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Elements of Number Theory and Polynomial Algebra

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Part of the Springer Series in Information Sciences book series (SSINF, volume 2)

Abstract

Many new digital signal processing algorithms are derived from elementary number theory or polynomial algebra, and some knowledge of these topics is necessary to understand these algorithms and to use them in practical applications.

Keywords

Diophantine Equation Polynomial Algebra Primitive Root Chinese Remainder Theorem Quadratic Residue 
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.

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References

  1. 2.1
    T. Nagell: Introduction to Number Theory, 2nd ed. ( Chelsea, New York 1964 )Google Scholar
  2. 2.2
    G. H. Hardy, E. M. Wright: An Introduction to the Theory of Numbers, 4th ed. ( Oxford University Press, Ely House, London 1960 )zbMATHGoogle Scholar
  3. 2.3
    N. H. McCoy: The Theory of Numbers ( MacMillan, New York 1965 )zbMATHGoogle Scholar
  4. 2.4
    J. H. McClellan, C. M. Rader: Number Theory in Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N. J. 1979 )zbMATHGoogle Scholar
  5. 2.5
    M. Abramowitz, I. Stegun: Handbook of Mathematical Functions, 7th ed. ( Dover, New York 1970 ) pp. 864–869Google Scholar
  6. 2.6
    W. Sierpinski: Elementary Theory of Numbers ( Polska Akademia Nauk Monographie Matematyczne, Warszawa 1964 )zbMATHGoogle Scholar
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    I. M. Vinogradov: Elements of Number Theory, ( Dover, New York 1954 )zbMATHGoogle Scholar
  8. 2.8
    D. J. Winter: The Structure of Fields, Graduate Texts in Mathematics, Vol. 16 ( Springer, Berlin, New York, Heidelberg 1974 )zbMATHGoogle Scholar
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    R. C. Agarwal, J. W. Cooley: New algorithms for digital convolution. IEEE Trans. 25, 392–410 (1977)zbMATHGoogle Scholar
  10. 2.10
    J. H. Griesmer, R. D. Jenks: “SCRATCHPAD I. An Interactive Facility for Symbolic Mathematics”, in Proc. Second Symposium on Symbolic and Algebraic Manipulation, ACM, New York, 42–58 (1971)CrossRefGoogle Scholar
  11. 2.11
    S. Winograd: On computing the discrete Fourier transform. Math. Comput. 32, 175–199 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 2.12
    S. Winograd: Some bilinear forms whose multiplicative complexity depends on the field of constants. Math. Syst. Th., 10, 169–180 (1977)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  1. 1.Department d’ElectricitéEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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