Is uniqueness lost for under-sampled continuous-time auto-regressive processes?

IEEE Signal Processing Letters

Volumn 19, Issue 4, 2012, Pages 183-186

  Ward, John Paul ^a   Kirshner, Hagai ^a   Unser, Michael ^a  

^a EPFL   (Switzerland)

Author keywords

Approximation theory; Sampling theory; Stochastic processes

Indexed keywords

APPROXIMATION THEOREM; AUTOREGRESSIVE PROCESS; COMPLEX PLANES; CONTINUOUS TIME; CONTINUOUS TIME MODELS; CURRENT ESTIMATION; LEBESGUE MEASURE; SAMPLED DATA; SAMPLING RATES; SAMPLING THEORY; STOCHASTIC PROCESS; UNIFORM GRIDS;

APPROXIMATION THEORY; RANDOM PROCESSES; SIGNAL ENCODING;

CONTINUOUS TIME SYSTEMS;

EID: 84857341198     PISSN: 10709908     EISSN: None     Source Type: Journal    
DOI: 10.1109/LSP.2012.2185695     Document Type: Article

References (16)

1. L. Ljung, System Identification. Upper Saddle River, NJ: Prentice-Hall, 1999.
2. S. Haykin, Adaptive Filter Theory. Upper Saddle River, NJ: Prentice-Hall, 2002.
3. I.-T. Lim and B. G. Lee, "Lossless pole-zero modeling for speech signals", IEEE Trans. Speech Audio Process., vol. 1, no. 3, pp. 269-276, Jul. 1993.
4. A. Feuer and G. Goodwin, Sampling in Digital Signal Processing and Control. Boston, MA: Birkhäuser, 1996.
5. H. Fan, T. Söderström, M. Mossberg, B. Carlsson, and Y. Zou, "Estimation of continuous-time AR process parameters from discrete-time data", IEEE Trans. Signal Process., vol. 47, no. 5, pp. 1232-1244, May 1999.
6. D.-T. Pham, "Estimation of continuous-time autoregressive model from finely sampled data", IEEE Trans. Signal Process., vol. 48, no. 9, pp. 2576-2584, Sep. 2000.
7. H. Garnier, M. Mensler, and A. Richard, "Continuous-time model identification from sampled data: Implementation issues and performance evaluation", Int. J. Contr., vol. 76, no. 13, pp. 1337-1357, Sep. 2003.
8. H. Garnier and P. Young, "Time-domain approaches to continuoustime model identification of dynamical systems from sampled data", in Proc. Amer. Control Conf., Boston, MA, June 2004.
9. G. C. Goodwin, J. I. Yuz, and H. Garnier, "Robustness issues in continuous-time system identification from sampled data", in Proc. 16th I FAC World Congress, Prague, Czech Republic, Jul. 2005.
10. E. K. Larsson, M. Mossberg, and T. Söderström, "An overview of important practical aspects of continuous-time ARMA system identification", Circuits Syst. Signal Process., vol. 25, no. 1, pp. 17-46, May 2006. (Pubitemid 44193478)
11. H. Garnier and L. Wang, Eds., Identification of Continuous-Time Models from Sampled Data. London, U. K.: Springer-Verlag, 2008.
12. G. C. Goodwin, J. C. Agäero, J. S. Welsh, J. I. Yuz, G. J. Adams, and C. R. Rojas, "Robust identification of process models from plant data", J. Process Contr., vol. 18, pp. 810-820, 2008.
13. M. Mossberg, "Estimation of continuous-time stochastic signals from sample covariances", IEEE Trans. Signal Process., vol. 56, no. 2, pp. 821-825, Feb. 2008. (Pubitemid 351285075)
14. J. Gillberg and L. Ljung, "Frequency-domain identification of continuous-time ARMA models from sampled data", Automatica, vol. 45, pp. 1371-1378, 2009.
15. H. Bohr and B. Jessen, "One more proof of Kronecker's theorem", J. London Math. Soc., vol. 7, no. 4, pp. 274-275, 1932.
16. H. Kirshner, S. Maggio, and M. Unser, "A sampling theorey approach to continuous ARMA identification", IEEE Trans. Signal Process., vol. 59, no. 10, pp. 4620-4634, Oct. 2011.