Gabor transform of time-varying systems: Exact representation and approximation

IEEE Transactions on Automatic Control

Volumn 44, Issue 4, 1999, Pages 729-741

  Rotstein, Héctor ^a,b   Raz, Shalom ^b  

^a IEEE

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; DISCRETE TIME CONTROL SYSTEMS; MATHEMATICAL TRANSFORMATIONS;

EXACT REPRESENTATION; GABOR TRANSFORMATION;

TIME VARYING CONTROL SYSTEMS;

EID: 0032675956     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.754810     Document Type: Article

References (25)

1. C. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties. New York: Academic, 1975.
2. E. Kamen, P. Khargonekar, and A. Tannenbaum, "Control of slowly-varying linear systems," IEEE Trans. Automat. Contr., vol. 34, pp. 1283-1285, Oct. 1985.
3. ∞ control for time-varying systems," SIAM J. Contr. Optim., vol. 30, no. 2, pp. 262-283, 1992.
4. M. Freedman and G. Zames, "Logarithmic variation criteria for the stability of systems with time-varying gains," SIAM J. Contr. Optim., vol. 6, no. 3, pp. 487-507, 1968.
5. ∞ adaptation: Part I - Inversion and stability," IEEE Trans. Automat. Contr., vol. 36, pp. 130-142, Feb. 1991.
6. ∞ adaptation: Part II - Optimization of stable plants," IEEE Trans. Automat. Contr., vol. 36, pp. 143-151, Feb. 1991.
7. M. Dahleh and M. A. Dahleh, "Optimal rejection of persistent and bounded disturbances: Continuity properties and adaptation," IEEE Trans. Automat. Contr., vol. 35, no. 6, pp. 687-696, 1990.
8. _, "On slowly time-varying systems," Automatica, vol. 27, no. 1, pp. 201-205, 1991.
9. R. C. Gonzalez, Digital Images Processing, 2nd ed. Addison-Wesley, 1987.
10. D. Gabor, "Theory of communication," J. Inst. Elec. Eng., vol. 93, no. 3, pp. 429-457, 1946.
11. S. Farkash and S. Raz, "Linear systems in Gabor time-frequency space," IEEE Trans. Signal Processing, vol. 42, no. 3, pp. 611-617, 1994.
12. M. J. Bastians, "On the sliding-window representation in digital signal processing," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 33, no. 4, pp. 868-873, 1985.
13. C. K. Chui, An Introduction to Wavelets Analysis and Its Applications. New York: Academic, 1992.
14. I. Daubechies, "The wavelet transform: Time-frequency localization and signal analysis," IEEE Trans. Inform. Theory, vol. 36, no. 5, pp. 961-1005, 1990.
15. M. Zibulski and Y. Y. Zeevi, "Oversampling in the Gabor scheme," IEEE Trans. Signal Processing, vol. 41, no. 8, pp. 2679-2687, 1993.
16. J. Wexler and S. Raz, "Discrete Gabor expansions," Signal Processing, vol. 21, no. 3, pp. 207-221, 1990.
17. R. S. Orr, "The order of computation of finite discrete Gabor transforms," IEEE Trans. Signal Processing, vol. 41, no. 1, pp. 122-130, 1993.
18. S. Qian and D. Chen, "Discrete Gabor transform," IEEE Trans. Signal Processing, vol. 41, pp. 2429-2438, 1993.
19. _, "Optimal biorthogonal analysis window function for discrete Gabor transform," IEEE Trans. Signal Processing, vol. 42, no. 3, pp. 694-697, 1994.
20. A. Janssen, "Duality and biorthogonality for discrete-time Weyl-Heisenberg frames," Nat. Lab., Tech. Rep. UR002/94, 1994.
21. M. Vidyasagar, Nonlinear Systems Analysis, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1993.
22. H. Rotstein, "On the computation of the discrete time Gabor biorthogonal function," 1994.
23. H. Rotstein and S. Raz, "Gabor transform of time-varying systems: Exact representation and approximation," Department of Electrical Engineering, The Technion, Haifa 32000, Israel, Tech. Rep., 1997.
24. W. Kozek, H. G. Feichtinger, and J. Scharinger, "Gabor analysis and linear system identification," in Proc. Int. Conf. Identification in Engineering Systems, Mar. 1996.
25. T. Genosar and M. Porat, "Optimal bi-orthonormal approximation of signals," IEEE Trans. Syst., Man Cybern., vol. 22, no. 3, pp. 449-460, 1992.