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Abstract

First the notion of a digital filter is briefly introduced. Next the part of the design process for such filters where approximation by polynomials with integral coefficients enters is outlined. Finally a result is stated and proved, which reduces the determination of the error involved in approximating a function by a polynomial whose coefficients are integers to a finite number of calculations.

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References

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    Andria, G.: Approximation of continuous functions by polynomials with integral coefficients, J. Approx. Theory 4 (1971), 357–362.CrossRefGoogle Scholar
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    Ferguson, L. B. O.: Existence and uniqueness in approximation by integral polynomials, J. Approx. Theory 10 (1974), 237–244.CrossRefGoogle Scholar
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    Liu, B.: Digital Filters and the Fast Fourier Transform. Beuchmark Papers in Electrical Engineering and Computer Science/12, Stroudsburg, Pennsylvania, Dowden, Hutchinson and Ross (distributed by Academic Press), 1975.Google Scholar
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    Oppenheim, A. V. and R. W. Schafer: Digital Signal Processing, Englewood Cliffs, New Jersey, Prentice Hall, 1975.Google Scholar
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Copyright information

© Springer Basel AG 1980

Authors and Affiliations

  • Le Baron
    • 1
  • O. Ferguson
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaRiversideUSA

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