Trispectral analysis of stationary random time series

Journal of the Acoustical Society of America

Volumn 97, Issue 5, 1995, Pages 2963-2978

  Molle, John W Dalle ^a   Hinich, Melvin J ^b  

^a INSTITUTO TECNOLÓGICO AUTÓNOMO DE MÉXICO   (Mexico)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; ARTICLE; ECHOLOCATION; FOURIER ANALYSIS; MULTIVARIATE ANALYSIS; NOISE; PRIORITY JOURNAL; SEA;

SPECTRAL ANALYSIS; TIME SERIES; TRISPECTRUM;

EID: 0029041165     PISSN: 00014966     EISSN: NA     Source Type: Journal    
DOI: 10.1121/1.411860     Document Type: Article

References (59)

1. Abraham, R., Marsden, J.E., and Ratiu, T. (1983). Manifolds, Tensor Analysis, and Applications (Addison-Wesley, Reading, MA).
2. Bartlett, M.S. (1950). “Periodogram analysis and continuous spectra,” Bi-ometrika 37, 1–16.
3. Blanc-Lapierre, A. and Fortet, R. (1968). Theory of Random Functions (Gordon and Breach, New York), Vol. 2.
4. Brillinger, D.R. (1965). “An introduction to polyspectra,” Ann. Math. Stat. 36, 1351–1374.
5. Brillinger, D.R. (1975). Time Series, Data Analysis, and Theory (Holt, Rinehart, and Winston, New York).
6. Brillinger, D.R., and Rosenblatt, M. (1967a). “Asymptotic theory of K-th order spectra,” in Spectral Analysis of Time Series, edited by B. Harris (Wiley, New York), pp. 153–158.
7. Brillinger, D.R., and Rosenblatt, M. (1967b). “Computation and interpretation of K-th order spectra,” in Spectral Analysis of Time Series, edited by B. Harris (Wiley, New York), pp. 189–232.
8. Chandran, V., and Elgar, S. (1994). “A general procedure for the derivation of principal domains of higher-order spectra,” IEEE Trans. Acoust. Speech Signal Process. 42, 229–233.
9. Dalle Molle, J.W. (1992). “Higher-order spectral analysis and the trispectrum,” Ph.D. dissertation, The University of Texas at Austin, Austin, Texas.
10. Dalle Molle, J.W. (1993). “The N-th order cumulant spectral principal domain, stationary set, and transient set,” in Proceedings of 1993 SPIE Conference on Advanced Signal Processing Algorithms, Architectures, and Implementation, San Diego, California (SPIE).
11. Dalle Molle, J.W., and Hinich, M.J. (1989). “The trispectrum,” in Proceedings of the Workshop on Higher-Order Spectral Analysis, edited by J.M. Mendel and C.L. Nikias, Vail, Colorado (Univ. of Virginia, Charlottsville), pp. 68–71.
12. Dalle Molle, J.W., and Hinich, M.J. (1991). “Cumulant spectra-based tests for the detection of a coherent signal in noise,” in Proceedings of the International Signal Processing Workshop on Higher-Order Statistics, edited by J.-L. Lacoume, M.A. Lagunas, and C.L. Nikias, Chamrousse, France (Elsevier North Holland, Amsterdam), pp. 151–154.
13. Dalle Molle, J.W., Hinich, M.J., and Morrice, D.J. (1992). “Higher-order cumulant spectral-based statistical tests of pseudo-random variate generators,” in 1992 Proceeding of the Winter Simulation Conference, edited by J.J. Swain, D. Goldsman, and J.R. Wilson (unpublished).
14. David, H.A. (1970). Order Statistics (Wiley, New York).
15. Dwyer, R.F. (1984). “Use of kurtosis in the frequency domain as an aid in detecting random signals,” IEEE J. Ocean Eng. OE-9, 85–92.
16. Dwyer, R.F. (1985). “Asymptotic detection of performance of discrete power and higher-order spectra estimates,” IEEE J. Ocean Eng. OE-10, 303–315.
17. Fisher, R.A. (1929). “Moments and product moments of sampling distributions,” Proc. London Math. Soc. Ser. 30, 199–238.
