Isomorphism between Continuous- and Discrete-Time Systems with Input Signals of Piecewise Polynomials

Kazuo TORAICHI  Takahiko HORIUCHI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.5   pp.771-777
Publication Date: 1994/05/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Processing and System Theory)
Category: 
Keyword: 
isomorphism,  piecewise polynomials,  digital signal processing,  signals and waves,  

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Summary: 
In order to realize a continuous-time system model in digital computers, we must construct a discrete-time system model simulating the continuous-time processes in some characteristic aspect. Though many discretization methods have been proposed, they do not necessarily provide a discrete-time system in which input, state and output are identical with the sampled values of the original continuous-time system. The isomorphism discretization that all of the input, state and output of a continuous-time system can be recovered from the corresponding discrete-time system is crucial for our analysis. This paper aims at guaranteeing the isomorphism between a continuous- and a discrete-time system models (fluency system model) which were proposed by the authors. The isomorphism of input space had been already shown in the previous works by one of the authors. In this paper, by showing the isomorphism of the state function and output spaces, the aim will be achieved.