諧波過程的高階廣義各態(tài)歷經(jīng)性的分析與應(yīng)用
Analysis and applications of higher-order ergodicity of harmonic process
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摘要: 高階統(tǒng)計在信號處理的許多領(lǐng)域得到了廣泛應(yīng)用。但在實際應(yīng)用的許多情況下,由于只能得到觀測過程的一個樣本,所以只能用樣本的時間平均來代替其統(tǒng)計平均。其前提是過程對該統(tǒng)計量具有廣義的各態(tài)歷經(jīng)性,該文分析了諧波過程高階統(tǒng)計量的各態(tài)歷經(jīng)性,得到了諧波過程滿足三階、四階矩和累積量廣義各態(tài)歷經(jīng)的充要條件。然后研究了這些條件在高階統(tǒng)計量的相位耦合識別、高階陣列處理方法等問題中的應(yīng)用,并進行了模擬實驗驗證。
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關(guān)鍵詞:
- 高階統(tǒng)計量; 各態(tài)歷經(jīng); 諧波過程; 累積量
Abstract: The higher-order statistics has found applications in the wide area of signal processing problem. However in some practical applications, only a sample of the objective process can be obtained. Thus the statistical average must be replaced by time average. The precondition to do this is the ergodicity of the processes. The ergodicity of the higher-order statistics of the harmonic processes is analyzed in this paper. Further more, the applications of the ergodicity in the phase coupling recognition and the array processing problems using higher-order statistics are proposed in this paper. Simulation examples verified those results. -
J.M. Mendel, Tutorial on higher-order statistics(spectra) in signal processing and system theory:theoretical results and some applications, Proc. IEEE, 1991, 79(3), 278-305.[2]C.L. Nikias, M. R. Raghuveer, Bispectrum estimation: A digital signal processing framework,Proc. IEEE, 1987, 75(7), 869-891.[3]B. Porat, B. Friedlander, Direction finding algorithms based on high-ordcr statistics, IEEE Trans.on SP, 1991, SP-39(9), 2016-2023.[4]M.C. Dogan, J. M. Mendel, Application of cumulants to array processing Part I: Aperture extension and array calibration, IEEE Trans. on SP, 1995 SP-43(5), 1200-1216. -
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