Linear time-variant transformations of generalized almost-cyclostationary signals - Part I: Theory and method

IEEE Transactions on Signal Processing

Volumn 50, Issue 12, 2002, Pages 2947-2961

  Izzo, Luciano ^a   Napolitano, Antonio ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Generalized almost cyclostationary signals; Linear time variant systems; Nonstochastic approach

Indexed keywords

COMMUNICATION CHANNELS (INFORMATION THEORY); PROBABILITY; RANDOM PROCESSES; STATISTICAL METHODS;

LINEAR TIME VARIANT SYSTEMS;

SIGNAL PROCESSING;

EID: 0036901844     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2002.805499     Document Type: Article

References (42)

1. P.A. Bello, "Characterization of randomly time-variant channels," IEEE Trans. Commun. Syst., vol. CS-11, pp. 360-393, Dec. 1963.
2. W.A. Brown, "On the theory of cyclostationary signals," Ph.D. dissertation, Univ. California, Dept. Elect. Eng. Comput. Sci., Davis, CA, 1987.
3. Y. Choquet-Bruhat and C. DeWitt-Morette, Analysis, Manifolds and Physics. Amsterdam, The Netherlands: North-Holland, 1982.
4. T.A.C.M. Claasen and W.F.G. Mecklenbräuker, "On stationary linear time-varying systems," IEEE Trans. Circuits Syst., vol. CAS-29, pp. 169-184, Mar. 1982.
5. A.V. Dandawaté and G.B. Giannakis, "Asymptotic theory of mixed time-averages and kth-order cyclic moment and cumulant statistics," IEEE Trans. Inform. Theory, vol. 41, pp. 216-232, Jan. 1995.
6. D. Dehay and H.L. Hurd, "Representation and estimation for periodically and almost periodically correlated random processes," in Cyclostationarity in Communications and Signal Processing, W.A. Gardner, Ed. New York: IEEE Press, 1994, pp. 295-326.
7. A. Duverdier, B. Lacaze, and D. Roviras, "Introduction of linear cyclostationary filters to model time-variant channels," in Proc. Global Telecommun. Conf., 1999.
8. P.A. Franaszek, "On linear systems which preserve wide sense stationarity," SIAM J. Appl. Math., vol. 15, pp. 1481-1484, Nov. 1967.
9. P.A. Franaszek and B. Liu, "On a class of linear time-varying filters," IEEE Trans. Inform. Theory, vol. IT-13, pp. 477-481, July 1967.
10. L.E. Franks, Signal Theory. Englewood Cliffs, NJ: Prentice-Hall, 1969.
11. H. Furstenberg, Stationary Processes and Prediction Theory. Princeton, NJ: Princeton University Press, 1960.
12. W.A. Gardner, Introduction to Random Processes with Applications to Signals and Systems. New York: Macmillan, 1985.
13. _, Statistical Spectral Analysis: A Nonprobabilistic Theory. Englewood Cliffs, NJ: Prentice-Hall, 1987.
14. _, "An introduction to cyclostationary signals," in Cyclostationarity in Communications and Signal Processing, W.A. Gardner, Ed. New York: IEEE Press, 1994, pp. 1-90.
15. W.A. Gardner and W.A. Brown, "Fraction-of-time probability for time-series that exhibit cyclostationarity," Signal Process., vol. 23, pp. 273-292, June 1991.
16. W.A. Gardner and C.M. Spooner, "The cumulant theory of cyclostationary time-series, Part I: Foundation," IEEE Trans. Signal Processing, vol. 42, pp. 3387-3408, Dec. 1994.
17. E.M. Hofstetter, "Random processes," in The Mathematics of Physics and Chemistry, H. Margenau and G.M. Murphy, Eds. Princeton, NJ: Van Nostrand, 1964, vol. II, ch. 3.
18. H.L. Hurd, "Correlation theory of almost periodically correlated processes," J. Multivariate Anal, vol. 37, pp. 24-45, Apr. 1991.
19. H.L. Hurd and T. Koski, "On the Wold isomorfism and Wold decomposition for prediction of cyclostationary sequences," in Proc. Workshop Cyclostationary Process., Noisy Le Grand, France, July 1996.
