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Duality Principle and New Forms of the Inverse Laplace Transform for Signal Propagation Analysis in Inhomogeneous Media with Dispersion

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Abstract

New equations for Laplace transform inversion are obtained. The equations satisfy the causality principle. The impulse response of a channel is determined in order to analyze dispersion distortions in inhomogeneous media. The impulse response excludes the possibility that the signal exceeds the speed of light in the medium. The transmission bandwidth, the angular spectrum, and the Doppler shift in the ionosphere are computed.

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ACKNOWLEDGMENTS

The authors are grateful to S.S. Matyugov, head of Laboratory no. 117 of the Fryazino Branch of the Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences for discussion and valuable comments.

Funding

This work was performed within a state assignment and was supported in part by program no. 12 of the Presidium of the Russian Academy of Sciences and by the Russian Foundation for Basic Research (grant no. 190200083A).

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Authors and Affiliations

  1. Kotelnikov Institute of Radio Engineering and Electronics, Fryazino Branch, Russian Academy of Sciences, 141190, Fryazino, Moscow oblast, Russia

    A. G. Pavelyev & A. A. Pavelyev

Authors
  1. A. G. Pavelyev
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  2. A. A. Pavelyev
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Correspondence to A. A. Pavelyev.

Additional information

Translated by I. Ruzanova

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Pavelyev, A.G., Pavelyev, A.A. Duality Principle and New Forms of the Inverse Laplace Transform for Signal Propagation Analysis in Inhomogeneous Media with Dispersion. Dokl. Math. 100, 594–599 (2019). https://doi.org/10.1134/S106456241906022X

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  • DOI: https://doi.org/10.1134/S106456241906022X

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