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Sampling and Rational Interpolation for Non-band-limited Signals

In: Mathematics Without Boundaries

Author

Listed:
  • Balázs Király

    (University of Pécs, Faculty of Sciences)

  • Margit Pap

    (University of Pécs, Faculty of Sciences)

  • Ákos Pilgermajer

    (University of Pécs, Pollack Mihály Faculty of Engineering and Information Technology)

Abstract

This paper concentrates on the frequency domain representation of non-band-limited continuous-time signals. Many LTI systems of practical interest can be represented using an Nth-order linear differential equation with constant coefficients. The frequency response of these systems is a rational function. Hence our aim is to give sampling and interpolation algorithms with good convergence properties for rational functions. A generalization of the Fourier-type representation is analyzed using special rational orthogonal bases: the Malmquist–Takenaka system for the upper and lower half plane. This representation is more efficient in particular classes of signals characterized with a priori fixed properties. Based on the discrete orthogonality of the Malmquist–Takenaka system we introduce new rational interpolation operators for the upper and lower half plane as well. Combining these two interpolations we can give exact interpolation for a large class of rational functions among them for the Runge test function. We study the properties of these rational interpolation operators.

Suggested Citation

  • Balázs Király & Margit Pap & Ákos Pilgermajer, 2014. "Sampling and Rational Interpolation for Non-band-limited Signals," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Mathematics Without Boundaries, edition 127, pages 383-408, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-1124-0_12
    DOI: 10.1007/978-1-4939-1124-0_12
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