Multidimensional Spectral Estimation

Proceedings of the IEEE

Volumn 70, Issue 9, 1982, Pages 1029-1039

  McClellan, James H ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TRANSFORMATIONS -FAST FOURIER TRANSFORMS; MAXIMUM ENTROPY METHOD; MAXIMUM LIKELIHOOD METHOD; MULTIDIMENSIONAL SPECTRUM ESTIMATION;

SPECTRUM ANALYSIS - THEORY;

EID: 0020189062     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1982.12431     Document Type: Article

References (62)

1. A. B. Baggeroer, “Recent signal processing advances in spectral and frequency wavenumber function estimation and their application to offshore structures,” in 2nd Int. Conf. on Behaviour of Off-Shore Structures (Imperial College, London, England, Aug. 1979), pp. 457-476.
2. A. B. Baggeroer, “Estimation errors in the measurement of cross spectral matrices for array processing,” in Workshop Italy-USA on Digital Processing (Portovenere-La Spezia, Italy, Aug. 1981), pp. 45-61.
3. A. B. Baggeroer and R. Falconer, “Array refraction profiles and crustal models,” J. Geophys. Res. (accepted for publication).
4. T. Barnard and J. P. Burg, “Analytical studies of techniques for the computation of high-resolution wavenumber spectra,” Advanced Array Res. Rep. 9, Texas Instruments, Inc., May 1969.
5. M. S. Bartlett, An Introduction to Stochastic Processes with Special Reference to Methods and Applications. New York: Cambridge Univ. Press, 1953.
6. J. P. Burg, “Maximum entropy spectral analysis,” presented at the 37th Int. Meet., Soc. Explor. Geophys., Oklahoma City, OK, Oct. 1968.
7. J. P. Burg, “Maximum entropy spectral analysis,” Ph.D. dissertation, Stanford University, Stanford, CA, May 1975.
8. J. A. Cadzow and K. Ogino, “Two-dimensional spectral estimation,” IEEE Trans. Acoust., Speech Signal Proc., vol. ASSP-29, pp. 396-401, June 1981.
9. A. Calderon and R. Pepinsky, “On the phases of Fourier coefficients for positive real functions,” in Computing Methods and the Phase Problem in X-Ray Crystal Analysis (The X-Ray Crystal Analysis Laboratory, Dep. Physics, Pennsylvania State College, 1952), pp. 339-348.
10. J. Capon, “High resolution frequency-wavenumber spectrum analysis,” Proc. IEEE, vol. 57, pp. 1408-1418, Aug. 1969.
11. B. W. Dickinson, “Two-dimensional Markov spectrum estimates need not exist,” IEEE Trans. Inform. Theory, vol. IT-26, pp. 120-121, Jan. 1980.
12. G. L. Duckworth, “Adaptive array processing for high-resolution acoustic imaging,” S. M. thesis, M.I.T., Cambridge, MA, Sept. 1979.
13. D. E. Dudgeon, “Fundamentals of digital array processing,” Proc. IEEE, vol. 65, pp. 898-904, June 1977.
14. D. J. Edelblute, J. M. Fisk, and G. L. Kinnison, “Criteria for optimum signal-detection theory for arrays,” J. Acoust. Soc. Amer.,vol. 41, pp. 199-205, 1965.
15. O. L. Frost and T. M. Sullivan, “High resolution two-dimensional spectral analysis,” in Proc. ICASSP 79 (Washington, DC, Apr. 1979), pp. 673-676.
16. O. L. Frost, “High-resolution 2-D spectral analysis at low SNR,” in Proc. ICASSP 80 (Denver, CO, Apr. 1980), pp. 580-583.
17. R. W. Gerchberg, “Super resolution through error energy reduction,” Optica Acta, vol. 21, pp. 709-720, 1974.
18. O. S. Halpeny and D. G. Childers, “Composite wavefront decomposition via multidimensional digital filtering of array data,” IEEE Trans. Circuits Syst., vol. CAS-22, pp. 552-563, June 1975.
