Spectral Estimation: An Overdetermined Rational Model Equation Approach

Proceedings of the IEEE

Volumn 70, Issue 9, 1982, Pages 907-939

  Cadzow, James A ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

RATIONAL MODEL EQUATION APPROACH;

SPECTRUM ANALYSIS - MATHEMATICAL MODELS;

EID: 0020186089     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1982.12424     Document Type: Article

References (66)

1. H. AKAIKE, “Fitting autoregressive models for prediction,” Ann. Inst. Statist. Math., vol. 21, pp. 243-247, 1969.
2. H. Akaike, “Power spectrum estimation through autoregressive model fitting,” Ann. Inst. Statist MAth., vol. 21, pp. 407-419, 1969.
3. H. Akaike, “Maximum likelihood identification of gaussian autoregressrve moving-average model's,” BiometriKa, vol. 60, no. 2, pp. 255-265, AUG. 1973.
4. H. Akaike, “A new look at the statistical model identificant,” IEEE Trans. Automat. Contr., vol. AC-19, pp. 716-723, Dec. 1974.
5. N. O. Anderson, “On the calculation of filter coefficients for maximum entropy spectral analysis,” Geophys., vol. 39, pp. 69-72, Feb. 1974.
6. G. F. Ansley, “An algorithm for the exact likelihood of a mixed autoregressive moving-average process,” Biometrika, vol. 66, no. 1, pp. 59-65, APR. 1979.
7. A. A. Beex AND L. L. Scharf, “Covariance sequence approximation for parametric spectrum modeling,” IEEE Trans. Acoust, Speech, Signal Processing, vol. ASSP-29, no. 5, pp. 1042-1052, OCT. 1981.
8. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra. New York: Dover 1959.
9. G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control (Revised ed.). San Francisco, CA: Holden Day, 1976.
10. T. P. Bronez and I. A. Cadzow, “An algebraic approach to superresolution array processing,” in 1981 ICASSP Proc., pp. 302-305 (Atlanta, GA, 1981) and accepted for publication in the IEEE Trans. Aerosp. Electron. Syst.
11. S. Bruzzone and M. Kaveh, “On some suboptimum arma spectral estimators,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-28, pp. 753-754, Dec. 1980.
12. K. J. Bry and J. Leroux, “Comparison of some algorithms for identifying autoregressive signals in the presence of observation noise,” in 1982 ICASSP (Paris, France), pp. 224-227, MAY 1982.
13. J. P. Burg, “Maximum entropy spectral analysis,” IN Proc. 37th Meet. Society of Exploration Geophysicists (Oklahoma City, OK, Oct. 31, 1967).
14. J. P. Burg, “Maximum entropy spectral analysis,” Ph.D. Dissertation, Dep. Geophysics, Stanford Univ., Stanford, CA, May 1975.
15. J. A. Cadzow, “Arma spectral estimation: an efficient closed form procedure,” in Proc. RA DC Spectrum Estimation Workshop, pp. 81-97, Oct. 1979.
16. J. A. Cadzow, “High performance spectral estimation—A new arma method,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-28, pp. 524-529, Oct. 1980.
17. J. A. Cadzow, “Autoregressive-moving average spectral estimation: A model equation error procedure,” IEEE Trans. Geosci Remote Sensing, vol. GE-19, pp. 24-28, Jan. 1981.
18. J. A. Cadzow AND K. Ogino, “Two-dimensional spectral estimation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, no. 3, pp. 396-401, June 1981.
19. J. A. Cadzow and R. L. Moses, “An adaptive ARMA Spectral Estimator, parts 1 and 2,” presented at the First ASSP Workshop on Spectral estimation, McMaster Univ., Hamilton, Ont., Canada, Aug. 1981.
20. J. A. Cadzow, “ARMA modeling of time series,” IEEE Trans. Patt. Analys. Mach. Intel (Special Issue on Digital Signal and Waveform Analysis), vol. PAMI-4, no. 2, pp. 124-128, Mar. 1982.
