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New results on periodic symbolic sequences of second order digital filters with two's complement arithmetic
Author(s) -
WingKuen Ling Bingo,
KwongShun Tam Peter
Publication year - 2003
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.240
Subject(s) - complement (music) , mathematics , arithmetic , eigenvalues and eigenvectors , unit circle , order (exchange) , digital filter , state (computer science) , filter (signal processing) , state vector , algorithm , computer science , mathematical analysis , biochemistry , chemistry , physics , finance , quantum mechanics , classical mechanics , complementation , economics , computer vision , gene , phenotype
In this article, the second order digital filter with two's complement arithmetic in Reference 1 is considered. Necessary conditions for the symbolic sequences to be periodic after a number of iterations are given when the filter parameters are at b =a+1 and b =‐ a +1. Furthermore, for some particular values of a , even when one of the eigenvalues is outside the unit circle, the system may behave as a linear system after a number of iterations and the state vector may toggle between two states or converge to a fixed point at the steady state. The necessary and sufficient conditions for these phenomena are given in this article. Copyright © 2003 John Wiley & Sons, Ltd.