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Volume 21 Issue 5
Sep.  1999
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Li Hongwei, Yuan Baozong. STRONG CONVERGENCE PROBLEM FOR CUMULANT ESTIMATORS IN HARMONIC RETRIEVAL[J]. Journal of Electronics & Information Technology, 1999, 21(5): 592-599.
Citation: Li Hongwei, Yuan Baozong. STRONG CONVERGENCE PROBLEM FOR CUMULANT ESTIMATORS IN HARMONIC RETRIEVAL[J]. Journal of Electronics & Information Technology, 1999, 21(5): 592-599.

STRONG CONVERGENCE PROBLEM FOR CUMULANT ESTIMATORS IN HARMONIC RETRIEVAL

  • Received Date: 1997-08-01
  • Rev Recd Date: 1999-01-09
  • Publish Date: 1999-09-19
  • This paper considers the single record estimators for cumulants of sinusoids in additive noise. The strong convergence of sample autocorrelation is proved, and the convergence rate is obtained. Conditions for the fourth-order ergodicity are given. Under these conditions, the strong convergence of sample estimates of the fourth-order moment and cumulant is established, and the convergence rate is obtained. Finally, a numerical example is given to verify the results.
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  • Swami A, Mendel J M. Cumulant-based approach to the harmonic retrieval problem. Proc ICASSP-88. New York. USA: 1988. 2264-2267.[2]Mendel J M. Tutorial on higher-order statistics (spectra) in signal processing and system theory:[3]Theoretical results and some applications. Proc[J].IEEE.1991, 79(3):278-305[4]Ferrari A, Alengrin G. Estimation of the frequencies of a complex sinusoidal noisy signal using fourth order statistics. Proc. ICASSP-91, Toronto, Canada: 1991, 3457-3460.[5]Swami A, Mendel J M. Cumulant-based approach to the harmonic retrieval and related problems.[6]IEEE Trans. on ASSP, 1991, SP-39(5): 1099-1109.[7]梁应敞,王树勋,戴逸松.正弦参量的四阶累积量ESPRIT方法.电子学报,1994, 22(4): 6-12.[8]Papadopoulos C K, Nikias C L. Parameter estimation of exponentially damped sinusoids using higher order statistics. IEEE Trans. on ASSP, 1990, ASSP-38(8): 1424-1435.[9]Zhang X D, Li Y D. Harmonic retrieval in mixed Gaussian and non-Gaussian noises. IEEE Trans. on SP, 1994, SP-42(12): 3539-3543.[10]Zhang X D, Liang Y C. Prefiltering-based ESPRIT for estimating sinusoidal parameters in non-[11]Gaussian ARMA noise. IEEE Trans. on SP, 1995, SP-43(1): 349-353.[12]Zhang X D, Liang Y C, Li Y D. A hybrid approach to harmonic retrieval in non-Gaussian noise.[13]IEEE Trans. on IT, 1994, IT-40(4): 1220-1226.[14]Rosenblatt M, Van Ness J W. Estimation of the bispectrum. Ann. Math. Stat., 1965, 36(4):[15]20-1136.[16]Anderson J M M, Giannakis G B, Swami A. Harmonic retrieval using higher order statistics: A deterministic formulation. IEEE Trans. on SP, 1995, SP-43(8): 1880-1889.[17]Li H W, Cheng (a S. Almost sure convergence analysis of mixed time averages and k-th-order[18]cyclic statistics. IEEE Trans. on IT, 1997, IT-43(4): 1265-1268.
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