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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Characterization of discrete linear shiftinvariant systems
 European Association for Signal Processing EURASIP; Institute of Electrical and Electronics Engineers IEEE; IEEE Signal Processing Society: 25th European Signal Processing Conference, EUSIPCO 2017 : 27 August  2 September 2017, Kos Island, Greece Piscataway, NJ: IEEE, 2017 ISBN: 9780992862671 ISBN: 9780992862688 ISBN: 9781538607510 pp.346350 
 European Signal Processing Conference (EUSIPCO) <25, 2017, Kos> 

 English 
 Conference Paper 
 Fraunhofer FKIE () 
Abstract
Linear timeinvariant (LTI) systems are of fundamental importance in classical digital signal processing. LTI systems are linear operators commuting with the timeshift operator. For Nperiodic discrete time series the timeshift operator is a circulant N × N permutation matrix. Sandryhaila and Moura developed a linear discrete signal processing framework and corresponding tools for datasets arising from social, biological, and physical networks. In their framework, the circulant permutation matrix is replaced by a networkspecific N × N matrix A, called a shift matrix, and the linear shiftinvariant (LSI) systems are all N × N matrices H over C commuting with the shift matrix: HA = AH. Sandryhaila and Moura described all those H for the nondegenerate case, in which all eigenspaces of A are onedimensional. Then the authors reduced the degenerate case to the nondegenerate one. As we show in this paper this reduction does, however, not generally hold, leaving open one gap in the proposed argument. In this paper we are able to close this gap and propose a complete characterization of all (i.e., degenerate and nondegenerate) LSI systems. Finally, we describe the corresponding spectral decompositions.