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New results on periodic symbolic sequences of second order digital filters with two’s complement arithmetic

By Wing-Kuen Ling and Peter Kwong-Shun Tam

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

Topics: H310 Dynamics
Publisher: John Wiley & Sons, Ltd.
Year: 2003
DOI identifier: 10.1002/cta.240
OAI identifier: oai:eprints.lincoln.ac.uk:3064

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Citations

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  3. (1990). Fractal pattern of second-order non-linear digital filters: a new symbolic analysis. doi
  4. (1993). On chaos in digital filters: case b=-1. doi
  5. (1992). On symbolic dynamics of a chaotic second-order digital filter. doi
  6. (2001). Periodic behaviors in a digital filter with two’s complement arithmetic. doi
  7. (1993). Properties of admissible symbolic sequences in a second-order digital filter with overflow non-linearity. doi

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