메뉴 건너뛰기




Volumn 37, Issue 2, 1998, Pages 429-460

Generalized Fourier and Toeplitz results for rational orthonormal bases

Author keywords

[No Author keywords available]

Indexed keywords

IDENTIFICATION (CONTROL SYSTEMS); POLES AND ZEROS; RANDOM PROCESSES;

EID: 0032201979     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0363012996305437     Document Type: Article
Times cited : (36)

References (53)
  • 1
    • 5844297152 scopus 로고
    • Theory of reproducing kernels
    • N. ARONSZAJN, Theory of reproducing kernels, Acta Math., (1950), pp. 337-404.
    • (1950) Acta Math. , pp. 337-404
    • Aronszajn, N.1
  • 3
    • 0001176891 scopus 로고
    • Discrete orthonormal sequences
    • P. W. BROOME, Discrete orthonormal sequences. J. Assoc. Comput. Mach., 12 (1965), pp. 151-168.
    • (1965) J. Assoc. Comput. Mach. , vol.12 , pp. 151-168
    • Broome, P.W.1
  • 5
    • 0004006123 scopus 로고
    • Wavelets: A tutorial in theory and applications
    • Academic Press, Boston
    • C. K. CHUI, Wavelets: A Tutorial in Theory and Applications, Wavelet Analysis and Its Applications 2, Academic Press, Boston, 1992.
    • (1992) Wavelet Analysis and Its Applications , vol.2
    • Chui, C.K.1
  • 6
    • 0020096032 scopus 로고
    • Laguerre functions in signal analysis and parameter identification
    • P. R. CLEMENT, Laguerre functions in signal analysis and parameter identification, J. Franklin Institute, 313 (1982), pp. 85-95.
    • (1982) J. Franklin Institute , vol.313 , pp. 85-95
    • Clement, P.R.1
  • 8
    • 0019589376 scopus 로고
    • Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences
    • P. DEWILDE AND H. DYM, Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences, IEEE Trans. Inform. Theory, IT-27 (1981), pp. 446-461.
    • (1981) IEEE Trans. Inform. Theory , vol.IT-27 , pp. 446-461
    • Dewilde, P.1    Dym, H.2
  • 9
    • 0018008220 scopus 로고
    • On a generalized Szegö-Levinson realization algorithm, for optimal linear predictors based on a network synthesis approach
    • P. DEWILDE, A. VIEIRA, AND T. KAILATH, On a generalized Szegö-Levinson realization algorithm, for optimal linear predictors based on a network synthesis approach, IEEE Trans. Circuits Systems, CAS-25 (1978), pp. 663-675.
    • (1978) IEEE Trans. Circuits Systems , vol.CAS-25 , pp. 663-675
    • Dewilde, P.1    Vieira, A.2    Kailath, T.3
  • 10
    • 0003845667 scopus 로고
    • Fourier series, A modern introduction
    • 2nd ed., Springer-Verlag, New York
    • R. EDWARDS, Fourier Series, A Modern Introduction, vol. 1, 2nd ed., Graduate Texts in Mathematics 64, Springer-Verlag, New York, 1979.
    • (1979) Graduate Texts in Mathematics 64 , vol.1
    • Edwards, R.1
  • 12
    • 0006449680 scopus 로고    scopus 로고
    • Asymptotic variance expressions for closed-loop identification and their relevance in identification for control
    • M. GEVERS, L. LJUNG, AND P. M. J. VAN DEN HOF, Asymptotic variance expressions for closed-loop identification and their relevance in identification for control, in Proc. 11th IFAC Symposium on System Identification, 1997, pp. 1449-1454.
    • (1997) Proc. 11th IFAC Symposium on System Identification , pp. 1449-1454
    • Gevers, M.1    Ljung, L.2    Van Den Hof, M.J.3
  • 13
    • 0004236492 scopus 로고
    • Johns Hopkins University Press, Baltimore, MD
    • G. GOLUB AND C. V. LOAN, Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1989.
    • (1989) Matrix Computations
    • Golub, G.1    Loan, C.V.2
  • 16
    • 0024701601 scopus 로고
    • Frequency domain tracking characteristics of adaptive algorithms
    • S. GUNNARSSON AND L. LJUNG, Frequency domain tracking characteristics of adaptive algorithms, IEEE Trans. Acoust. Speech Signal Process., 37 (1989), pp. 1072-1089.
    • (1989) IEEE Trans. Acoust. Speech Signal Process. , vol.37 , pp. 1072-1089
    • Gunnarsson, S.1    Ljung, L.2
  • 17
    • 0031235724 scopus 로고    scopus 로고
    • The role of model validation for assessing the size of the unmodeled dynamics
    • L. GUO AND L. LJUNG, The role of model validation for assessing the size of the unmodeled dynamics, IEEE Trans. Automat. Control, 42 (1997), pp. 1230-1239.
    • (1997) IEEE Trans. Automat. Control , vol.42 , pp. 1230-1239
