Zerlegung von LTI-Systemen und eine vollständige Charakterisierung der Systeme von Faltungstyp
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Übersicht
In der Arbeit wird das Verhalten von BIBO-stabilen linearen Systemen mit einem Eingang und einem Ausgang untersucht. Bisher wurde die Meinung vertreten, daß die Input-Output-Beziehung dieser Systeme durch die bekannte Faltungssumme gegeben ist. Diese Systeme werden Systeme vom Faltungstyp genannt. Es wurde jedoch von Boyd und Sandberg entdeckt, daß nicht alle BIBO-stabilen linearen Systeme mit einem Eingang und einem Ausgang Systeme vom Faltungstyp sind. In der Arbeit wird nun eine genaue Charakterisierung der Systeme vom Faltungstyp angegeben. Weiterhin werden die FIR-Systeme untersucht.
Analysis of LTI-Systems and complete characterization of systems of the convolution type
Abstract
In this paper the behaviour of discrete-time BIBO-stable linear systems is investigated. The main idea of the theory of discrete-time single-input single-output linear system is that every such system has an input-output map that can be represented by the well known convolution sum. These systems are called systems of the convolution type. It was recently discovered by Boyd and Sandberg that not all discrete-time single-input single-output linear systems are systems of the convolution type. Hence it would be interesting to characterize the systems of the convolution type. Such a characterization is given in the paper. FIR-systems are also investigated.
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