References
- Fliess , M and Sira-Ramírez , H . 2003 . An algebraic framework for linear identification . ESAIM: COCV , 9 : 151 – 168 . Available from: http://www.emath.fr/cocv
- Fliess , M , Mboup , M , Mounier , H and Sira-Ramírez , H . 2003 . “ Questioning some paradigms of signal processing via concrete examples ” . In Algebraic Methods in Flatness, Signal Processing and State Estimation , Edited by: Sira-Ramírez , GMH . 1 – 21 . México : Innovación ed. Lagares . chap. 1
- Buium , A . 1994 . Differential Algebra and Diophantine Geometry , Paris : Hermann .
- Kolchin , ER . 1973 . Differential Algebra and Algebraic Groups , New York : Academic Press .
- Mikusinski , J and Boehme , TK . 1987 . Operational Calculus , Vol. 2 , Oxford : PWN Varsovie & Oxford University Press .
- Yosida , K . 1984 . Operational Calculus–A Theory of Hyperfunctions , New York : Springer .
- Kahn , M , Mackisack , M , Osborne , MR and Smyth , GK . 1992 . On the consistency of Prony's method and related algorithms . J. Comput. Graph. Statist. , 1 : 329 – 349 .
- Trapero , JR , Sira-Ramírez , H and Batlle , VF . 2007 . An algebraic frequency estimator for a biased and noisy sinusoidal signal . Signal Process. , 87 : 1188 – 1201 .
- Bresler , Y and Macovski , A . 1986 . Exact maximum likelihood parameter estimation of superimposed exponential signals in noise . IEEE Trans. Acoust., Speech, Signal Process. , 34 : 1081 – 1089 .
- Kumaresan , R and Tufts , DW . 1982 . Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise . IEEE Trans. Acoust., Speech, Signal Process. , 30 : 833 – 840 .
- Hua , Y and Sarkar , TK . 1990 . Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise . IEEE Trans. Acoust., Speech, Signal Process. , 38 : 814 – 824 .
- Li , Y , Liu , K and Razavilar , J . 1997 . A parameter estimation scheme for damped sinusoidal signals based on low-rank hankel approximation . IEEE Trans. Signal Process. , 45 : 481 – 486 .
- Rahman , MA and Yu , KB . 1987 . Total least squares approach for frequency estimation using linear prediction . IEEE Trans. Acoust., Speech, Signal Process. , 35 : 1440 – 1454 .
- Osborne , MR and Smyth , GK . 1995 . A modified Prony algorithm for exponential function fitting . SIAM J. Sci. Comput. , 16 : 119 – 138 .
- Sira-Ramìrez , H and Fliess , M . 2002 . “ On discrete-time uncertain visual based control of planar manipulators: An on-line algebraic identification approach ” . In Proceedings of the 41st IEEE CDC Vol. 4 , 4509 – 4514 . Las Vegas
- Fuchshumer , S . 2006 . Algebraic Linear Identification, Modelling, and Applications of Flatness-based Control , Linz : Johannes Kepler Universität .
- Fliess , M , Fuchshumer , S , Schlacher , K and Sira-Ramírez , H . 2006 . “ Discrete-time linear parametric identification: An algebraic approach ” . In JIME'2006 , France : Poitiers .
- Perlin , K . 1985 . An image synthesizer . SIGGRAPH'85 , 19 ( 3 ) : 287 – 296 .
- Mikosch , T . 1998 . “ Elementary stochastic calculus with finance in view ” . In Advanced Series on statistical science and applied probability , Vol. 6 , London : World Scientific .
- Mboup , M , Join , C and Fliess , M . 2008 . Numerical differentiation with annihilators in noisy environment . to appear in Numerical Algorithms , (DOI: 10.1007/s11075-008-9236-1)
- Fliess , M . 2006 . Analyse non standard du bruit . CRAS, Série 1, Mathématiques , 342 : 797 – 802 .
- Stewart , GW . 1990 . Stochastic perturbation theory . SIAM Rev. , 32 : 579 – 610 .
- Higham , NJ . 1994 . “ A survey of componentwise perturbation theory in numerical linear algebra ” . In Mathematics of Computation 1943–1993: A Half Century of Computational Mathematics , Edited by: Gautschi , W . Vol. 48 , 49 – 77 . Providence, RI, , USA : AMS .
- Skeel , RD . 1979 . Scaling for numerical stability in Gaussian elimination . J. Assoc. Comput. Mach. , 26 : 494 – 526 .
- Saha , S and Kay , S . 2002 . Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling . IEEE Trans. Signal Process. , 50 : 224 – 230 .
- O'Neill , JC and Flandrin , P . 1998 . “ Chirp Hunting ” . In Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis , 425 – 428 . USA : PA .
- Djurić , P and Kay , SM . 1990 . Parameter estimation of chirp signal . IEEE Trans. Acoust., Speech, Signal Process. , 38 : 2118 – 2126 .
- Volcker , B and Ottersten , B . 2001 . Chirp parameter estimation from a sample covariance matrix . IEEE Trans. Signal Process. , 49 : 603 – 612 .
- Delprat , N , Escudié , B , Guillemain , P , Kronland-Martinet , R , Tchamitchian , P and Torrésani , B . 1992 . Asymptotic wavelet and Gabor analysis: Extraction of instantaneous frequencies . IEEE Trans. Inform. Theory , 38 : 644 – 664 .
- Mallat , S . 1999 . A Wavelet Tour of Signal Processing , 2nd , San Diego : Academic Press .
- Morvidone , M and Torresani , B . 2003 . Time Scale Approach for Chirp Detection . Int. J. Wavelets Multiresolut. Inf. Process. , 1 : 19 – 50 .
- Liu , D , Gibaru , O , Perruquetti , W , Fliess , M and Mboup , M . 2008 . “ An error analysis in the algebraic estimation of a noisy sinusoidal signal ” . In 16th Mediterranean Conference on Control and Automation 1296 – 1301 . Athens, , Greece