18. Fisher, R.A., and Wishart, J. (1931). “The derivation of the pattern formulae of two-way partitions from those of simpler patterns,” Proc. London Math. Soc. Ser. 2 33, 195–208.
19. Hald, A. (1981). “T.N. Thiele's contributions to statistics,” Int. Stat. Rev. 49, 1–20.
20. Hinich, M.J. (1982). “Testing for Gaussianity and linearity of a stationary time series,” J. Time Series Anal. 3, 169–176.
21. Hinich, M.J. (1990). “Detecting a transient signal by bispectral analysis,” IEEE Trans. Acoust. Speech Signal Process. 38, 1277–1283.
22. Hinich, M.J. (1994). “Higher-order cumulants and cumulant spectra,” Circuits Syst. Signals Process. 13(4), 391–402.
23. Hinich, M.J., and Clay, C. (1968). “The application of the discrete Fourier transform in the estimation of power spectra, coherence, and bispectra of geophysical data,” Rev. Geophys. 6, 347–363.
24. Hinich, M.J., and Wolinsky, M.A. (1988). “A test for aliasing using bispectral analysis,” J. Am. Stat. Assoc. 83, 499–502.
25. Keenan, D.M. (1987). “Limiting behavior of functionals of higher-order cumulant spectra,” Ann. Stat. 15, 134–151.
26. Kendall, M.G., Stuart, A., and Ord, J.K. (1987). Kendall's Advanced Theory of Statistics: Volume 1 (Griffin, London).
27. Kim, P.T. (1989). “Estimation of product moments of a stationary stochastic process with application to estimation of cumulants and cumulant spectral densities,” Can. J. Stat. 17, 285–299.
28. Kim, P.T. (1991). “Consistent estimation of the fourth-order cumulant spectral density,” J. Time Series Anal. 12, 63–71.
29. Kolmogorov, A.N. (1960). “On the of Fortet and Blanc-Lapierre,” Theory Probab. Its Appl. 5, 341/337.
30. Leonov, V.P. (1960). “The use of the characteristic functional and semi-invariants in the ergodic theory of stationary processes,” J. Sov. Math. 1, 878–881.
31. Leonov, V.P., and Shiryaev, A.N. (1959). “On a method of calculation of semi-invariants,” Theory Probab. Its Appl. 4, 319–329.
32. Leonov, V.P., and Shiryaev, A.N. (1960). “Some problems in the spectral theory of higher-order moments: II,” Theory Probab. Its Appl. 5, 417-421.
33. Lii, K.S., and Rosenblatt, M. (1985). “A fourth-order deconvolution technique for non-Gaussian linear processes,” in Multivariate Analysis VI, edited by P.R. Krishnaiah (Elsevier, Amsterdam), pp. 395–410.
34. Marks, R.J. (editor) (1993). Advanced Topics in Shannon Sampling and Interpolation Theory (Springer-Verlag, New York).
35. McCullagh, R (1987). Tensor Methods in Statistics (Chapman and Hall, London).
36. Mendel, J.M. (1991). “Tutorial on higher-order statistics (spectra) in signal processing and systems theory: Theoretical results and some applications,” Proc. IEEE 79, 278–305.
37. Nikias, Ci L., and Petropulu, A.P. (1993). Higher-Order Spectral Analysis: A Nonlinear Signal Processing Framework (Prentice-Hall, Englewood Cliffs, NJ).
38. Persson, L., and Sangfelt, E. (1992). “Detection of hydroacoustic transients by means of higher-order statistics,” Signal Processing VI: Theories and Applications, edited by J. Vandewalle, R. Boite, M. Moonen, and A. Oost-erlinck (Elsevier, Amsterdam), Vol. Ill, pp. 1817–1820.
