Skip to main content

Digital filters and continued fractions

Part of the Lecture Notes in Mathematics book series (LNM,volume 932)

Keywords

  • Transfer Function
  • Reflection Coefficient
  • Source Node
  • Directed Graph
  • Sink Node

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Claerbout, J.F., Fundamentals of Geophysical Data Processing, McGraw Hill, New York (1976).

    Google Scholar 

  2. Frank, Evelyn, On the zeros of polynomials with complex coefficients, Bull. Amer. Math. Soc., 52 (1946), 144–157.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Hamel, Georg, Eine charakteristische Eigenschaft beschränkter analytischer Funktionen, Math. Annal. 78 (1918), 257–269.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Hamming, R.W., Digital Filters, Prentice Hall, New Jersey (1977).

    Google Scholar 

  5. Henrici, P., Applied and Computational Complex Analysis, Vol. 1, Power Series, Integration, Conformal Mapping and Location of Zeros, John Wiley and Sons, New York, (1974).

    MATH  Google Scholar 

  6. Henrici, P., Applied and Computational Complex Analysis, Vol. 2, Special Functions, Integral Transforms, Asymptotics and Continued Fractions, John Wiley and Sons, New York (1977).

    MATH  Google Scholar 

  7. Huang, T.S. (ed.), Picture Processing and Digital Filtering, Topics in Applied Physics, Vol. 6, 2nd ed., Springer-Verlag, New York (1979).

    Google Scholar 

  8. Jones, William B. and Thron, W.J., Continued Fractions: Analytic Theory and Applications, Encyclopedia of Mathematics and Its Applications, No. 11, Addison-Wesley Publishing Company, Reading, Mass. (1980).

    MATH  Google Scholar 

  9. Markel, J.D. and Gray, A.H., Jr., Linear Prediction of Speech, Springer-Verlag, New York (1976).

    CrossRef  MATH  Google Scholar 

  10. McCabe, J.H. and J.A. Murphy, Continued fractions which correspond to power series expansions at two points, J. Inst. Maths. Applics 17 (1976), 233–247.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Mitra, S.K. and Sherwood, R.J., Canonic realizations of digital filters using the continued fraction expansion, IEEE Transactions on Audio and Electroacoustics, Vol. AU-20, No. 3 (August, 1972), 185–197.

    CrossRef  Google Scholar 

  12. Mullis, C.T. and Roberts, R.A., Roundoff noise in digital filters: frequency transformations and invariants, IEEE Trans. Acoust., Speech Signal Processing, Vol. ASSP-24 (December, 1976), 538–550.

    CrossRef  MathSciNet  Google Scholar 

  13. Oppenheim, A.V. and Shafer, R.W., Digital Signal Processing, Prentice Hall, New Jersey (1975).

    Google Scholar 

  14. Parker, S.R. and Griffiths, L.J., (ed.) Special Issue on Adoptive Signal Processing, IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-29, No. 3 (June 1981).

    Google Scholar 

  15. Schur, I., Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind, J. fur die reine und angewandte Mathematik 147 (1917) and 148 (1918).

    Google Scholar 

  16. Tanaka, K., A dynamic processing approach to phoneme recognition (Part I)-Feature extraction, IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-27 (Dec. 1979) 596–607.

    CrossRef  Google Scholar 

  17. Thron, W.J., Two-point Padé tables, T-fractions and sequences of Schur, Padé and Rational Approximation (ed. E.B. Saff and R.S. Varga), Academic Press, Inc., New York (1977), 215–226.

    CrossRef  Google Scholar 

  18. Van Trees, H.L., Detection, Estimation, and Modulation Theory, John Wiley and Sons, New York (1968).

    MATH  Google Scholar 

  19. Wall, H.S., Polynomials whose zeros have negative real parts, Amer. Math. Monthly, 52 (1945), 308–322.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Wall, H.S., Analytic Theory of Continued Fractions, D. Van Nostrand Co., New York (1948).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Jones, W.B., Steinhardt, A. (1982). Digital filters and continued fractions. In: Jones, W.B., Thron, W.J., Waadeland, H. (eds) Analytic Theory of Continued Fractions. Lecture Notes in Mathematics, vol 932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093311

Download citation

  • DOI: https://doi.org/10.1007/BFb0093311

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11567-0

  • Online ISBN: 978-3-540-39276-7

  • eBook Packages: Springer Book Archive