21. J. A. Cadzow, “Rational time series modeling: An effective method,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-18, Aug. 1982.
22. J. A. Cadzow and B. Baseghi, “Data adaptive ARMA modeling of time series,” in 1982 ICASSP (Paris, France), pp. 256-261, MAY 1982.
23. D. G. Childers, ed., Modern Spectral Analysis. New York: IEEE Press, 1978.
24. J. Durbin, “The fitting of time series models,” Rev. Inst Int. de Stat., vol 28, pp. 233-244, 1960.
25. B. Friedlander, M. Morf, T. Kailath, and L. Ljung, “New inversion formulas for matrices classified in terms of their distance from toeplitz matrices,” Linear Algebra Appl., vol. 27, pp. 31-60, 1979.
26. W. Gersh, “Estimation of the autoregressive parameters of mixed autoregressive moving-average time series,” IEEE Trans. Automat. Contr., vol. AC-15, pp. 583-588, Oct. 1970.
27. G. Golub and W. Kahan, “Calculating the singular values and pseudo-inverse of a matrix,” J. SIAM Numer. Anal (Ser. B), vol. 2, no. 2, pp. 205-224, 1965.
28. D. Graupe, D. J. Krause, and J. B. Moore, “Identification of autoregressive moving-average parameters of time series,” IEEE Trans. Automat. Contr., vol. AC-20, pp. 104-107, Feb. 1975.
29. N. K. Gupta and R. K. Mehra, “Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations,” IEEE Trans. Automat. Contr., vol. AC-19, no. 6, pp. 774-783, Dec. 1974.
30. P. R. Gutowski, E. A. Robinson, and S. Treitel, “Sepctral estimation: Fact or fiction?,” IEEE Trans. Geosci. Remote Sensing, vol. GE-16, pp. 80-84, APR. 1978.
31. S. S. Hay Kin, ed., Nonlinear Methods of Spectral Analysis. New York: Springer, 1979.
32. T. L. Henderson, “Geometric methods for determining system poles from transient response,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, no. 5, pp. 982-988, Oct. 1981.
33. G. M. Jenkins and D. G. Watts, Spectral Analysis and its Applications. San Francisco, CA: Holden-Day, 1968.
34. R. L. Kashyap, “Inconsistency of the aic rule for estimating the order of autoregressive models,” IEEE Trans. Automat. Contr., vol. AC-25, pp. 996-998, Oct. 1980.
35. M. Kaveh, “High resolution spectral estimation for noisy signals,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, pp. 286-287, June 1979.
36. S. M. Kay, “A new arma spectral estimator,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-28, pp. 585588, Oct. 1980.
37. S. M. Kay and S. L. Mar Pie, Jr., “Spectrum analysis-a modern perspective,” Proc. IEEE, vol. 69, pp. 1380-1419, Nov. 1981.
38. J. F. Kinkel, J. Perl, L. Scharf, and A. Stubberub, “A note on covariance-invariant digital filter design and autoregressive-moving average spectral estimation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, pp. 200-202, Apr. 1979.
39. V. C. Klema and A. J. Laub, “The singular value decomposition: Its computation and some applications,” IEEE Trans. Automat. Contr., vol. AC-25, pp. 164-176, Apr. 1980.
40. I. S. Konralinka and M. R. Matausek, “Simultaneous estimation of poles and zeroes in speech analysis and itif iterative inverse filtering algorithm,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, no. 5, pp. 485-492, Oct. 1979.
41. L. M. Koopmans, The Spectral Analysis of Time Series. New York: Academic Press, 1974.
42. R. Kumaresan and D. W. Tufts, “Singular value decomposition and spectral analysis,” presented at the First ASSP Workshop on spectral Estimation, McMasters Univ., Hamilton, Ont., Canada, Aug. 1981.