39. Picinbono, B. (1991). “Geometric concepts in higher-order statistics,” in Proceedings of the International Signal Processing Workshop on HigherOrder Statistics, edited by J.-L. Lacoume, M.A. Lagunas, and C.L. Nikias, Chamrousse, France (Elsevier North-Holland, Amsterdam), pp. 1-5. Plug, L.A., Ioup, G.E., Ioup, J.W., and Field, R.L. (1992a). “Properties of higher-order correlations and spectra, for bandlimited, deterministic transients” J. Acoust. Soc. Am. 91, 975–988.
40. Plug, L.A., loup, G.E., Ioup, J.W., Barnes, K.H., Field, R.L., and Rayborn, G.H. (1992b). “Detection of oscillatory and impulsive transients using higher-order correlations and spectra,” J. Acoust. Soc. Am. 91, 2763–2776.
41. Priestley, M.B. (1981). Spectral Analysis and Time Series (Academic, New York), Vols. 1 and 2.
42. Priestley, M.B. (1988). Non-Linear and Non-Stationary Time Series Analysis (Academic, New York).
43. Rosenblatt, M. (1983). “Cumulants and cumulant spectra,” Handbook of Statistics, edited by D.R. Brillinger and P.R. Krishnaiah (Elsevier, Amsterdam), Vol. 3, pp. 369–382.
44. Rosenblatt, M. (1985). Stationary Sequences and Random Fields (Birkhauser, Boston).
45. Shaman, P. (1966). “Large-sample approximation to the first- and second-order moments of bispectral estimates,” Technical Report, School of Engineering, New York University, New York, New York.
46. Shiryaev, A.N. (1960a). “Some problems in the spectral theory of higherorder moments: I,” Theory Probab. Its Appl. 5, 265–284.
47. Shiryaev, A.N. (1960b). “On conditions for ergodicity of stationary processes in terms of higher-order moments,” Theory Probab. Its Appl. 8, 436–439.
48. Shiryaev, A.N. (1984). Probability (Springer-Verlag, New York).
49. Sinai, Ya. G. (1960). “On higher-order spectral measures of ergodic stationary processes,” Theory Probab. Its Appl. 8, 429–436.
50. Solinsky, J.C. (1991). “Trispectrum utilization in higher order statistical applications,” in Proceedings of the International Signal Processing Workshop on Higher-Order Statistics, edited by J.-L. Lacoume, M.A. Lagunas, and C.L. Nikias, Chamrousse, France (Elsevier North-Holland, Amsterdam), pp. 317–320.
51. Speed, T.P. (1986). “Applications of cumulants and their generalizations,” in Pacific Statistical Congress, edited by B.F.J. Manly and F.C. Lam (Elsevier, Amsterdam), pp. 12–19.
52. Subba Rao, T., and Gabr, M. (1980). “A test for linearity of stationary time series,” J. Time Series Anal. 1, 145–158.
53. Subba Rao, T., and Gabr, M. (1984). An Introduction to Bispectral Analysis and Bilinear Time Series Models, Springer Lecture Notes in Statistics No. 24 (Springer-Verlag, New York).
54. Taniguchi, M. (1982). “On estimation of the integrals of the fourth order cumulant spectral density,” Biometrika 69, 117–122.
55. Tong, H. (1990). Nonlinear Time Series: A Dynamical System Approach (Clarendon, Oxford, England).
56. Tukey, J.W. (1984). “The spectral representation and transformation properties of the higher moments of stationary time series,” in The Collected Works of John W. Tukey, edited by D.R. Brillinger (Wadsworth, Monterey, CA), Vol. 1, Chap. 4.
57. Walden,; A.T., and Williams, M.L. (1993). “Deconvolution, bandwidth, and the trispectrum,” J. Am. Stat. Assoc. 88, 1323–1329.
58. Williams, M.L., and Dainty, J.C. (1991). “The use of the bispectrum in analyzing one dimensional signal,” in Digital Signal Processing-91, edited by V. Cappellini and A.G. Constantinides (Elsevier, Amsterdam), pp. 45–49.
59. Zurbenko, I.G. (1986). The Spectral Analysis of Time Series (North-Holland, Amsterdam), pp. 279–310.