19. R. A. Haubrich, “Array design,” Bull. Seismological Soc. America, pp. 977-991, June 1968.
20. T. S. Huang, “Two-dimensional windows,” IEEE Trans. Audio Electroacoust., vol. AU-20, pp. 88-90, Mar. 1972.
21. L. B. Jackson and H. C. Chien, “Frequency and bearing estimation by two-dimensional linear prediction,” in Proc. ICASSP 79 (Washington, DC, Apr. 1979), pp. 665-668.
22. P. L. Jackson, L. S. Joyce, and G. B. Feldkamp, “Application of maximum entropy frequency analysis to synthetic aperture radar,” in Proc. RADC Spectrum Estimation Workshop (Rome, NY, May 1978), pp. 217-225.
23. A. K. Jain and S. Raganath, “Two-dimensional spectral estimation,” in Proc. RADC Spectrum Estimation Workshop (Rome, NY, May 1978), pp. 151-157.
24. A. K. Jain, “Spectral estimation and signal extrapolation in one and two dimensions,” in Proc. RADC Spectrum Estimation Workshop (Rome, NY, Oct. 1979), pp. 195-214.
25. A. K. Jain and S. Raganath, “High resolution spectrum estimation in two dimensions,” in Proc. 1st ASSP Workshop on Spectral Estimation (Hamilton, Ont., Canada, Aug. 1981), pp. 3. 4.1-3.4.5.
26. A. K. Jain and S. Raganath, “Extrapolation algorithms for discrete signals with application in spectral estimation,” IEEE Trans. Acoust., Speech Signal Proc., vol. ASSP-29, pp. 830-845, Aug. 1981.
27. L. S. Joyce, “A separable 2-D autoregressive spectral estimation algorithm,” in Proc. ICASSP 79 (Washington, DC, Apr. 1979), pp. 677-680.
28. J. H. Justice, “A Levinson-type algorithm for two-dimensional Wiener filtering using bivariate Szegö polynomials,” Proc. IEEE, vol. 65, pp. 882-886, June 1977.
29. R. Kumaresan and D. W. Tufts, “A two-dimensional technique for frequency-wavenumber estimation,” Proc. IEEE, vol. 69, pp. 1515-1517, Nov. 1981.
30. S. W. Lang, “Spectral estimation for sensor arrays,” Ph.D. dissertation, M.I.T., Cambridge, MA., Aug. 1981.
31. S. W. Lang and J. H. McClellan, “Spectral estimation for sensor arrays,” in Proc. 1st ASSP Workshop on Spectral Estimation (Hamilton, Ont., Canada, Aug. 1981), pp. 3. 2.1-3.2.7.
32. S. W. Lang and J. H. McClellan, “MEM spectral estimation for sensor arrays,” in Proc. Int. Conf. on Digital Signal Processing (Florence, Italy, Sept. 1981), pp. 383-390.
33. S. W. Lang and J. H. McClellan, “The extension of Pisarenko's method to multiple dimen-sions,” in Proc. ICASSP 82 (Paris, France, May 1982), pp. 125-128.
34. S. W. Lang and J. H. McClellan, “Spectral estimation for sensor arrays,” IEEE Trans. Acoust., Speech, Signal Proc., (submitted for publication).
35. S. W. Lang and J. H. McClellan, “Multi-dimensional MEM spectral estimation,” IEEE Trans. Acoust., Speech, Signal Proc. (accepted for publication;.
36. J. S. Lim and N. A. Malik, “A new algorithm for two-dimensional maximum entropy power spectrum estimation,” IEEE Trans. Acoust., Speech, Signal Proc., vol. ASSP-29, pp. 401-413, June 1981.
37. D. G. Luenberger, Optimization by Vector Space Methods. New York: Wiley, 1969.
38. D. G. Luenberger, Introduction to Linear and Nonlinear Programming. Read-ing, MA: Addison-Wesley, 1973.
39. N. A. Malik, “One and two-dimensional maximum entropy spectral estimation,” Ph.D. dissertation, M.I.T., Cambridge, MA, Nov. 1981.
