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Verified inclusion for eigenvalues of the first order PLL equation with general phase detector characteristics

Verifizierter Einschluß von eigenwerten der PLL-Gleichung erster Ordnung mit allgemeiner Phasen Detektor-Charakteristik

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Abstract

We present a method depending on matrix continued fractions and Sturm's comparison theorem to obtain verified inclusions for eigenvalues of the underlying boundary value problem of the first-order phase locked loop equation\(pu'' + (\lambda + \tilde g)u = 0\),p = 1/SNR with general phase detector characteristic\(\tilde g(\phi )\).

Zusammenfassung

Wir stellen eine Methode vor, die mit Hilfe von Matrix-Kettenbrüchen und dem Sturm'schen Vergleichssatz die Verifikation von Eigenwerten des Randwertproblems der Phase-Locked-Loop-Gleichung erster Ordnung\(pu'' + (\lambda + \tilde g)u = 0\),p = 1/SNR, mit allgemeiner phasenvergleichender Charakteristik\(\tilde g(\phi )\) erlaubt.

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Authors and Affiliations

  1. FB 11/Informatik II, Universität-GH-Duisburg, Lotharstrasse 65, D-47048, Duisburg, Federal Republic of Germany

    W. J. Luther &  W. Otten

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  1. W. J. Luther
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  2. W. Otten
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Luther, W.J., Otten, W. Verified inclusion for eigenvalues of the first order PLL equation with general phase detector characteristics. Computing 52, 213–232 (1994). https://doi.org/10.1007/BF02246504

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  • DOI: https://doi.org/10.1007/BF02246504

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