Nonparametric Polyspectral Estimators for kth-Order (Almost) Cyclostationary Processes

IEEE Transactions on Information Theory

Volumn 40, Issue 1, 1994, Pages 67-84

  Dandawate, Amod V ^a   Giannakis, Georgios B ^a  

^a UNIVERSITY OF VIRGINIA   (United States)

Author keywords

asymptotic distribution and variance; cyclostationary sequences; higher order statistics; nonparametric cyclic polyspectrum estimation consistemcy; Nonstationary spectral analysis

Indexed keywords

COMPUTATIONAL METHODS; FREQUENCY DOMAIN ANALYSIS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; RANDOM PROCESSES; SIGNAL PROCESSING; SPECTRUM ANALYSIS; STATISTICS;

ASYMPTOTIC DISTRIBUTION AND VARIANCE; CYCLOSTATIONARY SEQUENCES; HIGHER ORDER STATISTICS; NONPARAMETRIC POLYSPECTRAL ESTIMATORS; SMOOTHED POLYPERIODOGRAMS;

INFORMATION THEORY;

EID: 0028313927     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.272456     Document Type: Article

References (43)

1. V. G. Alekseev, “Symmetry properties of higher-order spectral densities of stationary and periodic-nonstationary stochastic processes,” Problems of Information Transmission, p. 210, 1988.
2. J. C. Allen, “A survey of certain classes of non-stationary processes,” Rep. Code 732, Naval Ocean Syst. Center (NOSC), San Diego, CA, Dec. 1989.
3. W. R. Bennet, “Statistics of regenerative digital transmission,” Bell Syst. Techn. J., vol. 37, pp. 1501-1542, 1958.
4. A. S. Besicovitch, Almost periodic functions. Dover, 1954.
5. A. Blanc-Lapierre and R. Fortet, Theorie des Fonctions Aleatories, Paris, France: Masson, 1953.
6. D. R. Brillinger, Time Series: Data Analysis and Theory. San Francisco, Ca: Holden-Day, 1981.
7. _,”Some history of the study of higher-order moments and spectra,” Statistica Sinica, vol. 1, no. 2, pp. 465-476, July 1991.
8. D. R. Brillinger and M. Rosenblatt, “Asymptotic theory of estimates of kth-order spectra,” in: Spectral Analysis of Time Series, ed. B. Harris, New York: Wiley, 1967, pp. 153-188.
9. C. Corduneanu, Almost Periodic Functions. New York: Interscience (Wiley), 1968.
10. A. V. Dandawate, “Exploiting cyclostationarity and higher-order statistics in signal processes,” Ph.D. dissertation, Univ. Virginia, Char-lottesville, Va, Jan. 1993.
11. A. V. Dandawate and G. B. Giannakis, “Ergodicity and asymptotic normality for cumulant estimators of nonstationary signals,” Univ. Virginia, Rep. No. 192444B/EE91/125, June 1991; see also “Ergodic results for non-stationary processes: Cumulants, ambiguity functions and wavelets,” Proc. 25th Conf. on Informat. Sci. Syst., The Johns Hopkins Univ., Baltimore, Md, March 20-22, 1991, pp. 976-983.
12. “Polyspectral analysis of non-stationary signals: System Identification, classification, and ambiguity functions,” in Proc. Int. Workshop on Higher-Order Statistics, Chamrousse, France, July 1991, pp. 147-150.
13. “Nonparametric polyspectral estimators for almost periodically dependent nonstationary processes,” Univ. Virginia, Rep. UVA/192444B/EE91/126, Oct. 1991.
14. “Cyclic-cumulant based identification of almost periodically time-varying systems: Parametric methods,” in Proc. Int. Conf. Acoustics Speech Signal Process., vol. V, pp. 229-232, San Francisco, Ca, Mar. 23-26, 1992.
15. “Statistical tests for presence of cyclostationarity,” IEEE Trans. Signal Process., Jan., 1994 (accepted); see also Proc. Soc. Photo-Opt. Instr. Engr., Adv. Signal Process. Alg., Arch. Implem., San Diego, Ca, July 1992,m pp. 315-326.
16. “Nonparametric cyclic polyspectral analysis of AM signals and processes with missing observations, “ IEEE Trans. Inform. Theory, pp. 1864-1976, Nov. 1993.
17. A. V. Dandawate and G. B. Giannakis, “Asymptotic properties of generalized sample averages and consistent cyclic-moment and cumulant estimators,” Univ. Virginia, Rep. UVA/192444B/EE92/128b, May 1992.
18. W. A. Gardner, “Stationarizable random processes,” IEEE Trans. Informat. Theory, vol. IT-24, pp. 8-22, Jan. 1978.
