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Sampling and Rational Interpolation for Non-band-limited Signals

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Mathematics Without Boundaries

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.

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Authors and Affiliations

  1. Faculty of Sciences, University of Pécs, 7634, Pécs, Ifjúság út 6, Hungary

    Balázs Király & Margit Pap

  2. Pollack Mihály Faculty of Engineering and Information Technology, University of Pécs, 7624, Pécs, Boszorkány út 2, Hungary

    Ákos Pilgermajer

Authors
  1. Balázs Király
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  2. Margit Pap
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  3. Ákos Pilgermajer
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Correspondence to Margit Pap .

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Editors and Affiliations

  1. Dept. Industrial & Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Király, B., Pap, M., Pilgermajer, Á. (2014). Sampling and Rational Interpolation for Non-band-limited Signals. In: Pardalos, P., Rassias, T. (eds) Mathematics Without Boundaries. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1124-0_12

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