Elimination of overflow oscillations in 2-D digital filters employing saturation arithmetic: An LMI approach

IEEE Signal Processing Letters

Volumn 12, Issue 3, 2005, Pages 246-249

  Singh, Vimal ^a  

^a ATILIM UNIVERSITY   (Turkey)

Author keywords

2 D discrete systems; Asymptotic stability; Finite word length effects; Linear matrix inequality; Lyapunov methods; Multidimensional digital filters; Overflow oscillations

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; DIGITAL ARITHMETIC; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; STATE SPACE METHODS; THEOREM PROVING; TWO DIMENSIONAL;

FINITE WORD LENGTH EFFECTS; LINEAR MATRIX INEQUALITY (LMI); MULTIDIMENSIONAL DIGITAL FILTERS; OVERFLOW OSCILLATIONS; SATURATION ARITHMETIC;

DIGITAL FILTERS;

EID: 14644397240     PISSN: 10709908     EISSN: None     Source Type: Journal    
DOI: 10.1109/LSP.2004.842285     Document Type: Article

References (18)

1. R. P. Roesser, "A discrete state-space model for linear image processing," IEEE Trans. Autom. Control, vol. AC-20, no. 2, pp. 1-10, Feb. 1975.
2. T. Kaczorek, Two-Dimensional Linear Systems. Berlin, Germany: Springer-Verlag, 1985.
3. B. D. O. Anderson, P. Agathoklis, E. I. Jury, and M. Mansour, "Stability and the matrix Lyapunov equation for discrete 2-dimensional systems," IEEE Trans. Circuits Syst., vol. CAS-33, no. 3, pp. 261-267, Mar. 1986.
4. C. Xiao, D. J. Hill, and P. Agathoklis, "Stability and the Lyapunov equation for n-dimensional digital systems," IEEE Trans. Circuits Syst. I, vol. 44, no. 7, pp. 614-621, Jul. 1997.
5. N. G. El-Agizi and M. M. Fahmy, "Two-dimensional digital filters with no overflow oscillations," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-27, no. 10, pp. 465-469, Oct. 1979.
6. D. Liu and A. N. Michel, "Stability analysis of state-space realizations for two-dimensional filters with overflow nonlinearities," IEEE Trans. Circuits Syst. I, vol. 41, no. 2, pp. 127-137, Feb. 1994.
7. S. G. Tzafestas, A. Kanellakis, and N. J. Theodorous, "Two-dimensional digital filters without overflow oscillations and instability due to finite word length," IEEE Trans. Signal Process., vol. 40, no. 9, pp. 2311-2317, Sep. 1992.
8. C. Xiao and D. J. Hill, "Stability and absence of overflow oscillations for 2-D discrete-time systems," IEEE Trans. Signal Process., vol. 44, no. 8, pp. 2108-2110, Aug. 1996.
9. H. Kar and V. Singh, "Stability analysis of 2-D state-space digital filters using Lyapunov function: a caution," IEEE Trans. Signal Process., vol. 45, no. 10, pp. 2620-2621, Oct. 1997.
10. P. H. Bauer and K. R. Ralev, "Comments on 'Stability and absence of overflow oscillations for 2-D discrete-time systems'," IEEE Trans. Signal Process., vol. 46, no. 3, pp. 803-804, Mar. 1998.
11. C. Xiao and D. J. Hill, "Reply to 'Comments on 'Stability and absence of overflow oscillations for 2-D discrete-time systems"," IEEE Trans. Signal Process., vol. 47, no. 9, p. 2599, Sep. 1999.
12. H. Kar and V. Singh, "Stability analysis of 2-D state-space digital filters with overflow nonlinearities," IEEE Trans. Circuits Syst. I vol. 47, no. 4, pp. 598-601, Apr. 2000.
13. H. Kar, "Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities," IEEE Trans. Signal Process., vol. 49, no. 5, pp. 1097-1105, May 2001.
14. T. A. C. M. Classen, W. F. G. Mecklenbräuker, and J. B. H. Peek, "Effects of quantization and overflow in recursive digital filters," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-24, no. 12, pp. 517-529, Dec. 1976.
15. H. J. Butterweck, J. H. F. Ritzerfeld, and M. J. Werter, "Finite Worldlength Effects in Digital Filters - A Review," Eindhoven University of Technology, Eindhoven, The Netherlands, EUT Rep. 88-E-205, 1988.
16. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox - For Use With Matlab. Natic, MA: The MATH Works Inc., 1995.
17. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM,
18. V. Singh, "A new realizaility condition for limit cycle-free state-space digital filters employing saturation arithmetic," IEEE Trans. Circuits Syst., vol. CAS-32, no. 10, pp. 1070-1071, Oct. 1985.