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Sandberg's Representation Theorem and Classification of Linear Systems

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1 Author(s)
Borys, A. ; Inst. of Telecommun., Univ. of Technol. & Life Sci., Bydgoszcz

It is shown that the theorem on representation of linear time-invariant system input-output maps recently published by Sandberg can be used to formulate an interesting classification of the known linear system maps. A certain property of a system map defined in this theorem and closely related to the notion of approximately-finite or vanishing memory can be also used as the system classifier. Restricting in it to consideration of only causal systems, we can distinguish between three cases: systems with no memory, with vanishing memory, and with infinitely long memory. Each of these cases is specific with regard to possessing or not possessing its own representation.

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Circuits and Systems II: Express Briefs, IEEE Transactions on  (Volume:55 ,  Issue: 7 )