Z-Transformation Für Ingenieure: Grundlagen Und Anwendungen in Der Elektrotechnik, Informationstechnik Und Regelungstechnik
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Wozu eigentlich Z-Transformation? Diese Frage hört man häufig von Studenten, die bereits Grundregeln der F ourier-und der Laplace-Transformation verstanden haben und sich -wenn auch nach anfänglichem Zögern - sogar damit anfreunden konnten. Nun schon wieder eine neue Transformation? Ist sie wirklich nötig? Wo kann ich sie anwenden und welche Vorteile bringt sie mir? Diese Einfiihrung versucht, solche und ähnliche Fragen leicht fa lich und präzise zu beantworten. Sie richtet sich zuerst an den Anfänger, den weniger mathemati- sche Grundsatzfragen interessieren, der vielmehr das breit gefächerte Anwen- dungsspektrum der Z-Transformation kennenlernen möchte und nützliche Hin- weise sowie praxisbezogene Rechenbeispiele erwartet. Darüber hinaus wird auch der Fortgeschrittene angesprochen, der den Gebrauch der Z-Transformation in der Technik kennenlernen und sich in diese Thematik einarbeiten möchte, um daraus fiir eigene Problemstellungen Nutzen zu ziehen. Denn eines ist unbestritten: dynamische Vorgänge in zeitdiskreten technischen Anwendungen werden vorwiegend mit Methoden der Z-Transformation behan- delt; diese lineare Funktionaltransformation hat sich als leistungsfähiges Hilfs- mittel zur rechnerischen Behandlung solcher Problemkreise durchgesetzt. Dies gilt insbesondere fiir digitale AufgabensteIlungen der Systemtheorie, der Regelungs-und Automatisierungstechnik sowie der allgemeinen Elektrotechnik. Vorwiegend dort, wo Rechentechnik einsetzbar ist, hat sich die Z-Transformati- on bei numerischen Untersuchungen bewährt. So ist beispielsweise die Analyse von Me wertreihen selten an kontinuierliche Funktionen geknüpft, sie erfolgt vielmehr an Hand von gemessenen "Zahlenkolonnen", deren Verarbeitung eine Domäne der Z-Transformation darstellt. Zum Inhalt: Das 1. Kapitel stellt mathematische Grundlagen vor, soweit sie fiir den rechnen- den Ingenieur unverzichtbar sind.
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