Finite Systemtheorie
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Die zeitdiskreten Systeme, die in der Nachrichtentechnik und in der Regelungstechnik eine ständig wachsende Bedeutung bekommen, werden heute gewöhnlich durch die (infinite) Z-Transformation beschrieben. Gegenstand dieses Buches ist im Gegensatz dazu eine finite Beschrei- bung dieser Systeme (ohne die Begriffe "kontinuierlich", "unendlich" und "konvergent"), die unmittelbar auf dem Digitalrechner implementierbar ist. Das wird dadurch möglich, da man die Zeitfunktionen als per i- disehe Impulsfolgen annimmt. Das Buch ist das erweiterte Skriptum einer Vorlesung, die ich seit 1972 an der Technischen Hochschule Darmstadt halte. Abgesehen von 1, der einen kurzen Überblick über die konventionelle infinite Systemtheorie gibt, ist an mathematischen Vorkenntnissen lediglich die Matrizenalgebra erforder lieh. Ich danke den Herren Dr. -Ing. Hermann Kremer und Dipl. -Ing. Raimund L ü c k e r für fruchtbare Diskussionen und für die kritische Durchsicht des Manuskripts. Darmstadt, im Sommer 1976 Wilhelm Klein "Man kann die Ingenieure bedauern, die es so lange aufge- schoben haben, sich mit der Laplace-Transformation zu befreunden, bis sie ins Museum verwiesen wurde. Aber so etwas ist schon öfter geschehen. Wir Mathematiker werden auch für unsere Fahrlässigkeit bestraft: Unsere Strafe ist die Aufgabe, ihnen die Laplace-Transformation nun wieder auszutreiben. " Der Mathematiker Hans Freudenthai im Jahre 1958 [9. S]. INHALT Seite 1 1. überblick über die infinite Systemtheorie 1. 1. Der Begriff des Systems 1 2 1. 2. Infinite und finite Systemtheorie 6 1. 3. DerZeitbereich 6 1. 3. 1. Impuls und Impulsantwort 6 1. 3. 2. Das Faltungsintegral 9 1. 4.
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