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諧波恢復(fù)中累量估計(jì)的強(qiáng)收斂問(wèn)題

李宏偉 袁保宗

李宏偉, 袁保宗. 諧波恢復(fù)中累量估計(jì)的強(qiáng)收斂問(wèn)題[J]. 電子與信息學(xué)報(bào), 1999, 21(5): 592-599.
引用本文: 李宏偉, 袁保宗. 諧波恢復(fù)中累量估計(jì)的強(qiáng)收斂問(wèn)題[J]. 電子與信息學(xué)報(bào), 1999, 21(5): 592-599.
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.

諧波恢復(fù)中累量估計(jì)的強(qiáng)收斂問(wèn)題

STRONG CONVERGENCE PROBLEM FOR CUMULANT ESTIMATORS IN HARMONIC RETRIEVAL

  • 摘要: 本文討論有噪聲污染的諧波信號(hào)累量的單一記錄估計(jì)。證明了樣本自相關(guān)函數(shù)的強(qiáng)收斂性,并得到了強(qiáng)收斂速度。對(duì)于四階矩估計(jì),給出了四階遍歷條件。在這些遍歷條件下,建立了四階矩和四階累量樣本估計(jì)的強(qiáng)收斂性,并得到了強(qiáng)收斂速度。最后給出了數(shù)值仿真結(jié)果。
  • 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]梁應(yīng)敞,王樹(shù)勛,戴逸松.正弦參量的四階累積量ESPRIT方法.電子學(xué)報(bào),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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出版歷程
  • 收稿日期:  1997-08-01
  • 修回日期:  1999-01-09
  • 刊出日期:  1999-09-19

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