諧波隨機(jī)過程的四階平穩(wěn)性和四階遍歷性條件
CONDITIONS FOR FOURTH-ORDER STATIONARITY AND ERGODICITY OF A HARMONIC RANDOM PROCESS
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摘要: 本文分析了由隨機(jī)諧波構(gòu)成的復(fù)信號(hào)四階矩的有限數(shù)據(jù)估計(jì),得到了四階平穩(wěn)和四階遍歷的條件,給出了估計(jì)誤差及其方差,以及它們大樣本極限的顯式表達(dá)式。最后考慮了相應(yīng)于三次相位耦合的特例,說明這一情形下的方差由遍歷和非遍歷兩部分組成。
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關(guān)鍵詞:
- 諧波隨機(jī)過程; 四階平穩(wěn)性; 四階遍歷性
Abstract: The finite data estimates of the complex fourth-order moments of a signal consisting of random harmonics are analysed. Conditions for the fourth-order stationarity and ergodicity are obtained. Explicit formulas for the estimation error and its variance, as well as their limiting large sample values are derived. Finally, a special case relevant to cubic phase coupling is considered, and these results are stated for this case, the variance is shown to comprise an ergodic and a nonergodic part. -
Raghuveer M R, Nikias C L. IEEE Trans. on ASSP, 1985, ASSP-33(10): 1213-1230.[2]Raghuveer M R, Nikias C L. Proc[J].IEEE.1987, 75(7):869-891[3]Huber P J, Kleiner B, Gasser T, et al. IEEE Trans. on Audio Electroacoust., 1971, A)r19(1): ?8-86.[4]Kim Y C, Bean J M, Powers E J, et al. Phys[J].Fluids.1980, 23(2):258-263[5]Brillinger R, Rosenblatt M. Asymptotic theory of estimates of k-th order spectra. in B. Harris, Ed., Spectral Analysis of Time Series. New York: Whey, 1967, 153-188.[6]Brillinger R, Rosenblatt M. Computation and interpretation of k-th order spectra. in B. Harris, Ed.,[7]Spectral Analysis of Time Series. New York: Wiley, 1967, 189-232.[8]Parthasarathy H, Prasad S, Joshi S D. IEEE Trans. on SP, 1994, SP-42(1): 222-225. -
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