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Digital filters and continued fractions

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Analytic Theory of Continued Fractions

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

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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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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).

    Book  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Chapter  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

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William B. Jones W. J. Thron Haakon Waadeland

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© 1982 Springer-Verlag

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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

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

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11567-0

  • Online ISBN: 978-3-540-39276-7

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