    • Guo, L.1    Ljung, L.2
  • 20
    • 0020093063 scopus 로고
    • Parameter identification via Laguerre polynomials
    • C. HWANG AND Y.-P. SHIH, Parameter identification via Laguerre polynomials, Internat. J. Systems Sci., 13 (1982), pp. 209-217.
    • (1982) Internat. J. Systems Sci. , vol.13 , pp. 209-217
    • Hwang, C.1    Shih, Y.-P.2
  • 21
    • 0041500580 scopus 로고
    • Tech. report 209, Massachusetts Institute of Technology, Research Laboratory of Electronics, Boston, MA
    • W. H. KAUTZ, Network Synthesis for Specified Transient Response, Tech. report 209, Massachusetts Institute of Technology, Research Laboratory of Electronics, Boston, MA, 1952.
    • (1952) Network Synthesis for Specified Transient Response
    • Kautz, W.H.1
  • 23
    • 0003195582 scopus 로고
    • Interpolation und extrapolation von stationären zufälligen folgen
    • A. KOLMOGOROV, Interpolation und extrapolation von stationären zufälligen folgen, Bull. Acad. Sci. USSR, 5 (1941), pp. 3-14.
    • (1941) Bull. Acad. Sci. USSR , vol.5 , pp. 3-14
    • Kolmogorov, A.1
  • 24
    • 0003967444 scopus 로고
    • Cambridge University Press, Cambridge
    • T. KÖRNER, Fourier Analysis, Cambridge University Press, Cambridge, 1988.
    • (1988) Fourier Analysis
    • Körner, T.1
  • 26
    • 33747441485 scopus 로고
    • The Wiener RMS (root mean square) error criterion in filter design and prediction
    • N. LEVINSON, The Wiener RMS (root mean square) error criterion in filter design and prediction, J. Math. Phys., 25 (1947), pp. 261-278.
    • (1947) J. Math. Phys. , vol.25 , pp. 261-278
    • Levinson, N.1
  • 28
    • 0006475571 scopus 로고    scopus 로고
    • Identification in closed loop: Some aspects on direct and indirect approaches
    • L. LJUNG, Identification in closed loop: Some aspects on direct and indirect approaches, in Proc. 11th IFAC Symposium on System Identification, 1997, pp. 141-146.
    • (1997) Proc. 11th IFAC Symposium on System Identification , pp. 141-146
    • Ljung, L.1
  • 29
    • 0022115069 scopus 로고
    • Asymptotic variance expressions for identified black-box transfer function models
    • L. LJUNG, Asymptotic variance expressions for identified black-box transfer function models, IEEE Trans. Automat. Control, AC-30 (1985), pp. 834-844.
    • (1985) IEEE Trans. Automat. Control , vol.AC-30 , pp. 834-844
    • Ljung, L.1
  • 30
    • 0003134065 scopus 로고
    • Asymptotic properties of the least squares method for estimating transfer functions and disturbance spectra
    • L. LJUNG AND B. WAHLBERG, Asymptotic properties of the least squares method for estimating transfer functions and disturbance spectra, Adv. Appl. Probab., 24 (1992), pp. 412-440.
    • (1992) Adv. Appl. Probab. , vol.24 , pp. 412-440
    • Ljung, L.1    Wahlberg, B.2
  • 31
    • 0022083673 scopus 로고
    • Asymptotic properties of black-box identification of transfer functions
    • L. LJUNG AND Z. D. YUAN, Asymptotic properties of black-box identification of transfer functions, IEEE Trans. Automat. Control, 30 (1985), pp. 514-530.
    • (1985) IEEE Trans. Automat. Control , vol.30 , pp. 514-530
    • Ljung, L.1    Yuan, Z.D.2
  • 32
    • 0025398366 scopus 로고
    • Approximation of stable systems by Laguerre filters
    • P. MÄKILA, Approximation of stable systems by Laguerre filters, Automatica, 26 (1990), pp. 333-345.
    • (1990) Automatica , vol.26 , pp. 333-345
    • Mäkila, P.1
  • 33
    • 0029517202 scopus 로고
    • Worst-case control-relevant identification
    • P. MÄKILÄ, J. PARTINGTON, AND T. GUSTAFSSON, Worst-case control-relevant identification, Automatica, 31 (1995), pp. 1799-1820.
    • (1995) Automatica , vol.31 , pp. 1799-1820
    • Mäkilä, P.1    Partington, J.2    Gustafsson, T.3
  • 34
    • 0007422271 scopus 로고
    • Sur la détermination d'une classe de fonctions analytiques par leurs valeurs dans un ensemble donné de points
    • F. MALMQUIST, Sur la détermination d'une classe de fonctions analytiques par leurs valeurs dans un ensemble donné de points, in C. R. Dixième Congrès Math. Scandinaves (Copenhagen), 1925, pp. 253-259.
    • (1925) C. R. Dixième Congrès Math. Scandinaves (Copenhagen) , pp. 253-259
    • Malmquist, F.1
  • 35
    • 0344351500 scopus 로고
