Advertisement

On a Class of Almost Orthogonal Polynomials

  • Bratislav Danković
  • Predrag Rajković
  • Sladjana Marinković
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5434)

Abstract

In this paper, we define a new class of almost orthogonal polynomials which can be used successfully for modelling of electronic systems which generate orthonormal basis. Especially, for the classical weight function, they can be considered like a generalization of the classical orthogonal polynomials (Legendre, Laguerre, Hermite, ...). They are very suitable for analysis and synthesis of imperfect technical systems which are projected to generate orthogonal polynomials, but in the reality generate almost orthogonal polynomials.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    MacInnes, C.S.: The Reconstruction of Discontinuous Piecewise Polynomial Signals. IEEE Transactions on Signal Processing 53(7), 2603–2607 (2005)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Karam, L.J., McClellan, J.H.: Complex Chebyshev Approximation for FIR Filter Design. IEEE Transactions on Circuits-II: Analog and Digital Signal Processing 42(3), 207–216 (1995)zbMATHGoogle Scholar
  3. 3.
    Nie, X., Raghuramireddy, D., Unbehauen, R.: Orthonormal Expansion of Stable Rational Transfer Functions. Electronics Letters 27(16), 1492–1494 (1991)CrossRefGoogle Scholar
  4. 4.
    Tseng, C.C.: Digital Differentiator Design Using Fractional Delay Filter and Limit Computation. IEEE Transactions on Circuits and Systems-4, Regular Papers 52(10), 2248–2259 (2005)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Benyi, A., Torres, R.H.: Almost Orthogonality and a Class of Bounded Bilinear Pseudodifferential Operators. Mathematical Research Letters 11, 1–11 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ben-Yaacov, I., Wagner, F.O.: On Almost Orthogonality in Simple Theories. J. Symbolic Logic 69(2), 398–408 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cotlar, M.: A Combinatorial Inequality and Its Applications to L 2-Spaces. Rev. Mat. Cuyana 1, 41–55 (1955)MathSciNetGoogle Scholar
  8. 8.
    Szegő, G.: Orthogonal Polynomials, 4th edn., vol. 23. Amer. Math. Soc. Colloq. Publ. (1975)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Bratislav Danković
    • 1
  • Predrag Rajković
    • 2
  • Sladjana Marinković
    • 1
  1. 1.Department of Automatic Control, Faculty of Electronic EngineeringSerbia
  2. 2.Department of Mathematics, Faculty of Mechanical EngineeringUniversity of NišNišSerbia

Personalised recommendations