40. T. L. Marzetta, “A linear prediction approach to two-dimensional spectral factorization and spectral estimation,” Ph.D. dissertation, M.I.T., Cambridge, MA., Feb. 1978.
41. T. L. Marzetta, “Two-dimensional linear prediction: Autocorrelation arrays, minimum-phase prediction error filters, and reflection coefficient arrays,” IEEE Trans. Acoust., Speech, Signal Proc., vol. ASSP-28, pp. 725-733, Dec. 1980.
42. J. H. McClellan and S. W. Lang, “Multi-dimensional MEM spectral estimation,” presented at the Int. Conf. on Spectral Analysis and its Use in Underwater Acoustics, London, England, Apr. 1982.
43. W. I. Newman, “A new method of multi-dimensional power spectral analysis,” Astrm. Astrophys., vol. 54, pp. 369-380, 1977.
44. W. I. Newman, “Extension to the maximum entropy method II,” IEEE Trans. Inform. Theory, vol. IT-25, Nov. 1979.
45. W. I. Newman, “Extension to the maximum entropy method III,” in Proc. 1st ASSP Workshop on Spectral Estimation (Hamilton, Ont., Canada, Aug. 1981), pp. 1.7.1-1.7.6.
46. C. Ong, “An investigation of two new high-resolution two-dimensional spectral estimate techniques,” in Spec. Rep. 1, Long Period Array Processing Development, Texas Instruments, Inc., Apr. 1971.
47. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
48. A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst., vol. CAS-22, pp. 735-742, Sept. 1975.
49. I. V. Pendrell, “The maximum entropy principle in two-dimensional spectral analysis,” Ph.D. dissertation, York Univ., Toronto, Ont., Canada, Nov. 1979.
50. V. F. Pisarenko, “On the estimation of spectra by means of nonlinear functions of the covariance matrix,” Geophys. J. Roy. Astron. Soc, vol. 28, pp. 511-531, 1972.
51. V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys. J. Roy. Astron. Soc, vol. 33, pp. 347-366, 1973.
52. S. Roucos and D. G. Childers, “A two-dimensional maximum entropy spectral estimator,” in Proc. ICASSP 79 (Washington, DC, Apr. 1979), pp. 669-672.
53. W. Rudin, “The extension problem for positive-definite functions,” Ill. J. Math., vol. 7, pp. 532-539, 1963.
54. R. Schmidt, “Multiple emitter location and signal parameter estimation,” in Proc. RA DC Spectrum Estimation Workshop (Oct. 1979), pp. 243-258.
55. R. O. Schmidt, “A signal subspace approach to emitter location and spectral estimation,” Ph.D. dissertation, Stanford University, Stanford, CA, Aug. 1981.
56. C. W. Therrien, “Relations between 2-D and multichannel linear prediction,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 454-456, June 1981.
57. D. Tjostheim, “Autoregressive modeling and spectral analysis of array data in the plane,” IEEE Trans. Geosci. Remote Sensing, vol. GE-19, pp. 15-24, Jan. 1981.
58. P. D. Welch, “The use of FFT for the estimation of power spectra: A method based on time average over short, modified periodograms,” IEEE Trans. Audio Electroacoust., vol. AU-15, pp. 70-73, June 1967.
59. S. J. Wernecke and L. R. D'Addario, “Maximum entropy image reconstruction,” IEEE Trans. Comput., vol. C-26, pp. 351-364, Apr. 1977.
60. P. Whittle, “On stationary processes in the plane,” Biometrika,vol. 41, pp. 434-449, Dec. 1954.
61. J. W. Woods, “Two-dimensional discrete Markovian fields,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 232-240, Mar. 1972.
62. P. Whittle, “Two-dimensional Markov spectral estimation,” IEEE Trans. Inform. Theory, vol. IT-22, pp. 552-559, Sept. 1976.