43. N. Levinson, “The wiener (Root Mean Square) Error criterion in filter design and prediction,” J. Math. Phys., vol. 25, pp. 261278, 1947.
44. J. Makhoul, “Stable and efficient lattice methods for linear prediction,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, pp. 423-428, Oct. 1977.
45. R. K. Mehra, “On-line identification of linear dynamic systems with applications to kalman filtering,” IEEE Trans. Automat. Contr., vol. AC-16,NO. L,pp. 12-22, Feb. 1971.
46. M. Morf, T. Kailath, and L. Ljung, “Fast algorithms for recursive identification,” IN Proc. 1976 IEEE Conf. Decision and Control (Clearwater, FL), pp. 916-921, Dec. 1976.
47. M. Morf, B. Dickinson, T. Kailath, AND A. Vieira, “Efficient solutions of covariance equations for linear prediction,” IEEE Trans Acoust., Speech, Signal Processing, vol. ASSP-25, pp. 429-433, Oct. 1979.
48. P. Newbold, “The exact likelihood function of a mixed autoregressive moving-average process,” Biometrika, vol. 61, no. 3, pp. 423-426, Dec. 1974.
49. K. Ogino, “Computationally fast algorithms for ARMA spectral estimation,” Ph.D. dissertation, Viriginia Polytech. Inst., Blacksburg, VA, 1981.
50. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
51. Y. Pao and D. T. Lee, “Performance characteristics of the cadzow modified direct arma method for spectrum estimation,” presented at the First IEEE-ASSP Workshop on Spectral Estimation, McMaster Univ., Hamilton, Ontario, Canada, Aug. 1981.
52. E. Parzen, “Mathematical considerations in the stimation of spectra,” Technometrics, vol. 3, pp. 167-190, May 1961.
53. E. Parzen, “Statistical spectral analysis (Single Channel Case) in 1968,” Dept. Statistics, Stanford Univ., Stanford, CA, Tech. Rep. 11, June 1968.
54. E. Parzen, “Some recent advances in time series modeling,” IEEE Trans. Automat. Contr., vol. AC-19, pp. 723-730, Dec. 1974.
55. V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys J. Royal Astron. Soc, pp. 347-366, 1973.
56. R. Prony, “Essai experiméntale et analytique,” Paris J. l' Ecole Poly technique, vol. 1, pp. 24-76, 1795.
57. L. R. Rabiner and B. Gold, Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
58. A. Schuster, “On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena,” Terrestrial Magnetism, vol. 3, pp. 13-41, Mar. 1898.
59. J. L. Shanks, “Recursion filters for digital processing,” Geophys., vol. 32, pp. 33-51, Feb. 1967.
60. S. A. Tretter and K. Steiglitz, “Power spectrum identifications in terms of rational models,” IEEE Trans. Automat. Contr., vol. AC-12, pp. 185-188, Apr. 1967.
61. O. W. Tufts and R. Kumaresan, “Estimation of frequencies of multiple sinusoids: making linear prediction perform like maximum likelihood,” this issue, pp. 975-989.
62. T. J. Ulrych and R. W. Clayton, “Time series modelling and maximum entropy,” Phys. Earth Planetary Interiors, vol. 12, pp. 188-200, Aug. 1976.
63. G. Walker, “On periodicity in series of related terms,” Proc. Roy. Soc. London, Ser. A., vol. 131, pp. 518-532, 1931.
64. P. D. Welch, “The use of fast fourier transform for the estimation of power spectra,” IEEE Trans. Audio Electroacoust, vol. AU-15, pp. 70-73, June 1970.
65. B. Widrow et al., “Adaptive noise cancelling: principles and applications,” Proc IEEE, vol. 63, pp. 1694-1716, Dec. 1975.
66. G. U. Yule, “On a method of investigating periodicities in disturbed series with special reference to wolfer's sunspot numbers,” Philosoph. Trans. Roy. Soc. London, Ser. A., vol. 226, pp. 276298, July 1927.