual Science Conference Proc., A. Gelbart, ed. Vol. I, 1962–1964.

    Google Scholar 

  2. A. Beurling, P. Malliavin: On the closure of characters and the zeros of entire functions. Acta Math. 118 (1967), 79–95.

    Article  MathSciNet  MATH  Google Scholar 

  3. F. J. Beutler: Error-free recovery of signals from irregularly spaced samples. SIAM Review 8 (1966), 328–335.

    Article  MathSciNet  MATH  Google Scholar 

  4. P.L.Butzer, W. Splettstößer, R.Stens: The sampling theorem and linear prediction in signal analysis. Jber.d. Dt. Math.-Verein. 90 (1987), 1–70.

    Google Scholar 

  5. R.R. Coifman, R. Rochberg Representation theorems for holomorphic and harmonic functions in L p, Asterisque 77 (1980),11–66.

    MathSciNet  MATH  Google Scholar 

  6. R. Duffin, A. Schaeffer: A class of nonharmonic Fourier series. Trans. Amer. Math. Soc. 72(1952), 341–366.

    Article  MathSciNet  MATH  Google Scholar 

  7. H.G. Feichtinger: Discretization of convolution and reconstruction of band-limited functions. (To appear in J. Approx. Th.).

    Google Scholar 

  8. H.G. Feichtinger, K. Gröchenig: A unified approach to atomic decompositions via integrable group representations. Proc. Conf. Lund 1986, “Function Spaces and Applications”, Lecture Notes in Math. 1302 (1988), 52–73.

    Chapter  Google Scholar 

  9. H.G. Feichtinger, K. Gröchenig: Banach spaces related to integrable group representations and their atomic decompositions I. (To appear in J. Functional Anal.).

    Google Scholar 

  10. H.G. Feichtinger, K.Gröchenig: Reconstruction of Band-Limited Functions from Irregular Sampling Values. (Preprint).

    Google Scholar 

  11. H.G. Feichtinger, K. Gröchenig: Irregular sampling theorems and series expansions for band-limited functions. (Preprint).

    Google Scholar 

  12. H.G. Feichtinger, K. Gröchenig: Error analysis in irregular sampling theory, (in preparation).

    Google Scholar 

  13. M. Frazier, B. Jawerth: The ø-transform and applications to distribution spaces. Proc. Conf. Lund 1986, “Function Spaces and Applications”, Lecture Notes in Math. 1302 (1988), 223–246.

    Chapter  Google Scholar 

  14. K.Gröchenig. Describing functions: atomic decompositions versus frames. (Submitted).

    Google Scholar 

  15. J.R. Higgins: Five short stories about the cardinal series. Bull. Amer. Math. Soc. 12 (1985), 45–89.

    Article  MathSciNet  MATH  Google Scholar 

  16. A.J. Jerri: The Shannon sampling theorem — its various extensions and applications. A tutorial review. Proc. IEEE 65 (1977), 1565–1596.

    MATH  Google Scholar 

  17. S. Jaffard: A density criterium for frames of complex exponentials. Thèse de Doctorat de l’Ecole Polytechnique (1989)

    Google Scholar 

  18. H. Landau: Necessary density conditions for sampling and interpolation of certain entire functions. Acta Math. 117 (1967), 37–52.

    Article  MathSciNet  MATH  Google Scholar 

  19. N. Levinson: Gap and Density Theorems. Coll. Publ. 26, Amer. Math. Soc., New York, 1940.

    Google Scholar 

  20. F.A. Marvasti: A unified approach to zero-crossing and nonuniform sampling of single and multidimensional systems. Nonuniform, P.O.Box 1505, Oak Park, IL 60304. (1987).

    Google Scholar 

  21. A. Papoulis: Signal Analysis. McGraw-Hill. New York. 1977.

    MATH  Google Scholar 

  22. A. Papoulis: Error analysis in sampling theory. Proc. IEEE 54/7 (1966), 957–955.

    Google Scholar 

  23. W. Splettspöβer: Unregelmäβige Abtastungen determinierter und zufälliger Signale. In Kolloquium DFG-Schwerpunktprogramm Digitale Signalverarbeitung, H.G. Zimmer, V. Neuhoff, Eds., Gottingen, 1981, p. 1–4.

    Google Scholar 

  24. R. Young: An Introduction to Nonharmonic Fourier Series. Academic Press, New York. 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics U-9, Unicersity of Connecticut, Storrs, 06269-3009, Connecticut, USA

    Karlheinz Gröchenig

Authors
  1. Karlheinz Gröchenig
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Prometheus Inc., Newport, RI, USA

    J. S. Byrnes

  2. University of Massachusetts at Boston, Boston, MA, USA

    J. S. Byrnes

  3. Harvard University, Cambridge, MA, USA

    Jennifer L. Byrnes

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Kluwer Academic Publishers

About this chapter

Cite this chapter

Gröchenig, K. (1990). A New Approach to Irregular Sampling of Band-Limited Functions. In: Byrnes, J.S., Byrnes, J.L. (eds) Recent Advances in Fourier Analysis and Its Applications. NATO ASI Series, vol 315. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0665-5_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-0665-5_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6784-3

  • Online ISBN: 978-94-009-0665-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation