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z-Transformation

In: Einführung in die Systemtheorie

Author

Listed:
  • Bernd Girod

    (Universität Erlangen-Nürnberg)

  • Rudolf Rabenstein

    (Universität Erlangen-Nürnberg)

  • Alexander Stenger

    (Universität Erlangen-Nürnberg)

Abstract

Zusammenfassung Im Kapitel 12 hatten wir zeitdiskrete Signale x[k] und ihre Spektren X(e jΩ) in Gestalt der Fourier-Transformation für·Folgen ℱ*{x[k]} nach (12.13) kennengelernt. Die Verwandtschaft zwischen der Transformation ℱ* für zeitdiskrete Signale und zwischen der Fourier-Transformation ℱ{x(t)} für zeitkontinuierliche Signale kommt z.B. durch die Beziehung (12.43) zum Ausdruck. Daneben kennen wir aber für zeitkontinuierliche Signale auch die Laplace-Transformation ℒ{x(t)}, die dem Zeitsignal x(t) eine Funktion X(s)●—○x(t) der komplexen Frequenzvariablen s zuweist. Eine vergleichbare Transformation für zeitdiskrete Signale stellt die z-Transformation dar. Sie ist nicht nach einem berühmten Mathematiker, sondern einfach nach der üblichen Bezeichnung für ihre komplexe Frequenzvariable z benannt.

Suggested Citation

  • Bernd Girod & Rudolf Rabenstein & Alexander Stenger, 1997. "z-Transformation," Springer Books, in: Einführung in die Systemtheorie, chapter 13, pages 321-344, Springer.
    • Handle: RePEc:spr:sprchp:978-3-663-09883-6_13
    DOI: 10.1007/978-3-663-09883-6_13
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