Periodic, Strict, and Quasi-Invariance in Linear Systems

This brief deals with shift invariance in linear systems (LSs), using a group theoretical approach. The group approach is necessary to obtain general definitions, which can be applied to continuous-time, discrete-time, multirate and also multidimensional LSs. Thus, a unique definition is given for p...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. 2, Analog and digital signal processing Analog and digital signal processing, 2007-04, Vol.54 (4), p.333-337
Main Authors: Cariolaro, G., De Pellegrini, F., Cellini, V.
Format: Article
Language:English
Subjects:
Additives
Circuits
Filters
Invariance
Kernel
Life members
Linear systems
Linear systems (LSs)
Multidimensional systems
multirate systems
shift invariance (SI)
Signal representations
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Summary:This brief deals with shift invariance in linear systems (LSs), using a group theoretical approach. The group approach is necessary to obtain general definitions, which can be applied to continuous-time, discrete-time, multirate and also multidimensional LSs. Thus, a unique definition is given for periodic invariance and strict invariance (SI) and also for quasi-invariance (QI), a new concept, intermediate between periodic and SI. The importance of QI relies upon the fact that it is comprehensive of practically all multirate LSs
ISSN:1549-7747
1057-7130
1558-3791
DOI:10.1109/TCSII.2006.890408