Ling, Wing-Kuen and Tam, Peter Kwong-Shun (2003) New results on periodic symbolic sequences of second order digital filters with two’s complement arithmetic. International Journal of Circuit Theory and Applications, 31 (4). pp. 407-421. ISSN 0098-9886

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Abstract

In this article, the second order digital filter with two’s complement arithmetic in [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.

Item Type:	Article
Additional Information:	In this article, the second order digital filter with two’s complement arithmetic in [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.
Keywords:	second order digital filter, two’s complement arithmetic, symbolic sequences, eigenvalues
Subjects:	H Engineering > H310 Dynamics
Divisions:	College of Sciences > Faculty of Science > Lincoln School of Engineering
Depositing User:	Wing-Kuen Ling
Date Deposited:	06 Aug 2010 13:04
Last Modified:	13 Mar 2013 08:43
URI:	http://eprints.lincoln.ac.uk/id/eprint/3064

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