    • Tech. report EE9432, Department of Electrical and Computer Engineering, the University of Newcastle, Callaghan, Australia, August
    • B. NINNESS AND F. GUSTAFSSON, A unifying construction of orthonormal bases for system identification, Tech. report EE9432, Department of Electrical and Computer Engineering, the University of Newcastle, Callaghan, Australia, August 1994.
    • (1994) A Unifying Construction of Orthonormal Bases for System Identification
    • Ninness, B.1    Gustafsson, F.2
  • 36
    • 0031116933 scopus 로고    scopus 로고
    • A unifying construction of orthonormal bases for system identification
    • B. NINNESS AND F. GUSTAFSSON, A unifying construction of orthonormal bases for system identification, IEEE Trans. Automat. Control, 42 (1997), pp. 515-521.
    • (1997) IEEE Trans. Automat. Control , vol.42 , pp. 515-521
    • Ninness, B.1    Gustafsson, F.2
  • 38
    • 0022128496 scopus 로고
    • Levinson's algorithm, Wold's decomposition, and spectral estimation
    • A. PAPOULIS, Levinson's algorithm, Wold's decomposition, and spectral estimation, SIAM Rev., 27 (1985), pp. 405-441.
    • (1985) SIAM Rev. , vol.27 , pp. 405-441
    • Papoulis, A.1
  • 39
    • 0026153705 scopus 로고
    • Approximation of delay systems by Fourier-Laguerre series
    • J. R. PARTINGTON, Approximation of delay systems by Fourier-Laguerre series, Automatica, 27 (1991), pp. 569-572.
    • (1991) Automatica , vol.27 , pp. 569-572
    • Partington, J.R.1
  • 40
    • 0029515671 scopus 로고
    • System identification with generalized orthonormal basis functions
    • P. M. J. VAN DEN HOF, P. S. C. HEUBERGER, AND J. BOKOR, System identification with generalized orthonormal basis functions, Automatica, 31 (1995), pp. 1821-1834.
    • (1995) Automatica , vol.31 , pp. 1821-1834
    • Van Den Hof, P.M.J.1    Heuberger, P.S.C.2    Bokor, J.3
  • 43
    • 84943488562 scopus 로고
    • Bemerkungen zur theorie der beschränkten bilinearformen mit unendlich vielen Veränderlichen
    • I. SCHUR, Bemerkungen zur theorie der beschränkten bilinearformen mit unendlich vielen Veränderlichen, J. Reine Angew. Math., 140 (1911), pp. 1-28.
    • (1911) J. Reine Angew. Math. , vol.140 , pp. 1-28
    • Schur, I.1
  • 45
    • 0345646041 scopus 로고
    • Colloquium Publications, American Mathematical Society, New York
    • G. SZEGÖ, Orthogonal Polynomials, Colloquium Publications, vol. 23, American Mathematical Society, New York, 1939.
    • (1939) Orthogonal Polynomials , vol.23
    • Szegö, G.1
  • 46
    • 0026157695 scopus 로고
    • System identification using Laguerre models
    • B. WAHLBERG, System identification using Laguerre models, IEEE Trans. Automat. Control, AC-36 (1991), pp. 551-562.
    • (1991) IEEE Trans. Automat. Control , vol.AC-36 , pp. 551-562
    • Wahlberg, B.1
  • 47
    • 0028449531 scopus 로고
    • System identification using Kautz models
    • B. WAHLBERG, System identification using Kautz models, IEEE Trans. Automat. Control, AC-39 (1994), pp. 1276-1282.
    • (1994) IEEE Trans. Automat. Control , vol.AC-39 , pp. 1276-1282
    • Wahlberg, B.1
  • 48
    • 0038338242 scopus 로고
    • Parametric signal modelling using Laguerre filters
    • B. WAHLBERG AND E. HANNAH, Parametric signal modelling using Laguerre filters, Ann. Appl. Prob., 3 (1993), pp. 467-496.
    • (1993) Ann. Appl. Prob. , vol.3 , pp. 467-496
    • Wahlberg, B.1    Hannah, E.2
  • 50
    • 84973999973 scopus 로고
    • Studies in real and complex analysis
    • Prentice-Hall, Englewood Cliffs, NJ, chap. 7, Toeplitz Matrices
    • H. WIDOM, Studies in Real and Complex Analysis, MAA Studies in Mathematics, Prentice-Hall, Englewood Cliffs, NJ, 1965, chap. 7, Toeplitz Matrices.
    • (1965) MAA Studies in Mathematics
    • Widom, H.1
  • 53
    • 0021477142 scopus 로고
    • Black box identification of multivariable transfer functions: Asymptotic properties and optimal input design
    • Z. YUAN AND L. LJUNG, Black box identification of multivariable transfer functions: Asymptotic properties and optimal input design, Internat. J. Control, 40 (1984), pp. 233-256.
    • (1984) Internat. J. Control , vol.40 , pp. 233-256
    • Yuan, Z.1    Ljung, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.