20. H.L. Hurd and J. Leśkow, "Strongly consistent and asymptotically normal estimation for the covariance of almost periodically correlated processes," Statist. Dec., vol. 10, pp. 201-225, 1992.
21. L. Izzo and A. Napolitano, "Effects of nonrandom linear time-variant systems on higher order cyclostationarity," in Proc. Fifteenth GRETSI Symp. Signal Image Process., Juan-les-Pins, France, Sept. 1995.
22. _, "Characterization of higher order almost-periodically correlated time-series," in Proc. Workshop Cyclostationary Process., Noisy Le Grand, France, July 1996.
23. _, "Multirate processing of time series exhibiting higher order cyclostationarity," IEEE Trans. Signal Processing, vol. 46, pp. 429-439, Feb. 1998.
24. _, "The higher order theory of generalized almost-cyclostationary time-series," IEEE Trans. Signal Processing, vol. 46, pp. 2975-2989, Nov. 1998.
25. _, "Higher order characterization of linear time-variant systems operating on generalized almost-cyclostationary signals," Proc. IEEE Signal Process. Workshop Higher Order Statist., June 1999.
26. _, "Linear time-variant transformations of generalized almost-cyclostationary signals, Part II: Development and applications," IEEE Trans. Signal Processing, vol. 50, pp. 2962-2975, Dec. 2002.
27. J.L. Lacoume, P.O. Amblard, and P. Comon, Statistiques D'orde Supérieur Pour le Traitement du Signal. Paris: Masson, 1997.
28. H. Li aad Q. Cheng, "Almost sure convergence analysis of mixed time averages and Kth-order cyclic statistics," IEEE Trans. Inform. Theory, vol. 43, pp. 1265-1268, July 1997.
29. B. Liu and P.A. Franaszek, "A class of time-varying digital filters," IEEE Trans. Circuit Theory, vol. CT-16, pp. 467-471, Nov. 1969.
30. D. Middleton, "A statistical theory of reverberation and similar first-order scattered fields, Part I: Waveforms and general process," IEEE Trans. Inform. Theory, vol. IT-13, pp. 372-392, July 1967.
31. _, "A statistical theory of reverberation and similar first-order scattered fields, Part II: Moments, spectra, and special distributions," IEEE Trans. Inform. Theory, vol. IT-13, pp. 393-414, July 1967.
32. A. Napolitano, "Cyclic higher order statistics: Input/output relations for discrete- and continuous-time MIMO linear almost-periodically time-variant systems," Signal Process., vol. 42, pp. 147-166, Mar. 1995.
33. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. New York: McGraw-Hill, 1991.
34. E. Pfaffelhuber, "Generalized harmonic analysis for distributions," IEEE Trans. Inform. Theory, vol. IT-21, pp. 605-611, Nov. 1975.
35. J.G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill, 1995.
36. W.A. Sethares and T.W. Staley, "Periodicity transforms," IEEE Trans. Signal Processing, vol. 47, pp. 2953-2964, Nov. 1999.
37. C.M. Spooner and W.A. Gardner, "The cumulant theory of cyclostationary time-series, Part II: Development and applications," IEEE Trans. Signal Processing, vol. 42, pp. 3409-3429, Dec. 1994.
38. Y.H. Tsao, "Time-variant filtering for nonstationary random processes," J. Acoust. Soc. Amer., vol. 76, pp. 1098-1113, Oct. 1984.
39. K. Urbanik, "Effective processes in the sense of H. Steinhaus," Stadia Mathematica, 1958.
40. N. Wiener, "Generalized harmonic analysis," Acta Mathematica, vol. 55, pp. 117-258, 1930.
41. H.O.A. Wold, "On prediction in stationary time series," Ann. Math. Statist., vol. 19, pp. 558-567, 1948.
42. A.H. Zemanian, Distribution Theory and Transform Analysis. New York: Dover, 1987.