19. Statistical Spectral Analysis: A Nonprobabilistic Theory. Englewood Cliffs, NJ: Prentice-Hall, 1988.
20. Introduction to Random Processes, 2nd ed. New York: McGraw-Hill, 1990, Chap. 12.
21. “Spectral characterization of Nth-order cyclostationarity,” Proc. IEEE ASSP Workshop on Spectrum Estimation, New York, 1990.
22. “Exploitation of spectral redundancy in cyclostationary signals,” in IEEE Signal Processing Magazine, pp. 14-36, Apr. 1991.
23. W. A. Gardner and L. E. Franks, “Characterization of cyclostationary random processes,” IEEE Trans. Informat. Theory, vol. 21, pp. 4-14, 1975.
24. W. A. Gardner and C. M. Spooner, “Higher-order cyclostationarity, cyclic cumulants and cyclic poly spectra,” presented at the Internat. Symp. Informat. Theory Appl., Hawaii, Nov. 1990.
25. G. B. Giannakis and A. V. Dandawate, “Polyspectral analysis of (almost) cyclostationary signals: LPTV system identification and related applications,” in Proc. 25th Asilomar Conf Signals, Sys. Comput., Pacific Grove, Ca, Nov. 4-6, 1991, pp. 377-382.
26. E. G. Gladyšev, “Periodically correlated random sequences,” Soviet Mathematics, vol. 2, pp. 385-388, 1961.
27. L. I. Gudzenko, “On periodically nonstationary processes,” Rad. Elektr., pp. 1062-1064, 1959.
28. H. L. Hurd, “Stationarizing properties of random shifts,” SIAM J. Appl. Math., vol. 26, no. 1, pp. 203-211, 1974.
29. “Nonparametric time series analysis of periodically correlated processes,” IEEE Trans. Informat. Theory, vol. 35, no. 2, pp. 350-359, Mar. 1989.
30. H. L. Hurd and N. L. Gerr, “Graphical methods for determining the presence of periodic correlation,” J. Time Series Analysis, vol. 12, no. 4, pp. 337-350, 1991.
31. H. L. Hurd and J. Leskow, “Strongly consistent and asymptotically normal estimation for the covariance for almost periodically correlated processes,” Tech. Rep. 308 and 330, Dep. Statistics, Univ. North Carolina, Chapel Hill, NC, Sept. 1990.
32. IEEE Trans. Automat. Contr., Special Issue on Higher-order Spectral Analysis, vol. 35, pp. 4-56, Jan. 1990; see also IEEE Trans. Acoustics Speech Signal Process., Special Section on Higher-order Spectral Analysis, vol. 38, pp. 1238-1317, July 1990.
33. R. H. Jones and W. M. Brelsford, “Time series with periodic structure,” Biometrika, vol. 54, no. 3, pp. 403-408, 1967.
34. J. Leskow, “Asymptotic normality of the spectral density estimators for almost periodically correlated stochastic processes,” Tech. Rep. 170, Dep. Statistics Appl. Probabil., Univ. Calif., Santa Barbara, Ca, Apr. 1991.
35. G. Longo and B. Picinbono, eds., Time and Frequency Representation of Signals. New York: Springer-Verlag, 1989.
36. V. Z. Marmarelis, “A single record estimator for correlation functions of nonstationary random processes,” in Proc. IEEE, pp. 841-842, July 1981; see also IEEE Trans. Informat. Theory, pp. 937-938, Nov. 1983.
37. M. B. Priestley, Nonlinear and Nonstationary Time Series Analysis. New York: Academic, 1988.
38. E. Parzen, “On spectral analysis with missing observations and amplitude modulation,” SANKHYA: The Indian J. Statistics: Series A, pp. 383-392, 1963.
39. Proceedings of Higher-Order Spectral Analysis Workshop, Vail, CO, 1989; see also Proc. Intl. Conf. Higher-Order Statistics, Chamrousse, France, July 1991.
40. M. Rosenblatt, Stationary Sequences and Random Fields. Birkhauser 1985.
41. C. M. Spooner and W. A. Gardner, “Estimation of cyclic polyspectra,” in Proc. 25th Annual Asilomar Conf. Signals, Syst. Comput., pp. 370-376, Nov. 4-6, 1991, Pacific Grove, Ca.
42. A. Swami, “Multiplicative noise models: Parameter estimation using-cumulants,” in Proc. 5th ASSP Workshop Spectral Estimation and Modeling, Rochester, NY, Oct. 1990, pp. 212-216.
43. A. V. Vecchia, “Periodic autoregressive-moving average (PARMA) modeling with applications to water resources,” Water Resources Bulletin, vol. 21, no. 5, pp. 721-730, Oct. 1985.