Skip to main content
Article thumbnail
Location of Repository

Chaotic behaviors of stable second-order digital filters with two’s complement arithmetic

By Bingo Wing-Kuen Ling, Wai-Fung Hung and Peter Kwong-Shun Tam


In this paper, the behaviors of stable second-order digital filters with two’s complement arithmetic are investigated. It is found that even though the poles are inside the unit circle and the trajectory converges to a fixed point on the phase plane, that fixed point is not necessarily the origin. That fixed point is found and the set of initial conditions corresponding to such trajectories is determined. This set of initial conditions is a set of polygons inside the unit square, whereas it is an ellipse for the marginally stable case. Also, it is found that the occurrence of limit cycles and chaotic fractal pattern on the phase plane can be characterized by the periodic and aperiodic behaviors of the symbolic sequences, respectively. The fractal pattern is polygonal, whereas it is elliptical for the marginally stable case

Topics: H620 Electrical Engineering, H310 Dynamics
Publisher: John Wiley & Sons
Year: 2003
DOI identifier: 10.1002/cta.243
OAI identifier:

Suggested articles


  1. (1972). A bound on limit cycles in fixed-point implementations of digital filters. doi
  2. (1990). Chaos and fractals from third-order digital filters. doi
  3. (1988). Chaos in digital filters. doi
  4. (2004). Chaotic behaviors of a digital filter with two’s complement arithmetic and arbitrary initial conditions and order. doi
  5. (1996). Complex behavior in digital filters with overflow nonlinearity: analytical results. doi
  6. (1978). Digital filter realizations without overflow oscillations. doi
  7. (1990). Fractal pattern of second-order non-linear digital filters: a new symbolic analysis. doi
  8. (2003). Further investigation on chaos of real digital filters. doi
  9. (1976). Limit cycles in the combinatorial implementation of digital filters. doi
  10. (1971). Limit-cycle oscillations in digital filters. doi
  11. (1984). Maximum amplitude zero-input limit cycles in digital filters. doi
  12. (1977). Minimum norm recursive digital filters that are free of overflow limit cycles. doi
  13. (1990). Ogorzalek MJ. Bifurcation phenomena in second-order digital filter with saturationtype adder overflow characteristic. doi
  14. (1993). On chaos in digital filters: case b=-1. doi
  15. (1991). On chaos of digital filters in the real world. doi
  16. (1992). On symbolic dynamics of a chaotic second-order digital filter. doi
  17. (2001). Periodic behaviors in a digital filter with two’s complement arithmetic. doi
  18. (1993). Properties of admissible symbolic sequences in a second-order digital filter with overflow non-linearity. doi
  19. (2003). Some new trajectory patterns and periodic behaviors of unstable second-order digital filter with two’s complement arithmetic. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.